diff --git a/include/secp256k1.h b/include/secp256k1.h
index 9de45f1f7d..b7ec6a2283 100644
--- a/include/secp256k1.h
+++ b/include/secp256k1.h
@@ -6,6 +6,7 @@ extern "C" {
 #endif
 
 #include <stddef.h>
+#include <stdint.h>
 
 /** Unless explicitly stated all pointer arguments must not be NULL.
  *
@@ -404,6 +405,46 @@ SECP256K1_API void secp256k1_context_set_error_callback(
     const void *data
 ) SECP256K1_ARG_NONNULL(1);
 
+/** A pointer to a function implementing SHA256's internal compression function.
+ *
+ * This function processes one or more contiguous 64-byte message blocks and
+ * updates the internal SHA256 state accordingly. The function is not responsible
+ * for counting consumed blocks or bytes, nor for performing padding.
+ *
+ * In/Out:  state:     pointer to eight 32-bit words representing the current internal state;
+ *                     the state is updated in place.
+ * In:      blocks64:  pointer to concatenation of n_blocks blocks, of 64 bytes each.
+ *                     no alignment guarantees are made for this pointer.
+ *          n_blocks:  number of contiguous 64-byte blocks to process.
+ */
+typedef void (*secp256k1_sha256_compression_function)(
+    uint32_t *state,
+    const unsigned char *blocks64,
+    size_t n_blocks
+);
+
+/**
+ * Set a callback function to override the internal SHA256 compression function.
+ *
+ * This installs a function to replace the built-in block-compression
+ * step used by the library's internal SHA256 implementation.
+ * The provided callback must exactly implement the effect of n_blocks
+ * repeated applications of the SHA256 compression function.
+ *
+ * This API exists to support environments that wish to route the
+ * SHA256 compression step through a hardware-accelerated or otherwise
+ * specialized implementation. It is NOT meant for replacing SHA256
+ * with a different hash function.
+ *
+ * Args:    ctx:             pointer to a context object.
+ * In:      fn_compression:  pointer to a function implementing the compression function;
+ *                           passing NULL restores the default implementation.
+ */
+SECP256K1_API void secp256k1_context_set_sha256_compression(
+        secp256k1_context *ctx,
+        secp256k1_sha256_compression_function fn_compression
+) SECP256K1_ARG_NONNULL(1);
+
 /** Parse a variable-length public key into the pubkey object.
  *
  *  Returns: 1 if the public key was fully valid.
diff --git a/src/bench_ecmult.c b/src/bench_ecmult.c
index bcf8b43153..c7c6aded3b 100644
--- a/src/bench_ecmult.c
+++ b/src/bench_ecmult.c
@@ -259,7 +259,7 @@ static void bench_ecmult_multi_teardown(void* arg, int iters) {
     }
 }
 
-static void generate_scalar(uint32_t num, secp256k1_scalar* scalar) {
+static void generate_scalar(const secp256k1_context *ctx, uint32_t num, secp256k1_scalar* scalar) {
     secp256k1_sha256 sha256;
     unsigned char c[10] = {'e', 'c', 'm', 'u', 'l', 't', 0, 0, 0, 0};
     unsigned char buf[32];
@@ -269,8 +269,8 @@ static void generate_scalar(uint32_t num, secp256k1_scalar* scalar) {
     c[8] = num >> 16;
     c[9] = num >> 24;
     secp256k1_sha256_initialize(&sha256);
-    secp256k1_sha256_write(&sha256, c, sizeof(c));
-    secp256k1_sha256_finalize(&sha256, buf);
+    secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &sha256, c, sizeof(c));
+    secp256k1_sha256_finalize(secp256k1_get_hash_context(ctx), &sha256, buf);
     secp256k1_scalar_set_b32(scalar, buf, &overflow);
     CHECK(!overflow);
 }
@@ -362,7 +362,7 @@ int main(int argc, char **argv) {
     secp256k1_gej_set_ge(&data.pubkeys_gej[0], &secp256k1_ge_const_g);
     secp256k1_scalar_set_int(&data.seckeys[0], 1);
     for (i = 0; i < POINTS; ++i) {
-        generate_scalar(i, &data.scalars[i]);
+        generate_scalar(data.ctx, i, &data.scalars[i]);
         if (i) {
             secp256k1_gej_double_var(&data.pubkeys_gej[i], &data.pubkeys_gej[i - 1], NULL);
             secp256k1_scalar_add(&data.seckeys[i], &data.seckeys[i - 1], &data.seckeys[i - 1]);
diff --git a/src/bench_internal.c b/src/bench_internal.c
index 001bd25e08..44f8d2cba9 100644
--- a/src/bench_internal.c
+++ b/src/bench_internal.c
@@ -38,6 +38,7 @@ static void help(int default_iters) {
 }
 
 typedef struct {
+    const secp256k1_context* ctx;
     secp256k1_scalar scalar[2];
     secp256k1_fe fe[4];
     secp256k1_ge ge[2];
@@ -82,6 +83,9 @@ static void bench_setup(void* arg) {
         }
     };
 
+    /* Customize context if needed */
+    data->ctx = secp256k1_context_static;
+
     secp256k1_scalar_set_b32(&data->scalar[0], init[0], NULL);
     secp256k1_scalar_set_b32(&data->scalar[1], init[1], NULL);
     secp256k1_fe_set_b32_limit(&data->fe[0], init[0]);
@@ -344,11 +348,12 @@ static void bench_sha256(void* arg, int iters) {
     int i;
     bench_inv *data = (bench_inv*)arg;
     secp256k1_sha256 sha;
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(data->ctx);
 
     for (i = 0; i < iters; i++) {
         secp256k1_sha256_initialize(&sha);
-        secp256k1_sha256_write(&sha, data->data, 32);
-        secp256k1_sha256_finalize(&sha, data->data);
+        secp256k1_sha256_write(hash_ctx, &sha, data->data, 32);
+        secp256k1_sha256_finalize(hash_ctx, &sha, data->data);
     }
 }
 
@@ -356,11 +361,12 @@ static void bench_hmac_sha256(void* arg, int iters) {
     int i;
     bench_inv *data = (bench_inv*)arg;
     secp256k1_hmac_sha256 hmac;
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(data->ctx);
 
     for (i = 0; i < iters; i++) {
-        secp256k1_hmac_sha256_initialize(&hmac, data->data, 32);
-        secp256k1_hmac_sha256_write(&hmac, data->data, 32);
-        secp256k1_hmac_sha256_finalize(&hmac, data->data);
+        secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, data->data, 32);
+        secp256k1_hmac_sha256_write(hash_ctx, &hmac, data->data, 32);
+        secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, data->data);
     }
 }
 
@@ -368,10 +374,11 @@ static void bench_rfc6979_hmac_sha256(void* arg, int iters) {
     int i;
     bench_inv *data = (bench_inv*)arg;
     secp256k1_rfc6979_hmac_sha256 rng;
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(data->ctx);
 
     for (i = 0; i < iters; i++) {
-        secp256k1_rfc6979_hmac_sha256_initialize(&rng, data->data, 64);
-        secp256k1_rfc6979_hmac_sha256_generate(&rng, data->data, 32);
+        secp256k1_rfc6979_hmac_sha256_initialize(hash_ctx, &rng, data->data, 64);
+        secp256k1_rfc6979_hmac_sha256_generate(hash_ctx, &rng, data->data, 32);
     }
 }
 
diff --git a/src/ecmult_gen.h b/src/ecmult_gen.h
index 43dd10c38d..8bc4f14c31 100644
--- a/src/ecmult_gen.h
+++ b/src/ecmult_gen.h
@@ -7,6 +7,7 @@
 #ifndef SECP256K1_ECMULT_GEN_H
 #define SECP256K1_ECMULT_GEN_H
 
+#include "hash.h"
 #include "scalar.h"
 #include "group.h"
 
@@ -132,12 +133,12 @@ typedef struct {
     secp256k1_fe proj_blind;
 } secp256k1_ecmult_gen_context;
 
-static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx);
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx, const secp256k1_hash_ctx *hash_ctx);
 static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context* ctx);
 
 /** Multiply with the generator: R = a*G */
 static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context* ctx, secp256k1_gej *r, const secp256k1_scalar *a);
 
-static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32);
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const secp256k1_hash_ctx *hash_ctx, const unsigned char *seed32);
 
 #endif /* SECP256K1_ECMULT_GEN_H */
diff --git a/src/ecmult_gen_impl.h b/src/ecmult_gen_impl.h
index 2159eed5e1..5a954977eb 100644
--- a/src/ecmult_gen_impl.h
+++ b/src/ecmult_gen_impl.h
@@ -14,8 +14,8 @@
 #include "hash_impl.h"
 #include "precomputed_ecmult_gen.h"
 
-static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx) {
-    secp256k1_ecmult_gen_blind(ctx, NULL);
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, const secp256k1_hash_ctx *hash_ctx) {
+    secp256k1_ecmult_gen_blind(ctx, hash_ctx, NULL);
     ctx->built = 1;
 }
 
@@ -282,7 +282,7 @@ static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp25
 }
 
 /* Setup blinding values for secp256k1_ecmult_gen. */
-static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32) {
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const secp256k1_hash_ctx *hash_ctx, const unsigned char *seed32) {
     secp256k1_scalar b;
     secp256k1_scalar diff;
     secp256k1_gej gb;
@@ -309,17 +309,17 @@ static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const
      */
     VERIFY_CHECK(seed32 != NULL);
     memcpy(keydata + 32, seed32, 32);
-    secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, 64);
+    secp256k1_rfc6979_hmac_sha256_initialize(hash_ctx, &rng, keydata, 64);
     secp256k1_memclear_explicit(keydata, sizeof(keydata));
 
     /* Compute projective blinding factor (cannot be 0). */
-    secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+    secp256k1_rfc6979_hmac_sha256_generate(hash_ctx, &rng, nonce32, 32);
     secp256k1_fe_set_b32_mod(&f, nonce32);
     secp256k1_fe_cmov(&f, &secp256k1_fe_one, secp256k1_fe_normalizes_to_zero(&f));
     ctx->proj_blind = f;
 
     /* For a random blinding value b, set scalar_offset=diff-b, ge_offset=bG */
-    secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+    secp256k1_rfc6979_hmac_sha256_generate(hash_ctx, &rng, nonce32, 32);
     secp256k1_scalar_set_b32(&b, nonce32, NULL);
     /* The blinding value cannot be zero, as that would mean ge_offset = infinity,
      * which secp256k1_gej_add_ge cannot handle. */
diff --git a/src/hash.h b/src/hash.h
index 43cdd60c3f..79d97671e5 100644
--- a/src/hash.h
+++ b/src/hash.h
@@ -10,6 +10,12 @@
 #include <stdlib.h>
 #include <stdint.h>
 
+typedef struct {
+    secp256k1_sha256_compression_function fn_sha256_compression;
+} secp256k1_hash_ctx;
+
+static void secp256k1_hash_ctx_init(secp256k1_hash_ctx *hash_ctx);
+
 typedef struct {
     uint32_t s[8];
     unsigned char buf[64];
@@ -21,17 +27,17 @@ static void secp256k1_sha256_initialize(secp256k1_sha256 *hash);
  * The byte counter must be a multiple of 64, i.e., there must be no unwritten
  * bytes in the buffer. */
 static void secp256k1_sha256_initialize_midstate(secp256k1_sha256 *hash, uint64_t bytes, const uint32_t state[8]);
-static void secp256k1_sha256_write(secp256k1_sha256 *hash, const unsigned char *data, size_t size);
-static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out32);
+static void secp256k1_sha256_write(const secp256k1_hash_ctx *hash_ctx, secp256k1_sha256 *hash, const unsigned char *data, size_t size);
+static void secp256k1_sha256_finalize(const secp256k1_hash_ctx *hash_ctx, secp256k1_sha256 *hash, unsigned char *out32);
 static void secp256k1_sha256_clear(secp256k1_sha256 *hash);
 
 typedef struct {
     secp256k1_sha256 inner, outer;
 } secp256k1_hmac_sha256;
 
-static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t size);
-static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size);
-static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256 *hash, unsigned char *out32);
+static void secp256k1_hmac_sha256_initialize(const secp256k1_hash_ctx *hash_ctx, secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t size);
+static void secp256k1_hmac_sha256_write(const secp256k1_hash_ctx *hash_ctx, secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size);
+static void secp256k1_hmac_sha256_finalize(const secp256k1_hash_ctx *hash_ctx, secp256k1_hmac_sha256 *hash, unsigned char *out32);
 static void secp256k1_hmac_sha256_clear(secp256k1_hmac_sha256 *hash);
 
 typedef struct {
@@ -40,8 +46,8 @@ typedef struct {
     int retry;
 } secp256k1_rfc6979_hmac_sha256;
 
-static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen);
-static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen);
+static void secp256k1_rfc6979_hmac_sha256_initialize(const secp256k1_hash_ctx *hash_ctx, secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen);
+static void secp256k1_rfc6979_hmac_sha256_generate(const secp256k1_hash_ctx *hash_ctx, secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen);
 static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256 *rng);
 static void secp256k1_rfc6979_hmac_sha256_clear(secp256k1_rfc6979_hmac_sha256 *rng);
 
diff --git a/src/hash_impl.h b/src/hash_impl.h
index da3b466095..7c40f82e76 100644
--- a/src/hash_impl.h
+++ b/src/hash_impl.h
@@ -48,7 +48,7 @@ static void secp256k1_sha256_initialize_midstate(secp256k1_sha256 *hash, uint64_
 }
 
 /** Perform one SHA-256 transformation, processing 16 big endian 32-bit words. */
-static void secp256k1_sha256_transform(uint32_t* s, const unsigned char* buf) {
+static void secp256k1_sha256_transform_impl(uint32_t* s, const unsigned char* buf) {
     uint32_t a = s[0], b = s[1], c = s[2], d = s[3], e = s[4], f = s[5], g = s[6], h = s[7];
     uint32_t w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15;
 
@@ -130,26 +130,52 @@ static void secp256k1_sha256_transform(uint32_t* s, const unsigned char* buf) {
     s[7] += h;
 }
 
-static void secp256k1_sha256_write(secp256k1_sha256 *hash, const unsigned char *data, size_t len) {
+static void secp256k1_sha256_transform(uint32_t *state, const unsigned char *blocks64, size_t n_blocks) {
+    while (n_blocks--) {
+        secp256k1_sha256_transform_impl(state, blocks64);
+        blocks64 += 64;
+    }
+}
+
+static void secp256k1_hash_ctx_init(secp256k1_hash_ctx *hash_ctx) {
+    VERIFY_CHECK(hash_ctx != NULL);
+    hash_ctx->fn_sha256_compression = secp256k1_sha256_transform;
+}
+
+static void secp256k1_sha256_write(const secp256k1_hash_ctx *hash_ctx, secp256k1_sha256 *hash, const unsigned char *data, size_t len) {
+    size_t chunk_len;
     size_t bufsize = hash->bytes & 0x3F;
     hash->bytes += len;
     VERIFY_CHECK(hash->bytes >= len);
-    while (len >= 64 - bufsize) {
-        /* Fill the buffer, and process it. */
-        size_t chunk_len = 64 - bufsize;
+    VERIFY_CHECK(hash_ctx != NULL);
+    VERIFY_CHECK(hash_ctx->fn_sha256_compression != NULL);
+
+    /* If we exceed the 64-byte block size with this input, process it and wipe the buffer */
+    chunk_len = 64 - bufsize;
+    if (bufsize && len >= chunk_len) {
         memcpy(hash->buf + bufsize, data, chunk_len);
         data += chunk_len;
         len -= chunk_len;
-        secp256k1_sha256_transform(hash->s, hash->buf);
+        hash_ctx->fn_sha256_compression(hash->s, hash->buf, 1);
         bufsize = 0;
     }
+
+    /* If we still have data to process, invoke compression directly on the input */
+    if (len >= 64) {
+        const size_t n_blocks = len / 64;
+        const size_t advance = n_blocks * 64;
+        hash_ctx->fn_sha256_compression(hash->s, data, n_blocks);
+        data += advance;
+        len -= advance;
+    }
+
+    /* Fill the buffer with what remains */
     if (len) {
-        /* Fill the buffer with what remains. */
         memcpy(hash->buf + bufsize, data, len);
     }
 }
 
-static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out32) {
+static void secp256k1_sha256_finalize(const secp256k1_hash_ctx *hash_ctx, secp256k1_sha256 *hash, unsigned char *out32) {
     static const unsigned char pad[64] = {0x80};
     unsigned char sizedesc[8];
     int i;
@@ -157,8 +183,8 @@ static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out
     VERIFY_CHECK(hash->bytes < ((uint64_t)1 << 61));
     secp256k1_write_be32(&sizedesc[0], hash->bytes >> 29);
     secp256k1_write_be32(&sizedesc[4], hash->bytes << 3);
-    secp256k1_sha256_write(hash, pad, 1 + ((119 - (hash->bytes % 64)) % 64));
-    secp256k1_sha256_write(hash, sizedesc, 8);
+    secp256k1_sha256_write(hash_ctx, hash, pad, 1 + ((119 - (hash->bytes % 64)) % 64));
+    secp256k1_sha256_write(hash_ctx, hash, sizedesc, 8);
     for (i = 0; i < 8; i++) {
         secp256k1_write_be32(&out32[4*i], hash->s[i]);
         hash->s[i] = 0;
@@ -167,22 +193,22 @@ static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out
 
 /* Initializes a sha256 struct and writes the 64 byte string
  * SHA256(tag)||SHA256(tag) into it. */
-static void secp256k1_sha256_initialize_tagged(secp256k1_sha256 *hash, const unsigned char *tag, size_t taglen) {
+static void secp256k1_sha256_initialize_tagged(const secp256k1_hash_ctx *hash_ctx, secp256k1_sha256 *hash, const unsigned char *tag, size_t taglen) {
     unsigned char buf[32];
     secp256k1_sha256_initialize(hash);
-    secp256k1_sha256_write(hash, tag, taglen);
-    secp256k1_sha256_finalize(hash, buf);
+    secp256k1_sha256_write(hash_ctx, hash, tag, taglen);
+    secp256k1_sha256_finalize(hash_ctx, hash, buf);
 
     secp256k1_sha256_initialize(hash);
-    secp256k1_sha256_write(hash, buf, 32);
-    secp256k1_sha256_write(hash, buf, 32);
+    secp256k1_sha256_write(hash_ctx, hash, buf, 32);
+    secp256k1_sha256_write(hash_ctx, hash, buf, 32);
 }
 
 static void secp256k1_sha256_clear(secp256k1_sha256 *hash) {
     secp256k1_memclear_explicit(hash, sizeof(*hash));
 }
 
-static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t keylen) {
+static void secp256k1_hmac_sha256_initialize(const secp256k1_hash_ctx *hash_ctx, secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t keylen) {
     size_t n;
     unsigned char rkey[64];
     if (keylen <= sizeof(rkey)) {
@@ -191,8 +217,8 @@ static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256 *hash, const
     } else {
         secp256k1_sha256 sha256;
         secp256k1_sha256_initialize(&sha256);
-        secp256k1_sha256_write(&sha256, key, keylen);
-        secp256k1_sha256_finalize(&sha256, rkey);
+        secp256k1_sha256_write(hash_ctx, &sha256, key, keylen);
+        secp256k1_sha256_finalize(hash_ctx, &sha256, rkey);
         memset(rkey + 32, 0, 32);
     }
 
@@ -200,33 +226,33 @@ static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256 *hash, const
     for (n = 0; n < sizeof(rkey); n++) {
         rkey[n] ^= 0x5c;
     }
-    secp256k1_sha256_write(&hash->outer, rkey, sizeof(rkey));
+    secp256k1_sha256_write(hash_ctx, &hash->outer, rkey, sizeof(rkey));
 
     secp256k1_sha256_initialize(&hash->inner);
     for (n = 0; n < sizeof(rkey); n++) {
         rkey[n] ^= 0x5c ^ 0x36;
     }
-    secp256k1_sha256_write(&hash->inner, rkey, sizeof(rkey));
+    secp256k1_sha256_write(hash_ctx, &hash->inner, rkey, sizeof(rkey));
     secp256k1_memclear_explicit(rkey, sizeof(rkey));
 }
 
-static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size) {
-    secp256k1_sha256_write(&hash->inner, data, size);
+static void secp256k1_hmac_sha256_write(const secp256k1_hash_ctx *hash_ctx, secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size) {
+    secp256k1_sha256_write(hash_ctx, &hash->inner, data, size);
 }
 
-static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256 *hash, unsigned char *out32) {
+static void secp256k1_hmac_sha256_finalize(const secp256k1_hash_ctx *hash_ctx, secp256k1_hmac_sha256 *hash, unsigned char *out32) {
     unsigned char temp[32];
-    secp256k1_sha256_finalize(&hash->inner, temp);
-    secp256k1_sha256_write(&hash->outer, temp, 32);
+    secp256k1_sha256_finalize(hash_ctx, &hash->inner, temp);
+    secp256k1_sha256_write(hash_ctx, &hash->outer, temp, 32);
     secp256k1_memclear_explicit(temp, sizeof(temp));
-    secp256k1_sha256_finalize(&hash->outer, out32);
+    secp256k1_sha256_finalize(hash_ctx, &hash->outer, out32);
 }
 
 static void secp256k1_hmac_sha256_clear(secp256k1_hmac_sha256 *hash) {
     secp256k1_memclear_explicit(hash, sizeof(*hash));
 }
 
-static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen) {
+static void secp256k1_rfc6979_hmac_sha256_initialize(const secp256k1_hash_ctx *hash_ctx, secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen) {
     secp256k1_hmac_sha256 hmac;
     static const unsigned char zero[1] = {0x00};
     static const unsigned char one[1] = {0x01};
@@ -235,47 +261,47 @@ static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha2
     memset(rng->k, 0x00, 32); /* RFC6979 3.2.c. */
 
     /* RFC6979 3.2.d. */
-    secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
-    secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
-    secp256k1_hmac_sha256_write(&hmac, zero, 1);
-    secp256k1_hmac_sha256_write(&hmac, key, keylen);
-    secp256k1_hmac_sha256_finalize(&hmac, rng->k);
-    secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
-    secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
-    secp256k1_hmac_sha256_finalize(&hmac, rng->v);
+    secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, zero, 1);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, key, keylen);
+    secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->k);
+    secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+    secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->v);
 
     /* RFC6979 3.2.f. */
-    secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
-    secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
-    secp256k1_hmac_sha256_write(&hmac, one, 1);
-    secp256k1_hmac_sha256_write(&hmac, key, keylen);
-    secp256k1_hmac_sha256_finalize(&hmac, rng->k);
-    secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
-    secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
-    secp256k1_hmac_sha256_finalize(&hmac, rng->v);
+    secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, one, 1);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, key, keylen);
+    secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->k);
+    secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+    secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->v);
     rng->retry = 0;
 }
 
-static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen) {
+static void secp256k1_rfc6979_hmac_sha256_generate(const secp256k1_hash_ctx *hash_ctx, secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen) {
     /* RFC6979 3.2.h. */
     static const unsigned char zero[1] = {0x00};
     if (rng->retry) {
         secp256k1_hmac_sha256 hmac;
-        secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
-        secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
-        secp256k1_hmac_sha256_write(&hmac, zero, 1);
-        secp256k1_hmac_sha256_finalize(&hmac, rng->k);
-        secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
-        secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
-        secp256k1_hmac_sha256_finalize(&hmac, rng->v);
+        secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+        secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+        secp256k1_hmac_sha256_write(hash_ctx, &hmac, zero, 1);
+        secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->k);
+        secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+        secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+        secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->v);
     }
 
     while (outlen > 0) {
         secp256k1_hmac_sha256 hmac;
         size_t now = outlen;
-        secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
-        secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
-        secp256k1_hmac_sha256_finalize(&hmac, rng->v);
+        secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+        secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+        secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->v);
         if (now > 32) {
             now = 32;
         }
diff --git a/src/modules/ecdh/main_impl.h b/src/modules/ecdh/main_impl.h
index 9f2dfdd56a..b0359b2c41 100644
--- a/src/modules/ecdh/main_impl.h
+++ b/src/modules/ecdh/main_impl.h
@@ -10,20 +10,24 @@
 #include "../../../include/secp256k1_ecdh.h"
 #include "../../ecmult_const_impl.h"
 
-static int ecdh_hash_function_sha256(unsigned char *output, const unsigned char *x32, const unsigned char *y32, void *data) {
+static int ecdh_hash_function_sha256_impl(const secp256k1_hash_ctx *hash_ctx, unsigned char *output, const unsigned char *x32, const unsigned char *y32, void *data) {
     unsigned char version = (y32[31] & 0x01) | 0x02;
     secp256k1_sha256 sha;
     (void)data;
 
     secp256k1_sha256_initialize(&sha);
-    secp256k1_sha256_write(&sha, &version, 1);
-    secp256k1_sha256_write(&sha, x32, 32);
-    secp256k1_sha256_finalize(&sha, output);
+    secp256k1_sha256_write(hash_ctx, &sha, &version, 1);
+    secp256k1_sha256_write(hash_ctx, &sha, x32, 32);
+    secp256k1_sha256_finalize(hash_ctx, &sha, output);
     secp256k1_sha256_clear(&sha);
 
     return 1;
 }
 
+static int ecdh_hash_function_sha256(unsigned char *output, const unsigned char *x32, const unsigned char *y32, void *data) {
+    return ecdh_hash_function_sha256_impl(secp256k1_get_hash_context(secp256k1_context_static), output, x32, y32, data);
+}
+
 const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_sha256 = ecdh_hash_function_sha256;
 const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_default = ecdh_hash_function_sha256;
 
@@ -41,10 +45,6 @@ int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *output, const se
     ARG_CHECK(point != NULL);
     ARG_CHECK(scalar != NULL);
 
-    if (hashfp == NULL) {
-        hashfp = secp256k1_ecdh_hash_function_default;
-    }
-
     secp256k1_pubkey_load(ctx, &pt, point);
     secp256k1_scalar_set_b32(&s, scalar, &overflow);
 
@@ -60,7 +60,12 @@ int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *output, const se
     secp256k1_fe_get_b32(x, &pt.x);
     secp256k1_fe_get_b32(y, &pt.y);
 
-    ret = hashfp(output, x, y, data);
+    if (hashfp == NULL) {
+        /* Use ctx-aware function by default */
+        ret = ecdh_hash_function_sha256_impl(secp256k1_get_hash_context(ctx), output, x, y, data);
+    } else {
+        ret = hashfp(output, x, y, data);
+    }
 
     secp256k1_memclear_explicit(x, sizeof(x));
     secp256k1_memclear_explicit(y, sizeof(y));
diff --git a/src/modules/ecdh/tests_impl.h b/src/modules/ecdh/tests_impl.h
index cb1d953d2a..c75ce9ff67 100644
--- a/src/modules/ecdh/tests_impl.h
+++ b/src/modules/ecdh/tests_impl.h
@@ -8,6 +8,7 @@
 #define SECP256K1_MODULE_ECDH_TESTS_H
 
 #include "../../unit_test.h"
+#include "../../testutil.h"
 
 static int ecdh_hash_function_test_xpassthru(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) {
     (void)y;
@@ -83,13 +84,37 @@ static void test_ecdh_generator_basepoint(void) {
         /* compute "explicitly" */
         CHECK(secp256k1_ec_pubkey_serialize(CTX, point_ser, &point_ser_len, &point[1], SECP256K1_EC_COMPRESSED) == 1);
         secp256k1_sha256_initialize(&sha);
-        secp256k1_sha256_write(&sha, point_ser, point_ser_len);
-        secp256k1_sha256_finalize(&sha, output_ser);
+        secp256k1_sha256_write(secp256k1_get_hash_context(CTX), &sha, point_ser, point_ser_len);
+        secp256k1_sha256_finalize(secp256k1_get_hash_context(CTX), &sha, output_ser);
         /* compare */
         CHECK(secp256k1_memcmp_var(output_ecdh, output_ser, 32) == 0);
     }
 }
 
+DEFINE_SHA256_TRANSFORM_PROBE(sha256_ecdh)
+static void test_ecdh_ctx_sha256(void) {
+    /* Check ctx-provided SHA256 compression override takes effect */
+    secp256k1_context *ctx = secp256k1_context_clone(CTX);
+    unsigned char out_default[65], out_custom[65];
+    const unsigned char sk[32] = {1};
+    secp256k1_pubkey pubkey;
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, sk) == 1);
+
+    /* Default behavior */
+    CHECK(secp256k1_ecdh(ctx, out_default, &pubkey, sk, NULL, NULL) == 1);
+    CHECK(!sha256_ecdh_called);
+
+    /* Override SHA256 compression directly, bypassing the ctx setter sanity checks */
+    ctx->hash_ctx.fn_sha256_compression = sha256_ecdh;
+    CHECK(secp256k1_ecdh(ctx, out_custom, &pubkey, sk, NULL, NULL) == 1);
+
+    /* Outputs must differ if custom compression was used */
+    CHECK(secp256k1_memcmp_var(out_default, out_custom, 32) != 0);
+    CHECK(sha256_ecdh_called);
+
+    secp256k1_context_destroy(ctx);
+}
+
 static void test_bad_scalar(void) {
     unsigned char s_zero[32] = { 0 };
     unsigned char s_overflow[32] = { 0 };
@@ -187,6 +212,7 @@ static const struct tf_test_entry tests_ecdh[] = {
     CASE1(test_bad_scalar),
     CASE1(test_result_basepoint),
     CASE1(test_ecdh_wycheproof),
+    CASE1(test_ecdh_ctx_sha256),
 };
 
 #endif /* SECP256K1_MODULE_ECDH_TESTS_H */
diff --git a/src/modules/ellswift/main_impl.h b/src/modules/ellswift/main_impl.h
index f9ef0ac86c..27cb3db65e 100644
--- a/src/modules/ellswift/main_impl.h
+++ b/src/modules/ellswift/main_impl.h
@@ -307,7 +307,7 @@ static int secp256k1_ellswift_xswiftec_inv_var(secp256k1_fe *t, const secp256k1_
  * hasher is a SHA256 object to which an incrementing 4-byte counter is written to generate randomness.
  * Writing 13 bytes (4 bytes for counter, plus 9 bytes for the SHA256 padding) cannot cross a
  * 64-byte block size boundary (to make sure it only triggers a single SHA256 compression). */
-static void secp256k1_ellswift_prng(unsigned char* out32, const secp256k1_sha256 *hasher, uint32_t cnt) {
+static void secp256k1_ellswift_prng(const secp256k1_hash_ctx *hash_ctx, unsigned char* out32, const secp256k1_sha256 *hasher, uint32_t cnt) {
     secp256k1_sha256 hash = *hasher;
     unsigned char buf4[4];
 #ifdef VERIFY
@@ -317,8 +317,8 @@ static void secp256k1_ellswift_prng(unsigned char* out32, const secp256k1_sha256
     buf4[1] = cnt >> 8;
     buf4[2] = cnt >> 16;
     buf4[3] = cnt >> 24;
-    secp256k1_sha256_write(&hash, buf4, 4);
-    secp256k1_sha256_finalize(&hash, out32);
+    secp256k1_sha256_write(hash_ctx, &hash, buf4, 4);
+    secp256k1_sha256_finalize(hash_ctx, &hash, out32);
 
     /* Writing and finalizing together should trigger exactly one SHA256 compression. */
     VERIFY_CHECK(((hash.bytes) >> 6) == (blocks + 1));
@@ -330,7 +330,7 @@ static void secp256k1_ellswift_prng(unsigned char* out32, const secp256k1_sha256
  * needs encoding.
  *
  * hasher is a hasher in the secp256k1_ellswift_prng sense, with the same restrictions. */
-static void secp256k1_ellswift_xelligatorswift_var(unsigned char *u32, secp256k1_fe *t, const secp256k1_fe *x, const secp256k1_sha256 *hasher) {
+static void secp256k1_ellswift_xelligatorswift_var(const secp256k1_context *ctx, unsigned char *u32, secp256k1_fe *t, const secp256k1_fe *x, const secp256k1_sha256 *hasher) {
     /* Pool of 3-bit branch values. */
     unsigned char branch_hash[32];
     /* Number of 3-bit values in branch_hash left. */
@@ -346,14 +346,14 @@ static void secp256k1_ellswift_xelligatorswift_var(unsigned char *u32, secp256k1
         secp256k1_fe u;
         /* If the pool of branch values is empty, populate it. */
         if (branches_left == 0) {
-            secp256k1_ellswift_prng(branch_hash, hasher, cnt++);
+            secp256k1_ellswift_prng(secp256k1_get_hash_context(ctx), branch_hash, hasher, cnt++);
             branches_left = 64;
         }
         /* Take a 3-bit branch value from the branch pool (top bit is discarded). */
         --branches_left;
         branch = (branch_hash[branches_left >> 1] >> ((branches_left & 1) << 2)) & 7;
         /* Compute a new u value by hashing. */
-        secp256k1_ellswift_prng(u32, hasher, cnt++);
+        secp256k1_ellswift_prng(secp256k1_get_hash_context(ctx), u32, hasher, cnt++);
         /* overflow is not a problem (we prefer uniform u32 over uniform u). */
         secp256k1_fe_set_b32_mod(&u, u32);
         /* Since u is the output of a hash, it should practically never be 0. We could apply the
@@ -372,8 +372,8 @@ static void secp256k1_ellswift_xelligatorswift_var(unsigned char *u32, secp256k1
  * as input, and returns an encoding that matches the provided Y coordinate rather than a random
  * one.
  */
-static void secp256k1_ellswift_elligatorswift_var(unsigned char *u32, secp256k1_fe *t, const secp256k1_ge *p, const secp256k1_sha256 *hasher) {
-    secp256k1_ellswift_xelligatorswift_var(u32, t, &p->x, hasher);
+static void secp256k1_ellswift_elligatorswift_var(const secp256k1_context *ctx, unsigned char *u32, secp256k1_fe *t, const secp256k1_ge *p, const secp256k1_sha256 *hasher) {
+    secp256k1_ellswift_xelligatorswift_var(ctx, u32, t, &p->x, hasher);
     secp256k1_fe_normalize_var(t);
     if (secp256k1_fe_is_odd(t) != secp256k1_fe_is_odd(&p->y)) {
         secp256k1_fe_negate(t, t, 1);
@@ -406,11 +406,11 @@ int secp256k1_ellswift_encode(const secp256k1_context *ctx, unsigned char *ell64
          * BIP340 tagged hash with tag "secp256k1_ellswift_encode". */
         secp256k1_ellswift_sha256_init_encode(&hash);
         secp256k1_eckey_pubkey_serialize33(&p, p64);
-        secp256k1_sha256_write(&hash, p64, sizeof(p64));
-        secp256k1_sha256_write(&hash, rnd32, 32);
+        secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &hash, p64, sizeof(p64));
+        secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &hash, rnd32, 32);
 
         /* Compute ElligatorSwift encoding and construct output. */
-        secp256k1_ellswift_elligatorswift_var(ell64, &t, &p, &hash); /* puts u in ell64[0..32] */
+        secp256k1_ellswift_elligatorswift_var(ctx, ell64, &t, &p, &hash); /* puts u in ell64[0..32] */
         secp256k1_fe_get_b32(ell64 + 32, &t); /* puts t in ell64[32..64] */
         return 1;
     }
@@ -452,13 +452,13 @@ int secp256k1_ellswift_create(const secp256k1_context *ctx, unsigned char *ell64
     /* Set up hasher state. The used RNG is H(privkey || "\x00"*32 [|| auxrnd32] || cnt++),
      * using BIP340 tagged hash with tag "secp256k1_ellswift_create". */
     secp256k1_ellswift_sha256_init_create(&hash);
-    secp256k1_sha256_write(&hash, seckey32, 32);
-    secp256k1_sha256_write(&hash, zero32, sizeof(zero32));
+    secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &hash, seckey32, 32);
+    secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &hash, zero32, sizeof(zero32));
     secp256k1_declassify(ctx, &hash, sizeof(hash)); /* private key is hashed now */
-    if (auxrnd32) secp256k1_sha256_write(&hash, auxrnd32, 32);
+    if (auxrnd32) secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &hash, auxrnd32, 32);
 
     /* Compute ElligatorSwift encoding and construct output. */
-    secp256k1_ellswift_elligatorswift_var(ell64, &t, &p, &hash); /* puts u in ell64[0..32] */
+    secp256k1_ellswift_elligatorswift_var(ctx, ell64, &t, &p, &hash); /* puts u in ell64[0..32] */
     secp256k1_fe_get_b32(ell64 + 32, &t); /* puts t in ell64[32..64] */
 
     secp256k1_memczero(ell64, 64, !ret);
@@ -482,20 +482,24 @@ int secp256k1_ellswift_decode(const secp256k1_context *ctx, secp256k1_pubkey *pu
     return 1;
 }
 
-static int ellswift_xdh_hash_function_prefix(unsigned char *output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) {
+static int ellswift_xdh_hash_function_prefix_impl(const secp256k1_hash_ctx *hash_ctx, unsigned char *output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) {
     secp256k1_sha256 sha;
 
     secp256k1_sha256_initialize(&sha);
-    secp256k1_sha256_write(&sha, data, 64);
-    secp256k1_sha256_write(&sha, ell_a64, 64);
-    secp256k1_sha256_write(&sha, ell_b64, 64);
-    secp256k1_sha256_write(&sha, x32, 32);
-    secp256k1_sha256_finalize(&sha, output);
+    secp256k1_sha256_write(hash_ctx, &sha, data, 64);
+    secp256k1_sha256_write(hash_ctx, &sha, ell_a64, 64);
+    secp256k1_sha256_write(hash_ctx, &sha, ell_b64, 64);
+    secp256k1_sha256_write(hash_ctx, &sha, x32, 32);
+    secp256k1_sha256_finalize(hash_ctx, &sha, output);
     secp256k1_sha256_clear(&sha);
 
     return 1;
 }
 
+static int ellswift_xdh_hash_function_prefix(unsigned char *output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) {
+    return ellswift_xdh_hash_function_prefix_impl(secp256k1_get_hash_context(secp256k1_context_static), output, x32, ell_a64, ell_b64, data);
+}
+
 /** Set hash state to the BIP340 tagged hash midstate for "bip324_ellswift_xonly_ecdh". */
 static void secp256k1_ellswift_sha256_init_bip324(secp256k1_sha256* hash) {
     static const uint32_t midstate[8] = {
@@ -505,21 +509,25 @@ static void secp256k1_ellswift_sha256_init_bip324(secp256k1_sha256* hash) {
     secp256k1_sha256_initialize_midstate(hash, 64, midstate);
 }
 
-static int ellswift_xdh_hash_function_bip324(unsigned char* output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) {
+static int ellswift_xdh_hash_function_bip324_impl(const secp256k1_hash_ctx *hash_ctx, unsigned char* output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) {
     secp256k1_sha256 sha;
 
     (void)data;
 
     secp256k1_ellswift_sha256_init_bip324(&sha);
-    secp256k1_sha256_write(&sha, ell_a64, 64);
-    secp256k1_sha256_write(&sha, ell_b64, 64);
-    secp256k1_sha256_write(&sha, x32, 32);
-    secp256k1_sha256_finalize(&sha, output);
+    secp256k1_sha256_write(hash_ctx, &sha, ell_a64, 64);
+    secp256k1_sha256_write(hash_ctx, &sha, ell_b64, 64);
+    secp256k1_sha256_write(hash_ctx, &sha, x32, 32);
+    secp256k1_sha256_finalize(hash_ctx, &sha, output);
     secp256k1_sha256_clear(&sha);
 
     return 1;
 }
 
+static int ellswift_xdh_hash_function_bip324(unsigned char* output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) {
+    return ellswift_xdh_hash_function_bip324_impl(secp256k1_get_hash_context(secp256k1_context_static), output, x32, ell_a64, ell_b64, data);
+}
+
 const secp256k1_ellswift_xdh_hash_function secp256k1_ellswift_xdh_hash_function_prefix = ellswift_xdh_hash_function_prefix;
 const secp256k1_ellswift_xdh_hash_function secp256k1_ellswift_xdh_hash_function_bip324 = ellswift_xdh_hash_function_bip324;
 
@@ -554,8 +562,14 @@ int secp256k1_ellswift_xdh(const secp256k1_context *ctx, unsigned char *output,
     secp256k1_fe_normalize(&px);
     secp256k1_fe_get_b32(sx, &px);
 
-    /* Invoke hasher */
-    ret = hashfp(output, sx, ell_a64, ell_b64, data);
+    /* Invoke hasher. Use ctx-aware function by default */
+    if (hashfp == secp256k1_ellswift_xdh_hash_function_bip324) {
+        ret = ellswift_xdh_hash_function_bip324_impl(secp256k1_get_hash_context(ctx), output, sx, ell_a64, ell_b64, data);
+    } else if (hashfp == secp256k1_ellswift_xdh_hash_function_prefix) {
+        ret = ellswift_xdh_hash_function_prefix_impl(secp256k1_get_hash_context(ctx), output, sx, ell_a64, ell_b64, data);
+    } else {
+        ret = hashfp(output, sx, ell_a64, ell_b64, data);
+    }
 
     secp256k1_memclear_explicit(sx, sizeof(sx));
     secp256k1_fe_clear(&px);
diff --git a/src/modules/ellswift/tests_impl.h b/src/modules/ellswift/tests_impl.h
index e309041127..a849c8e833 100644
--- a/src/modules/ellswift/tests_impl.h
+++ b/src/modules/ellswift/tests_impl.h
@@ -431,9 +431,44 @@ void ellswift_xdh_correctness_tests(void) {
     }
 }
 
+DEFINE_SHA256_TRANSFORM_PROBE(sha256_ellswift_xdh)
+void ellswift_xdh_ctx_sha256_tests(void) {
+    /* Check ctx-provided SHA256 compression override takes effect */
+    secp256k1_context *ctx = secp256k1_context_clone(CTX);
+    unsigned char out_default[65], out_custom[65];
+    const unsigned char skA[32] = {1}, skB[32] = {2};
+    unsigned char keyA[64], keyB[64], data[64] = {0};
+    const secp256k1_ellswift_xdh_hash_function hash_funcs[2] = {secp256k1_ellswift_xdh_hash_function_bip324, secp256k1_ellswift_xdh_hash_function_prefix};
+    int i;
+
+    CHECK(secp256k1_ellswift_create(ctx, keyA, skA, NULL));
+    CHECK(secp256k1_ellswift_create(ctx, keyB, skB, NULL));
+
+    for (i = 0; i < 2; i++) {
+        const secp256k1_ellswift_xdh_hash_function hash_fn = hash_funcs[i];
+        /* Default behavior. No ctx-provided SHA256 compression */
+        CHECK(secp256k1_ellswift_xdh(ctx, out_default, keyA, keyB, skA, 0, hash_fn, data));
+        CHECK(!sha256_ellswift_xdh_called);
+
+        /* Override SHA256 compression directly, bypassing the ctx setter sanity checks */
+        ctx->hash_ctx.fn_sha256_compression = sha256_ellswift_xdh;
+        CHECK(secp256k1_ellswift_xdh(ctx, out_custom, keyA, keyB, skA, 0, hash_fn, data));
+        CHECK(sha256_ellswift_xdh_called);
+        /* Outputs must differ if custom compression was used */
+        CHECK(secp256k1_memcmp_var(out_default, out_custom, 32) != 0);
+
+        /* Restore defaults */
+        sha256_ellswift_xdh_called = 0;
+        secp256k1_context_set_sha256_compression(ctx, NULL);
+    }
+
+    secp256k1_context_destroy(ctx);
+}
+
 /* Test hash initializers */
 void ellswift_hash_init_tests(void) {
     secp256k1_sha256 sha_optimized;
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
     /* "secp256k1_ellswift_encode" */
     static const unsigned char encode_tag[] = {'s', 'e', 'c', 'p', '2', '5', '6', 'k', '1', '_', 'e', 'l', 'l', 's', 'w', 'i', 'f', 't', '_', 'e', 'n', 'c', 'o', 'd', 'e'};
     /* "secp256k1_ellswift_create" */
@@ -445,19 +480,19 @@ void ellswift_hash_init_tests(void) {
      * secp256k1_ellswift_sha256_init_encode has the expected
      * state. */
     secp256k1_ellswift_sha256_init_encode(&sha_optimized);
-    test_sha256_tag_midstate(&sha_optimized, encode_tag, sizeof(encode_tag));
+    test_sha256_tag_midstate(hash_ctx, &sha_optimized, encode_tag, sizeof(encode_tag));
 
     /* Check that hash initialized by
      * secp256k1_ellswift_sha256_init_create has the expected
      * state. */
     secp256k1_ellswift_sha256_init_create(&sha_optimized);
-    test_sha256_tag_midstate(&sha_optimized, create_tag, sizeof(create_tag));
+    test_sha256_tag_midstate(hash_ctx, &sha_optimized, create_tag, sizeof(create_tag));
 
     /* Check that hash initialized by
      * secp256k1_ellswift_sha256_init_bip324 has the expected
      * state. */
     secp256k1_ellswift_sha256_init_bip324(&sha_optimized);
-    test_sha256_tag_midstate(&sha_optimized, bip324_tag, sizeof(bip324_tag));
+    test_sha256_tag_midstate(hash_ctx, &sha_optimized, bip324_tag, sizeof(bip324_tag));
 }
 
 void ellswift_xdh_bad_scalar_tests(void) {
@@ -498,6 +533,7 @@ static const struct tf_test_entry tests_ellswift[] = {
     CASE1(ellswift_xdh_correctness_tests),
     CASE1(ellswift_hash_init_tests),
     CASE1(ellswift_xdh_bad_scalar_tests),
+    CASE1(ellswift_xdh_ctx_sha256_tests),
 };
 
 #endif
diff --git a/src/modules/musig/keyagg.h b/src/modules/musig/keyagg.h
index a0b37252f8..30e77aa951 100644
--- a/src/modules/musig/keyagg.h
+++ b/src/modules/musig/keyagg.h
@@ -27,6 +27,6 @@ typedef struct {
 
 static int secp256k1_keyagg_cache_load(const secp256k1_context* ctx, secp256k1_keyagg_cache_internal *cache_i, const secp256k1_musig_keyagg_cache *cache);
 
-static void secp256k1_musig_keyaggcoef(secp256k1_scalar *r, const secp256k1_keyagg_cache_internal *cache_i, secp256k1_ge *pk);
+static void secp256k1_musig_keyaggcoef(const secp256k1_hash_ctx *hash_ctx, secp256k1_scalar *r, const secp256k1_keyagg_cache_internal *cache_i, secp256k1_ge *pk);
 
 #endif
diff --git a/src/modules/musig/keyagg_impl.h b/src/modules/musig/keyagg_impl.h
index 4eb48ddc87..f67245d56d 100644
--- a/src/modules/musig/keyagg_impl.h
+++ b/src/modules/musig/keyagg_impl.h
@@ -82,9 +82,9 @@ static int secp256k1_musig_compute_pks_hash(const secp256k1_context *ctx, unsign
             return 0;
         }
         VERIFY_CHECK(ser_len == sizeof(ser));
-        secp256k1_sha256_write(&sha, ser, sizeof(ser));
+        secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &sha, ser, sizeof(ser));
     }
-    secp256k1_sha256_finalize(&sha, pks_hash);
+    secp256k1_sha256_finalize(secp256k1_get_hash_context(ctx), &sha, pks_hash);
     return 1;
 }
 
@@ -103,7 +103,7 @@ static void secp256k1_musig_keyaggcoef_sha256(secp256k1_sha256 *sha) {
  * second_pk is the point at infinity in case there is no second_pk. Assumes
  * that pk is not the point at infinity and that the Y-coordinates of pk and
  * second_pk are normalized. */
-static void secp256k1_musig_keyaggcoef_internal(secp256k1_scalar *r, const unsigned char *pks_hash, secp256k1_ge *pk, const secp256k1_ge *second_pk) {
+static void secp256k1_musig_keyaggcoef_internal(const secp256k1_hash_ctx *hash_ctx, secp256k1_scalar *r, const unsigned char *pks_hash, secp256k1_ge *pk, const secp256k1_ge *second_pk) {
     VERIFY_CHECK(!secp256k1_ge_is_infinity(pk));
 
     if (!secp256k1_ge_is_infinity(second_pk)
@@ -113,20 +113,20 @@ static void secp256k1_musig_keyaggcoef_internal(secp256k1_scalar *r, const unsig
         secp256k1_sha256 sha;
         unsigned char buf[33];
         secp256k1_musig_keyaggcoef_sha256(&sha);
-        secp256k1_sha256_write(&sha, pks_hash, 32);
+        secp256k1_sha256_write(hash_ctx, &sha, pks_hash, 32);
         /* Serialization does not fail since the pk is not the point at infinity
          * (according to this function's precondition). */
         secp256k1_eckey_pubkey_serialize33(pk, buf);
-        secp256k1_sha256_write(&sha, buf, sizeof(buf));
-        secp256k1_sha256_finalize(&sha, buf);
+        secp256k1_sha256_write(hash_ctx, &sha, buf, sizeof(buf));
+        secp256k1_sha256_finalize(hash_ctx, &sha, buf);
         secp256k1_scalar_set_b32(r, buf, NULL);
     }
 }
 
 /* Assumes that pk is not the point at infinity and that the Y-coordinates of pk
  * and cache_i->second_pk are normalized. */
-static void secp256k1_musig_keyaggcoef(secp256k1_scalar *r, const secp256k1_keyagg_cache_internal *cache_i, secp256k1_ge *pk) {
-    secp256k1_musig_keyaggcoef_internal(r, cache_i->pks_hash, pk, &cache_i->second_pk);
+static void secp256k1_musig_keyaggcoef(const secp256k1_hash_ctx *hash_ctx, secp256k1_scalar *r, const secp256k1_keyagg_cache_internal *cache_i, secp256k1_ge *pk) {
+    secp256k1_musig_keyaggcoef_internal(hash_ctx, r, cache_i->pks_hash, pk, &cache_i->second_pk);
 }
 
 typedef struct {
@@ -149,7 +149,7 @@ static int secp256k1_musig_pubkey_agg_callback(secp256k1_scalar *sc, secp256k1_g
 #else
     (void) ret;
 #endif
-    secp256k1_musig_keyaggcoef_internal(sc, ctx->pks_hash, pt, &ctx->second_pk);
+    secp256k1_musig_keyaggcoef_internal(secp256k1_get_hash_context(ctx->ctx), sc, ctx->pks_hash, pt, &ctx->second_pk);
     return 1;
 }
 
diff --git a/src/modules/musig/session_impl.h b/src/modules/musig/session_impl.h
index 42fcd81e12..6a37bfdf8e 100644
--- a/src/modules/musig/session_impl.h
+++ b/src/modules/musig/session_impl.h
@@ -289,20 +289,20 @@ int secp256k1_musig_partial_sig_serialize(const secp256k1_context* ctx, unsigned
 }
 
 /* Write optional inputs into the hash */
-static void secp256k1_nonce_function_musig_helper(secp256k1_sha256 *sha, unsigned int prefix_size, const unsigned char *data, unsigned char len) {
+static void secp256k1_nonce_function_musig_helper(const secp256k1_hash_ctx *hash_ctx, secp256k1_sha256 *sha, unsigned int prefix_size, const unsigned char *data, unsigned char len) {
     unsigned char zero[7] = { 0 };
     /* The spec requires length prefixes to be between 1 and 8 bytes
      * (inclusive) */
     VERIFY_CHECK(prefix_size >= 1 && prefix_size <= 8);
     /* Since the length of all input data fits in a byte, we can always pad the
      * length prefix with prefix_size - 1 zero bytes. */
-    secp256k1_sha256_write(sha, zero, prefix_size - 1);
+    secp256k1_sha256_write(hash_ctx, sha, zero, prefix_size - 1);
     if (data != NULL) {
-        secp256k1_sha256_write(sha, &len, 1);
-        secp256k1_sha256_write(sha, data, len);
+        secp256k1_sha256_write(hash_ctx, sha, &len, 1);
+        secp256k1_sha256_write(hash_ctx, sha, data, len);
     } else {
         len = 0;
-        secp256k1_sha256_write(sha, &len, 1);
+        secp256k1_sha256_write(hash_ctx, sha, &len, 1);
     }
 }
 
@@ -326,7 +326,7 @@ static void secp256k1_nonce_function_musig_sha256_tagged(secp256k1_sha256 *sha)
     secp256k1_sha256_initialize_midstate(sha, 64, midstate);
 }
 
-static void secp256k1_nonce_function_musig(secp256k1_scalar *k, const unsigned char *session_secrand, const unsigned char *msg32, const unsigned char *seckey32, const unsigned char *pk33, const unsigned char *agg_pk32, const unsigned char *extra_input32) {
+static void secp256k1_nonce_function_musig(const secp256k1_hash_ctx *hash_ctx, secp256k1_scalar *k, const unsigned char *session_secrand, const unsigned char *msg32, const unsigned char *seckey32, const unsigned char *pk33, const unsigned char *agg_pk32, const unsigned char *extra_input32) {
     secp256k1_sha256 sha;
     unsigned char rand[32];
     unsigned char i;
@@ -334,8 +334,8 @@ static void secp256k1_nonce_function_musig(secp256k1_scalar *k, const unsigned c
 
     if (seckey32 != NULL) {
         secp256k1_nonce_function_musig_sha256_tagged_aux(&sha);
-        secp256k1_sha256_write(&sha, session_secrand, 32);
-        secp256k1_sha256_finalize(&sha, rand);
+        secp256k1_sha256_write(hash_ctx, &sha, session_secrand, 32);
+        secp256k1_sha256_finalize(hash_ctx, &sha, rand);
         for (i = 0; i < 32; i++) {
             rand[i] ^= seckey32[i];
         }
@@ -344,21 +344,21 @@ static void secp256k1_nonce_function_musig(secp256k1_scalar *k, const unsigned c
     }
 
     secp256k1_nonce_function_musig_sha256_tagged(&sha);
-    secp256k1_sha256_write(&sha, rand, sizeof(rand));
-    secp256k1_nonce_function_musig_helper(&sha, 1, pk33, 33);
-    secp256k1_nonce_function_musig_helper(&sha, 1, agg_pk32, 32);
+    secp256k1_sha256_write(hash_ctx, &sha, rand, sizeof(rand));
+    secp256k1_nonce_function_musig_helper(hash_ctx, &sha, 1, pk33, 33);
+    secp256k1_nonce_function_musig_helper(hash_ctx, &sha, 1, agg_pk32, 32);
     msg_present = msg32 != NULL;
-    secp256k1_sha256_write(&sha, &msg_present, 1);
+    secp256k1_sha256_write(hash_ctx, &sha, &msg_present, 1);
     if (msg_present) {
-        secp256k1_nonce_function_musig_helper(&sha, 8, msg32, 32);
+        secp256k1_nonce_function_musig_helper(hash_ctx, &sha, 8, msg32, 32);
     }
-    secp256k1_nonce_function_musig_helper(&sha, 4, extra_input32, 32);
+    secp256k1_nonce_function_musig_helper(hash_ctx, &sha, 4, extra_input32, 32);
 
     for (i = 0; i < 2; i++) {
         unsigned char buf[32];
         secp256k1_sha256 sha_tmp = sha;
-        secp256k1_sha256_write(&sha_tmp, &i, 1);
-        secp256k1_sha256_finalize(&sha_tmp, buf);
+        secp256k1_sha256_write(hash_ctx, &sha_tmp, &i, 1);
+        secp256k1_sha256_finalize(hash_ctx, &sha_tmp, buf);
         secp256k1_scalar_set_b32(&k[i], buf, NULL);
 
         /* Attempt to erase secret data */
@@ -407,7 +407,7 @@ static int secp256k1_musig_nonce_gen_internal(const secp256k1_context* ctx, secp
     /* A pubkey cannot be the point at infinity */
     secp256k1_eckey_pubkey_serialize33(&pk, pk_ser);
 
-    secp256k1_nonce_function_musig(k, input_nonce, msg32, seckey, pk_ser, aggpk_ser_ptr, extra_input32);
+    secp256k1_nonce_function_musig(secp256k1_get_hash_context(ctx), k, input_nonce, msg32, seckey, pk_ser, aggpk_ser_ptr, extra_input32);
     VERIFY_CHECK(!secp256k1_scalar_is_zero(&k[0]));
     VERIFY_CHECK(!secp256k1_scalar_is_zero(&k[1]));
     secp256k1_musig_secnonce_save(secnonce, k, &pk);
@@ -541,7 +541,7 @@ static void secp256k1_musig_compute_noncehash_sha256_tagged(secp256k1_sha256 *sh
 }
 
 /* tagged_hash(aggnonce[0], aggnonce[1], agg_pk, msg) */
-static void secp256k1_musig_compute_noncehash(unsigned char *noncehash, secp256k1_ge *aggnonce, const unsigned char *agg_pk32, const unsigned char *msg) {
+static void secp256k1_musig_compute_noncehash(const secp256k1_hash_ctx *hash_ctx, unsigned char *noncehash, secp256k1_ge *aggnonce, const unsigned char *agg_pk32, const unsigned char *msg) {
     unsigned char buf[33];
     secp256k1_sha256 sha;
     int i;
@@ -549,11 +549,11 @@ static void secp256k1_musig_compute_noncehash(unsigned char *noncehash, secp256k
     secp256k1_musig_compute_noncehash_sha256_tagged(&sha);
     for (i = 0; i < 2; i++) {
         secp256k1_musig_ge_serialize_ext(buf, &aggnonce[i]);
-        secp256k1_sha256_write(&sha, buf, sizeof(buf));
+        secp256k1_sha256_write(hash_ctx, &sha, buf, sizeof(buf));
     }
-    secp256k1_sha256_write(&sha, agg_pk32, 32);
-    secp256k1_sha256_write(&sha, msg, 32);
-    secp256k1_sha256_finalize(&sha, noncehash);
+    secp256k1_sha256_write(hash_ctx, &sha, agg_pk32, 32);
+    secp256k1_sha256_write(hash_ctx, &sha, msg, 32);
+    secp256k1_sha256_finalize(hash_ctx, &sha, noncehash);
 }
 
 /* out_nonce = nonce_pts[0] + b*nonce_pts[1] */
@@ -565,12 +565,12 @@ static void secp256k1_effective_nonce(secp256k1_gej *out_nonce, const secp256k1_
     secp256k1_gej_add_ge_var(out_nonce, out_nonce, &nonce_pts[0], NULL);
 }
 
-static void secp256k1_musig_nonce_process_internal(int *fin_nonce_parity, unsigned char *fin_nonce, secp256k1_scalar *b, secp256k1_ge *aggnonce_pts, const unsigned char *agg_pk32, const unsigned char *msg) {
+static void secp256k1_musig_nonce_process_internal(const secp256k1_context *ctx, int *fin_nonce_parity, unsigned char *fin_nonce, secp256k1_scalar *b, secp256k1_ge *aggnonce_pts, const unsigned char *agg_pk32, const unsigned char *msg) {
     unsigned char noncehash[32];
     secp256k1_ge fin_nonce_pt;
     secp256k1_gej fin_nonce_ptj;
 
-    secp256k1_musig_compute_noncehash(noncehash, aggnonce_pts, agg_pk32, msg);
+    secp256k1_musig_compute_noncehash(secp256k1_get_hash_context(ctx), noncehash, aggnonce_pts, agg_pk32, msg);
     secp256k1_scalar_set_b32(b, noncehash, NULL);
     /* fin_nonce = aggnonce_pts[0] + b*aggnonce_pts[1] */
     secp256k1_effective_nonce(&fin_nonce_ptj, aggnonce_pts, b);
@@ -607,8 +607,8 @@ int secp256k1_musig_nonce_process(const secp256k1_context* ctx, secp256k1_musig_
         return 0;
     }
 
-    secp256k1_musig_nonce_process_internal(&session_i.fin_nonce_parity, fin_nonce, &session_i.noncecoef, aggnonce_pts, agg_pk32, msg32);
-    secp256k1_schnorrsig_challenge(&session_i.challenge, fin_nonce, msg32, 32, agg_pk32);
+    secp256k1_musig_nonce_process_internal(ctx, &session_i.fin_nonce_parity, fin_nonce, &session_i.noncecoef, aggnonce_pts, agg_pk32, msg32);
+    secp256k1_schnorrsig_challenge(secp256k1_get_hash_context(ctx), &session_i.challenge, fin_nonce, msg32, 32, agg_pk32);
 
     /* If there is a tweak then set `challenge` times `tweak` to the `s`-part.*/
     secp256k1_scalar_set_int(&session_i.s_part, 0);
@@ -678,7 +678,7 @@ int secp256k1_musig_partial_sign(const secp256k1_context* ctx, secp256k1_musig_p
     }
 
     /* Multiply KeyAgg coefficient */
-    secp256k1_musig_keyaggcoef(&mu, &cache_i, &pk);
+    secp256k1_musig_keyaggcoef(secp256k1_get_hash_context(ctx), &mu, &cache_i, &pk);
     secp256k1_scalar_mul(&sk, &sk, &mu);
 
     if (!secp256k1_musig_session_load(ctx, &session_i, session)) {
@@ -738,7 +738,7 @@ int secp256k1_musig_partial_sig_verify(const secp256k1_context* ctx, const secp2
     /* Multiplying the challenge by the KeyAgg coefficient is equivalent
      * to multiplying the signer's public key by the coefficient, except
      * much easier to do. */
-    secp256k1_musig_keyaggcoef(&mu, &cache_i, &pkp);
+    secp256k1_musig_keyaggcoef(secp256k1_get_hash_context(ctx), &mu, &cache_i, &pkp);
     secp256k1_scalar_mul(&e, &session_i.challenge, &mu);
 
     /* Negate e if secp256k1_fe_is_odd(&cache_i.pk.y)) XOR cache_i.parity_acc.
diff --git a/src/modules/musig/tests_impl.h b/src/modules/musig/tests_impl.h
index de09c5e280..cbeb1e285a 100644
--- a/src/modules/musig/tests_impl.h
+++ b/src/modules/musig/tests_impl.h
@@ -505,12 +505,12 @@ static void musig_api_tests(void) {
     CHECK(secp256k1_musig_partial_sig_agg(CTX, pre_sig, &session, partial_sig_ptr, 2) == 1);
 }
 
-static void musig_nonce_bitflip(unsigned char **args, size_t n_flip, size_t n_bytes) {
+static void musig_nonce_bitflip(const secp256k1_hash_ctx *hash_ctx, unsigned char **args, size_t n_flip, size_t n_bytes) {
     secp256k1_scalar k1[2], k2[2];
 
-    secp256k1_nonce_function_musig(k1, args[0], args[1], args[2], args[3], args[4], args[5]);
+    secp256k1_nonce_function_musig(hash_ctx, k1, args[0], args[1], args[2], args[3], args[4], args[5]);
     testrand_flip(args[n_flip], n_bytes);
-    secp256k1_nonce_function_musig(k2, args[0], args[1], args[2], args[3], args[4], args[5]);
+    secp256k1_nonce_function_musig(hash_ctx, k2, args[0], args[1], args[2], args[3], args[4], args[5]);
     CHECK(secp256k1_scalar_eq(&k1[0], &k2[0]) == 0);
     CHECK(secp256k1_scalar_eq(&k1[1], &k2[1]) == 0);
 }
@@ -526,6 +526,7 @@ static void musig_nonce_test(void) {
     int i, j;
     secp256k1_scalar k[6][2];
 
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
     testrand_bytes_test(session_secrand, sizeof(session_secrand));
     testrand_bytes_test(sk, sizeof(sk));
     testrand_bytes_test(pk, sizeof(pk));
@@ -541,12 +542,12 @@ static void musig_nonce_test(void) {
     args[4] = agg_pk;
     args[5] = extra_input;
     for (i = 0; i < COUNT; i++) {
-        musig_nonce_bitflip(args, 0, sizeof(session_secrand));
-        musig_nonce_bitflip(args, 1, sizeof(msg));
-        musig_nonce_bitflip(args, 2, sizeof(sk));
-        musig_nonce_bitflip(args, 3, sizeof(pk));
-        musig_nonce_bitflip(args, 4, sizeof(agg_pk));
-        musig_nonce_bitflip(args, 5, sizeof(extra_input));
+        musig_nonce_bitflip(hash_ctx, args, 0, sizeof(session_secrand));
+        musig_nonce_bitflip(hash_ctx, args, 1, sizeof(msg));
+        musig_nonce_bitflip(hash_ctx, args, 2, sizeof(sk));
+        musig_nonce_bitflip(hash_ctx, args, 3, sizeof(pk));
+        musig_nonce_bitflip(hash_ctx, args, 4, sizeof(agg_pk));
+        musig_nonce_bitflip(hash_ctx, args, 5, sizeof(extra_input));
     }
     /* Check that if any argument is NULL, a different nonce is produced than if
      * any other argument is NULL. */
@@ -555,12 +556,12 @@ static void musig_nonce_test(void) {
     memcpy(pk, session_secrand, sizeof(session_secrand));
     memcpy(agg_pk, session_secrand, sizeof(agg_pk));
     memcpy(extra_input, session_secrand, sizeof(extra_input));
-    secp256k1_nonce_function_musig(k[0], args[0], args[1], args[2], args[3], args[4], args[5]);
-    secp256k1_nonce_function_musig(k[1], args[0], NULL, args[2], args[3], args[4], args[5]);
-    secp256k1_nonce_function_musig(k[2], args[0], args[1], NULL, args[3], args[4], args[5]);
-    secp256k1_nonce_function_musig(k[3], args[0], args[1], args[2], NULL, args[4], args[5]);
-    secp256k1_nonce_function_musig(k[4], args[0], args[1], args[2], args[3], NULL, args[5]);
-    secp256k1_nonce_function_musig(k[5], args[0], args[1], args[2], args[3], args[4], NULL);
+    secp256k1_nonce_function_musig(hash_ctx, k[0], args[0], args[1], args[2], args[3], args[4], args[5]);
+    secp256k1_nonce_function_musig(hash_ctx, k[1], args[0], NULL, args[2], args[3], args[4], args[5]);
+    secp256k1_nonce_function_musig(hash_ctx, k[2], args[0], args[1], NULL, args[3], args[4], args[5]);
+    secp256k1_nonce_function_musig(hash_ctx, k[3], args[0], args[1], args[2], NULL, args[4], args[5]);
+    secp256k1_nonce_function_musig(hash_ctx, k[4], args[0], args[1], args[2], args[3], NULL, args[5]);
+    secp256k1_nonce_function_musig(hash_ctx, k[5], args[0], args[1], args[2], args[3], args[4], NULL);
     for (i = 0; i < 6; i++) {
         CHECK(!secp256k1_scalar_eq(&k[i][0], &k[i][1]));
         for (j = i+1; j < 6; j++) {
@@ -574,35 +575,36 @@ static void musig_nonce_test(void) {
  * state. */
 static void sha256_tag_test(void) {
     secp256k1_sha256 sha;
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
     {
         /* "KeyAgg list" */
         static const unsigned char tag[] = {'K', 'e', 'y', 'A', 'g', 'g', ' ', 'l', 'i', 's', 't'};
         secp256k1_musig_keyagglist_sha256(&sha);
-        test_sha256_tag_midstate(&sha, tag, sizeof(tag));
+        test_sha256_tag_midstate(hash_ctx, &sha, tag, sizeof(tag));
     }
     {
         /* "KeyAgg coefficient" */
         static const unsigned char tag[] = {'K', 'e', 'y', 'A', 'g', 'g', ' ', 'c', 'o', 'e', 'f', 'f', 'i', 'c', 'i', 'e', 'n', 't'};
         secp256k1_musig_keyaggcoef_sha256(&sha);
-        test_sha256_tag_midstate(&sha, tag, sizeof(tag));
+        test_sha256_tag_midstate(hash_ctx, &sha, tag, sizeof(tag));
     }
     {
         /* "MuSig/aux" */
         static const unsigned char tag[] = { 'M', 'u', 'S', 'i', 'g', '/', 'a', 'u', 'x' };
         secp256k1_nonce_function_musig_sha256_tagged_aux(&sha);
-        test_sha256_tag_midstate(&sha, tag, sizeof(tag));
+        test_sha256_tag_midstate(hash_ctx, &sha, tag, sizeof(tag));
     }
     {
         /* "MuSig/nonce" */
         static const unsigned char tag[] = { 'M', 'u', 'S', 'i', 'g', '/', 'n', 'o', 'n', 'c', 'e' };
         secp256k1_nonce_function_musig_sha256_tagged(&sha);
-        test_sha256_tag_midstate(&sha, tag, sizeof(tag));
+        test_sha256_tag_midstate(hash_ctx, &sha, tag, sizeof(tag));
     }
     {
         /* "MuSig/noncecoef" */
         static const unsigned char tag[] = { 'M', 'u', 'S', 'i', 'g', '/', 'n', 'o', 'n', 'c', 'e', 'c', 'o', 'e', 'f' };
         secp256k1_musig_compute_noncehash_sha256_tagged(&sha);
-        test_sha256_tag_midstate(&sha, tag, sizeof(tag));
+        test_sha256_tag_midstate(hash_ctx, &sha, tag, sizeof(tag));
     }
 }
 
diff --git a/src/modules/schnorrsig/main_impl.h b/src/modules/schnorrsig/main_impl.h
index 21c1f41298..5100557f4d 100644
--- a/src/modules/schnorrsig/main_impl.h
+++ b/src/modules/schnorrsig/main_impl.h
@@ -37,7 +37,7 @@ static const unsigned char bip340_algo[] = {'B', 'I', 'P', '0', '3', '4', '0', '
 
 static const unsigned char schnorrsig_extraparams_magic[4] = SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC;
 
-static int nonce_function_bip340(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) {
+static int nonce_function_bip340_impl(const secp256k1_hash_ctx *hash_ctx, unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) {
     secp256k1_sha256 sha;
     unsigned char masked_key[32];
     int i;
@@ -48,8 +48,8 @@ static int nonce_function_bip340(unsigned char *nonce32, const unsigned char *ms
 
     if (data != NULL) {
         secp256k1_nonce_function_bip340_sha256_tagged_aux(&sha);
-        secp256k1_sha256_write(&sha, data, 32);
-        secp256k1_sha256_finalize(&sha, masked_key);
+        secp256k1_sha256_write(hash_ctx, &sha, data, 32);
+        secp256k1_sha256_finalize(hash_ctx, &sha, masked_key);
         for (i = 0; i < 32; i++) {
             masked_key[i] ^= key32[i];
         }
@@ -73,20 +73,24 @@ static int nonce_function_bip340(unsigned char *nonce32, const unsigned char *ms
             && secp256k1_memcmp_var(algo, bip340_algo, algolen) == 0) {
         secp256k1_nonce_function_bip340_sha256_tagged(&sha);
     } else {
-        secp256k1_sha256_initialize_tagged(&sha, algo, algolen);
+        secp256k1_sha256_initialize_tagged(hash_ctx, &sha, algo, algolen);
     }
 
     /* Hash masked-key||pk||msg using the tagged hash as per the spec */
-    secp256k1_sha256_write(&sha, masked_key, 32);
-    secp256k1_sha256_write(&sha, xonly_pk32, 32);
-    secp256k1_sha256_write(&sha, msg, msglen);
-    secp256k1_sha256_finalize(&sha, nonce32);
+    secp256k1_sha256_write(hash_ctx, &sha, masked_key, 32);
+    secp256k1_sha256_write(hash_ctx, &sha, xonly_pk32, 32);
+    secp256k1_sha256_write(hash_ctx, &sha, msg, msglen);
+    secp256k1_sha256_finalize(hash_ctx, &sha, nonce32);
     secp256k1_sha256_clear(&sha);
     secp256k1_memclear_explicit(masked_key, sizeof(masked_key));
 
     return 1;
 }
 
+static int nonce_function_bip340(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) {
+    return nonce_function_bip340_impl(secp256k1_get_hash_context(secp256k1_context_static), nonce32, msg, msglen, key32, xonly_pk32, algo, algolen, data);
+}
+
 const secp256k1_nonce_function_hardened secp256k1_nonce_function_bip340 = nonce_function_bip340;
 
 /* Initializes SHA256 with fixed midstate. This midstate was computed by applying
@@ -99,17 +103,17 @@ static void secp256k1_schnorrsig_sha256_tagged(secp256k1_sha256 *sha) {
     secp256k1_sha256_initialize_midstate(sha, 64, midstate);
 }
 
-static void secp256k1_schnorrsig_challenge(secp256k1_scalar* e, const unsigned char *r32, const unsigned char *msg, size_t msglen, const unsigned char *pubkey32)
+static void secp256k1_schnorrsig_challenge(const secp256k1_hash_ctx *hash_ctx, secp256k1_scalar* e, const unsigned char *r32, const unsigned char *msg, size_t msglen, const unsigned char *pubkey32)
 {
     unsigned char buf[32];
     secp256k1_sha256 sha;
 
     /* tagged hash(r.x, pk.x, msg) */
     secp256k1_schnorrsig_sha256_tagged(&sha);
-    secp256k1_sha256_write(&sha, r32, 32);
-    secp256k1_sha256_write(&sha, pubkey32, 32);
-    secp256k1_sha256_write(&sha, msg, msglen);
-    secp256k1_sha256_finalize(&sha, buf);
+    secp256k1_sha256_write(hash_ctx, &sha, r32, 32);
+    secp256k1_sha256_write(hash_ctx, &sha, pubkey32, 32);
+    secp256k1_sha256_write(hash_ctx, &sha, msg, msglen);
+    secp256k1_sha256_finalize(hash_ctx, &sha, buf);
     /* Set scalar e to the challenge hash modulo the curve order as per
      * BIP340. */
     secp256k1_scalar_set_b32(e, buf, NULL);
@@ -133,10 +137,6 @@ static int secp256k1_schnorrsig_sign_internal(const secp256k1_context* ctx, unsi
     ARG_CHECK(msg != NULL || msglen == 0);
     ARG_CHECK(keypair != NULL);
 
-    if (noncefp == NULL) {
-        noncefp = secp256k1_nonce_function_bip340;
-    }
-
     ret &= secp256k1_keypair_load(ctx, &sk, &pk, keypair);
     /* Because we are signing for a x-only pubkey, the secret key is negated
      * before signing if the point corresponding to the secret key does not
@@ -147,7 +147,15 @@ static int secp256k1_schnorrsig_sign_internal(const secp256k1_context* ctx, unsi
 
     secp256k1_scalar_get_b32(seckey, &sk);
     secp256k1_fe_get_b32(pk_buf, &pk.x);
-    ret &= !!noncefp(nonce32, msg, msglen, seckey, pk_buf, bip340_algo, sizeof(bip340_algo), ndata);
+
+    /* Compute nonce */
+    if (noncefp == NULL || noncefp == secp256k1_nonce_function_bip340) {
+        /* Use context-aware nonce function by default */
+        ret &= nonce_function_bip340_impl(secp256k1_get_hash_context(ctx), nonce32, msg, msglen, seckey, pk_buf, bip340_algo, sizeof(bip340_algo), ndata);
+    } else {
+        ret &= !!noncefp(nonce32, msg, msglen, seckey, pk_buf, bip340_algo, sizeof(bip340_algo), ndata);
+    }
+
     secp256k1_scalar_set_b32(&k, nonce32, NULL);
     ret &= !secp256k1_scalar_is_zero(&k);
     secp256k1_scalar_cmov(&k, &secp256k1_scalar_one, !ret);
@@ -165,7 +173,7 @@ static int secp256k1_schnorrsig_sign_internal(const secp256k1_context* ctx, unsi
     secp256k1_fe_normalize_var(&r.x);
     secp256k1_fe_get_b32(&sig64[0], &r.x);
 
-    secp256k1_schnorrsig_challenge(&e, &sig64[0], msg, msglen, pk_buf);
+    secp256k1_schnorrsig_challenge(secp256k1_get_hash_context(ctx), &e, &sig64[0], msg, msglen, pk_buf);
     secp256k1_scalar_mul(&e, &e, &sk);
     secp256k1_scalar_add(&e, &e, &k);
     secp256k1_scalar_get_b32(&sig64[32], &e);
@@ -235,7 +243,7 @@ int secp256k1_schnorrsig_verify(const secp256k1_context* ctx, const unsigned cha
 
     /* Compute e. */
     secp256k1_fe_get_b32(buf, &pk.x);
-    secp256k1_schnorrsig_challenge(&e, &sig64[0], msg, msglen, buf);
+    secp256k1_schnorrsig_challenge(secp256k1_get_hash_context(ctx), &e, &sig64[0], msg, msglen, buf);
 
     /* Compute rj =  s*G + (-e)*pkj */
     secp256k1_scalar_negate(&e, &e);
diff --git a/src/modules/schnorrsig/tests_exhaustive_impl.h b/src/modules/schnorrsig/tests_exhaustive_impl.h
index 601b54975d..a8298f65ba 100644
--- a/src/modules/schnorrsig/tests_exhaustive_impl.h
+++ b/src/modules/schnorrsig/tests_exhaustive_impl.h
@@ -105,7 +105,7 @@ static void test_exhaustive_schnorrsig_verify(const secp256k1_context *ctx, cons
                 secp256k1_scalar e;
                 unsigned char msg32[32];
                 testrand256(msg32);
-                secp256k1_schnorrsig_challenge(&e, sig64, msg32, sizeof(msg32), pk32);
+                secp256k1_schnorrsig_challenge(secp256k1_get_hash_context(ctx), &e, sig64, msg32, sizeof(msg32), pk32);
                 /* Only do work if we hit a challenge we haven't tried before. */
                 if (!e_done[e]) {
                     /* Iterate over the possible valid last 32 bytes in the signature.
@@ -162,7 +162,7 @@ static void test_exhaustive_schnorrsig_sign(const secp256k1_context *ctx, unsign
             while (e_count_done < EXHAUSTIVE_TEST_ORDER) {
                 secp256k1_scalar e;
                 testrand256(msg32);
-                secp256k1_schnorrsig_challenge(&e, xonly_pubkey_bytes[k - 1], msg32, sizeof(msg32), xonly_pubkey_bytes[d - 1]);
+                secp256k1_schnorrsig_challenge(secp256k1_get_hash_context(ctx), &e, xonly_pubkey_bytes[k - 1], msg32, sizeof(msg32), xonly_pubkey_bytes[d - 1]);
                 /* Only do work if we hit a challenge we haven't tried before. */
                 if (!e_done[e]) {
                     secp256k1_scalar expected_s = (actual_k + e * actual_d) % EXHAUSTIVE_TEST_ORDER;
diff --git a/src/modules/schnorrsig/tests_impl.h b/src/modules/schnorrsig/tests_impl.h
index 9a1b15f0b2..56812e7f04 100644
--- a/src/modules/schnorrsig/tests_impl.h
+++ b/src/modules/schnorrsig/tests_impl.h
@@ -38,18 +38,20 @@ static void run_nonce_function_bip340_tests(void) {
     unsigned char *args[5];
     int i;
 
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
+
     /* Check that hash initialized by
      * secp256k1_nonce_function_bip340_sha256_tagged has the expected
      * state. */
     secp256k1_nonce_function_bip340_sha256_tagged(&sha_optimized);
-    test_sha256_tag_midstate(&sha_optimized, tag, sizeof(tag));
+    test_sha256_tag_midstate(hash_ctx, &sha_optimized, tag, sizeof(tag));
 
 
    /* Check that hash initialized by
     * secp256k1_nonce_function_bip340_sha256_tagged_aux has the expected
     * state. */
     secp256k1_nonce_function_bip340_sha256_tagged_aux(&sha_optimized);
-    test_sha256_tag_midstate(&sha_optimized, aux_tag, sizeof(aux_tag));
+    test_sha256_tag_midstate(hash_ctx, &sha_optimized, aux_tag, sizeof(aux_tag));
 
     testrand256(msg);
     testrand256(key);
@@ -162,8 +164,9 @@ static void test_schnorrsig_sha256_tagged(void) {
     unsigned char tag[] = {'B', 'I', 'P', '0', '3', '4', '0', '/', 'c', 'h', 'a', 'l', 'l', 'e', 'n', 'g', 'e'};
     secp256k1_sha256 sha;
     secp256k1_sha256 sha_optimized;
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
 
-    secp256k1_sha256_initialize_tagged(&sha, (unsigned char *) tag, sizeof(tag));
+    secp256k1_sha256_initialize_tagged(hash_ctx, &sha, (unsigned char *) tag, sizeof(tag));
     secp256k1_schnorrsig_sha256_tagged(&sha_optimized);
     test_sha256_eq(&sha, &sha_optimized);
 }
@@ -849,6 +852,29 @@ static void test_schnorrsig_sign_internal(void) {
     CHECK(secp256k1_memcmp_var(sig, sig2, sizeof(sig)) == 0);
 }
 
+DEFINE_SHA256_TRANSFORM_PROBE(sha256_schnorrsig)
+static void test_schnorrsig_ctx_sha256(void) {
+    /* Check ctx-provided SHA256 compression override takes effect */
+    secp256k1_context *ctx = secp256k1_context_clone(CTX);
+    unsigned char out_default[64], out_custom[64];
+    unsigned char sk[32] = {1}, msg32[32] = {1};
+    secp256k1_keypair keypair;
+    CHECK(secp256k1_keypair_create(ctx, &keypair, sk));
+
+    /* Default behavior. No ctx-provided SHA256 compression */
+    CHECK(secp256k1_schnorrsig_sign32(ctx, out_default, msg32, &keypair, NULL));
+    CHECK(!sha256_schnorrsig_called);
+
+    /* Override SHA256 compression directly, bypassing the ctx setter sanity checks */
+    ctx->hash_ctx.fn_sha256_compression = sha256_schnorrsig;
+    CHECK(secp256k1_schnorrsig_sign32(ctx, out_custom, msg32, &keypair, NULL));
+    CHECK(sha256_schnorrsig_called);
+    /* Outputs must differ if custom compression was used */
+    CHECK(secp256k1_memcmp_var(out_default, out_custom, 64) != 0);
+
+    secp256k1_context_destroy(ctx);
+}
+
 #define N_SIGS 3
 /* Creates N_SIGS valid signatures and verifies them with verify and
  * verify_batch (TODO). Then flips some bits and checks that verification now
@@ -978,6 +1004,7 @@ static const struct tf_test_entry tests_schnorrsig[] = {
     CASE1(test_schnorrsig_sign),
     CASE1(test_schnorrsig_sign_verify),
     CASE1(test_schnorrsig_taproot),
+    CASE1(test_schnorrsig_ctx_sha256),
 };
 
 #endif
diff --git a/src/secp256k1.c b/src/secp256k1.c
index 218ceafb31..e4b80fff24 100644
--- a/src/secp256k1.c
+++ b/src/secp256k1.c
@@ -60,6 +60,7 @@
  * context_eq function. */
 struct secp256k1_context_struct {
     secp256k1_ecmult_gen_context ecmult_gen_ctx;
+    secp256k1_hash_ctx hash_ctx;
     secp256k1_callback illegal_callback;
     secp256k1_callback error_callback;
     int declassify;
@@ -67,6 +68,7 @@ struct secp256k1_context_struct {
 
 static const secp256k1_context secp256k1_context_static_ = {
     { 0 },
+    { secp256k1_sha256_transform },
     { secp256k1_default_illegal_callback_fn, 0 },
     { secp256k1_default_error_callback_fn, 0 },
     0
@@ -129,10 +131,11 @@ secp256k1_context* secp256k1_context_preallocated_create(void* prealloc, unsigne
     ret = (secp256k1_context*)prealloc;
     ret->illegal_callback = default_illegal_callback;
     ret->error_callback = default_error_callback;
+    secp256k1_hash_ctx_init(&ret->hash_ctx);
 
     /* Flags have been checked by secp256k1_context_preallocated_size. */
     VERIFY_CHECK((flags & SECP256K1_FLAGS_TYPE_MASK) == SECP256K1_FLAGS_TYPE_CONTEXT);
-    secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx);
+    secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx, &ret->hash_ctx);
     ret->declassify = !!(flags & SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY);
 
     return ret;
@@ -220,6 +223,22 @@ void secp256k1_context_set_error_callback(secp256k1_context* ctx, void (*fun)(co
     ctx->error_callback.data = data;
 }
 
+void secp256k1_context_set_sha256_compression(secp256k1_context *ctx, secp256k1_sha256_compression_function fn_compression) {
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK_VOID(secp256k1_context_is_proper(ctx));
+    if (!fn_compression) { /* Reset hash context */
+        secp256k1_hash_ctx_init(&ctx->hash_ctx);
+        return;
+    }
+    /* Check and set */
+    ARG_CHECK_VOID(secp256k1_selftest_sha256(fn_compression));
+    ctx->hash_ctx.fn_sha256_compression = fn_compression;
+}
+
+static SECP256K1_INLINE const secp256k1_hash_ctx* secp256k1_get_hash_context(const secp256k1_context *ctx) {
+    return &ctx->hash_ctx;
+}
+
 static secp256k1_scratch_space* secp256k1_scratch_space_create(const secp256k1_context* ctx, size_t max_size) {
     VERIFY_CHECK(ctx != NULL);
     return secp256k1_scratch_create(&ctx->error_callback, max_size);
@@ -476,7 +495,7 @@ static SECP256K1_INLINE void buffer_append(unsigned char *buf, unsigned int *off
     *offset += len;
 }
 
-static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+static int nonce_function_rfc6979_impl(const secp256k1_hash_ctx *hash_ctx, unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
    unsigned char keydata[112];
    unsigned int offset = 0;
    secp256k1_rfc6979_hmac_sha256 rng;
@@ -501,9 +520,9 @@ static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *m
    if (algo16 != NULL) {
        buffer_append(keydata, &offset, algo16, 16);
    }
-   secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, offset);
+   secp256k1_rfc6979_hmac_sha256_initialize(hash_ctx, &rng, keydata, offset);
    for (i = 0; i <= counter; i++) {
-       secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+       secp256k1_rfc6979_hmac_sha256_generate(hash_ctx, &rng, nonce32, 32);
    }
    secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 
@@ -512,6 +531,10 @@ static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *m
    return 1;
 }
 
+static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+    return nonce_function_rfc6979_impl(secp256k1_get_hash_context(secp256k1_context_static), nonce32, msg32, key32, algo16, data, counter);
+}
+
 const secp256k1_nonce_function secp256k1_nonce_function_rfc6979 = nonce_function_rfc6979;
 const secp256k1_nonce_function secp256k1_nonce_function_default = nonce_function_rfc6979;
 
@@ -527,9 +550,6 @@ static int secp256k1_ecdsa_sign_inner(const secp256k1_context* ctx, secp256k1_sc
     if (recid) {
         *recid = 0;
     }
-    if (noncefp == NULL) {
-        noncefp = secp256k1_nonce_function_default;
-    }
 
     /* Fail if the secret key is invalid. */
     is_sec_valid = secp256k1_scalar_set_b32_seckey(&sec, seckey);
@@ -537,7 +557,14 @@ static int secp256k1_ecdsa_sign_inner(const secp256k1_context* ctx, secp256k1_sc
     secp256k1_scalar_set_b32(&msg, msg32, NULL);
     while (1) {
         int is_nonce_valid;
-        ret = !!noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count);
+
+        if (noncefp == NULL) {
+            /* Use ctx-aware function by default */
+            ret = nonce_function_rfc6979_impl(secp256k1_get_hash_context(ctx), nonce32, msg32, seckey, NULL, (void*)noncedata, count);
+        } else {
+            ret = !!noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count);
+        }
+
         if (!ret) {
             break;
         }
@@ -757,7 +784,7 @@ int secp256k1_context_randomize(secp256k1_context* ctx, const unsigned char *see
     ARG_CHECK(secp256k1_context_is_proper(ctx));
 
     if (secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)) {
-        secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
+        secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, secp256k1_get_hash_context(ctx), seed32);
     }
     return 1;
 }
@@ -795,9 +822,9 @@ int secp256k1_tagged_sha256(const secp256k1_context* ctx, unsigned char *hash32,
     ARG_CHECK(tag != NULL);
     ARG_CHECK(msg != NULL);
 
-    secp256k1_sha256_initialize_tagged(&sha, tag, taglen);
-    secp256k1_sha256_write(&sha, msg, msglen);
-    secp256k1_sha256_finalize(&sha, hash32);
+    secp256k1_sha256_initialize_tagged(secp256k1_get_hash_context(ctx), &sha, tag, taglen);
+    secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &sha, msg, msglen);
+    secp256k1_sha256_finalize(secp256k1_get_hash_context(ctx), &sha, hash32);
     secp256k1_sha256_clear(&sha);
     return 1;
 }
diff --git a/src/selftest.h b/src/selftest.h
index d083ac9524..de0e0597f5 100644
--- a/src/selftest.h
+++ b/src/selftest.h
@@ -11,7 +11,8 @@
 
 #include <string.h>
 
-static int secp256k1_selftest_sha256(void) {
+static int secp256k1_selftest_sha256(secp256k1_sha256_compression_function fn_compression) {
+    secp256k1_hash_ctx hash_ctx;
     static const char *input63 = "For this sample, this 63-byte string will be used as input data";
     static const unsigned char output32[32] = {
         0xf0, 0x8a, 0x78, 0xcb, 0xba, 0xee, 0x08, 0x2b, 0x05, 0x2a, 0xe0, 0x70, 0x8f, 0x32, 0xfa, 0x1e,
@@ -20,13 +21,15 @@ static int secp256k1_selftest_sha256(void) {
     unsigned char out[32];
     secp256k1_sha256 hasher;
     secp256k1_sha256_initialize(&hasher);
-    secp256k1_sha256_write(&hasher, (const unsigned char*)input63, 63);
-    secp256k1_sha256_finalize(&hasher, out);
+    hash_ctx.fn_sha256_compression = fn_compression;
+    secp256k1_sha256_write(&hash_ctx, &hasher, (const unsigned char*)input63, 63);
+    secp256k1_sha256_finalize(&hash_ctx, &hasher, out);
     return secp256k1_memcmp_var(out, output32, 32) == 0;
 }
 
 static int secp256k1_selftest_passes(void) {
-    return secp256k1_selftest_sha256();
+    /* Use default sha256 compression */
+    return secp256k1_selftest_sha256(secp256k1_sha256_transform);
 }
 
 #endif /* SECP256K1_SELFTEST_H */
diff --git a/src/testrand_impl.h b/src/testrand_impl.h
index b84f5730a9..e1e5d858c1 100644
--- a/src/testrand_impl.h
+++ b/src/testrand_impl.h
@@ -22,12 +22,13 @@ SECP256K1_INLINE static void testrand_seed(const unsigned char *seed16) {
     unsigned char out32[32];
     secp256k1_sha256 hash;
     int i;
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(secp256k1_context_static);
 
     /* Use SHA256(PREFIX || seed16) as initial state. */
     secp256k1_sha256_initialize(&hash);
-    secp256k1_sha256_write(&hash, PREFIX, sizeof(PREFIX));
-    secp256k1_sha256_write(&hash, seed16, 16);
-    secp256k1_sha256_finalize(&hash, out32);
+    secp256k1_sha256_write(hash_ctx, &hash, PREFIX, sizeof(PREFIX));
+    secp256k1_sha256_write(hash_ctx, &hash, seed16, 16);
+    secp256k1_sha256_finalize(hash_ctx, &hash, out32);
     for (i = 0; i < 4; ++i) {
         uint64_t s = 0;
         int j;
diff --git a/src/tests.c b/src/tests.c
index fa580cc97e..7c3a96bcdd 100644
--- a/src/tests.c
+++ b/src/tests.c
@@ -132,6 +132,7 @@ static int ecmult_gen_context_eq(const secp256k1_ecmult_gen_context *a, const se
 static int context_eq(const secp256k1_context *a, const secp256k1_context *b) {
     return a->declassify == b->declassify
             && ecmult_gen_context_eq(&a->ecmult_gen_ctx, &b->ecmult_gen_ctx)
+            && a->hash_ctx.fn_sha256_compression == b->hash_ctx.fn_sha256_compression
             && a->illegal_callback.fn == b->illegal_callback.fn
             && a->illegal_callback.data == b->illegal_callback.data
             && a->error_callback.fn == b->error_callback.fn
@@ -432,6 +433,146 @@ static void run_scratch_tests(void) {
     secp256k1_scratch_space_destroy(CTX, NULL); /* no-op */
 }
 
+/* A compression function that does nothing */
+static void invalid_sha256_compression(uint32_t *s, const unsigned char *msg, size_t rounds) {
+    (void)s; (void)msg; (void)rounds;
+}
+
+static int own_transform_called = 0;
+static void good_sha256_compression(uint32_t *s, const unsigned char *msg, size_t rounds) {
+    own_transform_called = 1;
+    secp256k1_sha256_transform(s, msg, rounds);
+}
+
+static void run_plug_sha256_compression_tests(void) {
+    secp256k1_context *ctx, *ctx_cloned;
+    secp256k1_sha256 sha;
+    unsigned char sha_out[32];
+    /* 1) Verify the context is initialized with the default compression function */
+    ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+    CHECK(ctx->hash_ctx.fn_sha256_compression == secp256k1_sha256_transform);
+
+    /* 2) Verify providing a bad compression function fails during set */
+    CHECK_ILLEGAL_VOID(ctx, secp256k1_context_set_sha256_compression(ctx, invalid_sha256_compression));
+    CHECK(ctx->hash_ctx.fn_sha256_compression == secp256k1_sha256_transform);
+
+    /* 3) Provide sha256 to ctx and verify it is called when provided */
+    own_transform_called = 0;
+    secp256k1_context_set_sha256_compression(ctx, good_sha256_compression);
+    CHECK(own_transform_called);
+
+    /* 4) Verify callback makes it across clone */
+    ctx_cloned = secp256k1_context_clone(ctx);
+    CHECK(ctx_cloned->hash_ctx.fn_sha256_compression == good_sha256_compression);
+
+    /* 5) A hash operation should invoke the installed callback */
+    own_transform_called = 0;
+    secp256k1_sha256_initialize(&sha);
+    secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &sha, (const unsigned char*)"a", 1);
+    secp256k1_sha256_finalize(secp256k1_get_hash_context(ctx), &sha, sha_out);
+    CHECK(own_transform_called);
+
+    /* 6) Unset sha256 and verify the default one is set again */
+    secp256k1_context_set_sha256_compression(ctx, NULL);
+    CHECK(ctx->hash_ctx.fn_sha256_compression == secp256k1_sha256_transform);
+
+    secp256k1_context_destroy(ctx);
+    secp256k1_context_destroy(ctx_cloned);
+}
+
+static void run_sha256_multi_block_compression_tests(void) {
+    secp256k1_hash_ctx hash_ctx;
+    secp256k1_sha256 sha256_one;
+    secp256k1_sha256 sha256_two;
+    unsigned char out_one[32], out_two[32];
+
+    hash_ctx.fn_sha256_compression = secp256k1_sha256_transform;
+
+    {   /* 1) Writing one 64-byte full block vs two 32-byte blocks */
+        const unsigned char data[64] = "totally serious test message to hash, definitely no random data";
+        unsigned char data32[32];
+
+        secp256k1_sha256_initialize(&sha256_one);
+        secp256k1_sha256_initialize(&sha256_two);
+
+        /* Write the 64-byte block */
+        secp256k1_sha256_write(&hash_ctx, &sha256_one, data, 64);
+        secp256k1_sha256_finalize(&hash_ctx, &sha256_one, out_one);
+
+        /* Write the two 32-byte blocks */
+        memcpy(data32, data, 32);
+        secp256k1_sha256_write(&hash_ctx, &sha256_two, data32, 32);
+        memcpy(data32, data + 32, 32);
+        secp256k1_sha256_write(&hash_ctx, &sha256_two, data32, 32);
+        secp256k1_sha256_finalize(&hash_ctx, &sha256_two, out_two);
+
+        CHECK(secp256k1_memcmp_var(out_one, out_two, 32) == 0);
+    }
+
+    {   /* 2) Writing one 80-byte block vs two 40-byte blocks */
+        const unsigned char data[80] = "Genesis: The Times 03/Jan/2009 Chancellor on brink of second bailout for banks ";
+        unsigned char data40[40];
+
+        secp256k1_sha256_initialize(&sha256_one);
+        secp256k1_sha256_initialize(&sha256_two);
+
+        /* Write the 80-byte block */
+        secp256k1_sha256_write(&hash_ctx, &sha256_one, data, 80);
+        secp256k1_sha256_finalize(&hash_ctx, &sha256_one, out_one);
+
+        /* Write the two 40-byte blocks */
+        memcpy(data40, data, 40);
+        secp256k1_sha256_write(&hash_ctx, &sha256_two, data40, 40);
+        memcpy(data40, data + 40, 40);
+        secp256k1_sha256_write(&hash_ctx, &sha256_two, data40, 40);
+        secp256k1_sha256_finalize(&hash_ctx, &sha256_two, out_two);
+
+        CHECK(secp256k1_memcmp_var(out_one, out_two, 32) == 0);
+    }
+
+    {   /* 3) Writing multiple consecutive full blocks in one write (128 bytes) */
+        unsigned char data[128];
+        unsigned char i;
+        for (i = 0; i < 128; i++) data[i] = i;
+
+        secp256k1_sha256_initialize(&sha256_one);
+        secp256k1_sha256_initialize(&sha256_two);
+
+        /* Single write of 128 bytes (two full 64-byte blocks) */
+        secp256k1_sha256_write(&hash_ctx, &sha256_one, data, 128);
+        secp256k1_sha256_finalize(&hash_ctx, &sha256_one, out_one);
+
+        /* Two separate writes of 64 bytes each */
+        secp256k1_sha256_write(&hash_ctx, &sha256_two, data, 64);
+        secp256k1_sha256_write(&hash_ctx, &sha256_two, data + 64, 64);
+        secp256k1_sha256_finalize(&hash_ctx, &sha256_two, out_two);
+
+        CHECK(secp256k1_memcmp_var(out_one, out_two, 32) == 0);
+    }
+
+    {   /* 4) Mixed small + large writes in sequence */
+        unsigned char data[150];
+        unsigned char i;
+        for (i = 0; i < 150; i++) data[i] = i;
+
+        secp256k1_sha256_initialize(&sha256_one);
+        secp256k1_sha256_initialize(&sha256_two);
+
+        /* Single write of 150 bytes */
+        secp256k1_sha256_write(&hash_ctx, &sha256_one, data, 150);
+        secp256k1_sha256_finalize(&hash_ctx, &sha256_one, out_one);
+
+        /* Split writes: 10, 64, 64, 12 bytes */
+        secp256k1_sha256_write(&hash_ctx, &sha256_two, data, 10);
+        secp256k1_sha256_write(&hash_ctx, &sha256_two, data + 10, 64);
+        secp256k1_sha256_write(&hash_ctx, &sha256_two, data + 74, 64);
+        secp256k1_sha256_write(&hash_ctx, &sha256_two, data + 138, 12);
+        secp256k1_sha256_finalize(&hash_ctx, &sha256_two, out_two);
+
+        CHECK(secp256k1_memcmp_var(out_one, out_two, 32) == 0);
+    }
+}
+
 static void run_ctz_tests(void) {
     static const uint32_t b32[] = {1, 0xffffffff, 0x5e56968f, 0xe0d63129};
     static const uint64_t b64[] = {1, 0xffffffffffffffff, 0xbcd02462139b3fc3, 0x98b5f80c769693ef};
@@ -454,6 +595,7 @@ static void run_ctz_tests(void) {
 /***** HASH TESTS *****/
 
 static void run_sha256_known_output_tests(void) {
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
     static const char *inputs[] = {
         "", "abc", "message digest", "secure hash algorithm", "SHA256 is considered to be safe",
         "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq",
@@ -489,10 +631,10 @@ static void run_sha256_known_output_tests(void) {
         j = repeat[i];
         secp256k1_sha256_initialize(&hasher);
         while (j > 0) {
-            secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
+            secp256k1_sha256_write(hash_ctx, &hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
             j--;
         }
-        secp256k1_sha256_finalize(&hasher, out);
+        secp256k1_sha256_finalize(hash_ctx, &hasher, out);
         CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
         /* 2. Run: split the input bytestrings randomly before writing */
         if (strlen(inputs[i]) > 0) {
@@ -500,11 +642,11 @@ static void run_sha256_known_output_tests(void) {
             secp256k1_sha256_initialize(&hasher);
             j = repeat[i];
             while (j > 0) {
-                secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
-                secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
+                secp256k1_sha256_write(hash_ctx, &hasher, (const unsigned char*)(inputs[i]), split);
+                secp256k1_sha256_write(hash_ctx, &hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
                 j--;
             }
-            secp256k1_sha256_finalize(&hasher, out);
+            secp256k1_sha256_finalize(hash_ctx, &hasher, out);
             CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
         }
     }
@@ -602,12 +744,13 @@ static void run_sha256_counter_tests(void) {
         {0x2c, 0xf3, 0xa9, 0xf6, 0x15, 0x25, 0x80, 0x70, 0x76, 0x99, 0x7d, 0xf1, 0xc3, 0x2f, 0xa3, 0x31, 0xff, 0x92, 0x35, 0x2e, 0x8d, 0x04, 0x13, 0x33, 0xd8, 0x0d, 0xdb, 0x4a, 0xf6, 0x8c, 0x03, 0x34},
         {0xec, 0x12, 0x24, 0x9f, 0x35, 0xa4, 0x29, 0x8b, 0x9e, 0x4a, 0x95, 0xf8, 0x61, 0xaf, 0x61, 0xc5, 0x66, 0x55, 0x3e, 0x3f, 0x2a, 0x98, 0xea, 0x71, 0x16, 0x6b, 0x1c, 0xd9, 0xe4, 0x09, 0xd2, 0x8e},
     };
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
     unsigned int i;
     for (i = 0; i < sizeof(midstates)/sizeof(midstates[0]); i++) {
         unsigned char out[32];
         secp256k1_sha256 hasher = midstates[i];
-        secp256k1_sha256_write(&hasher, (const unsigned char*)input, strlen(input));
-        secp256k1_sha256_finalize(&hasher, out);
+        secp256k1_sha256_write(hash_ctx, &hasher, (const unsigned char*)input, strlen(input));
+        secp256k1_sha256_finalize(hash_ctx, &hasher, out);
         CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
     }
 }
@@ -624,9 +767,9 @@ static void test_sha256_eq(const secp256k1_sha256 *sha1, const secp256k1_sha256
 }
 /* Convenience function for using test_sha256_eq to verify the correctness of a
  * tagged hash midstate. This function is used by some module tests. */
-static void test_sha256_tag_midstate(secp256k1_sha256 *sha_tagged, const unsigned char *tag, size_t taglen) {
+static void test_sha256_tag_midstate(const secp256k1_hash_ctx *hash_ctx, secp256k1_sha256 *sha_tagged, const unsigned char *tag, size_t taglen) {
     secp256k1_sha256 sha;
-    secp256k1_sha256_initialize_tagged(&sha, tag, taglen);
+    secp256k1_sha256_initialize_tagged(hash_ctx, &sha, tag, taglen);
     test_sha256_eq(&sha, sha_tagged);
 }
 
@@ -656,19 +799,20 @@ static void run_hmac_sha256_tests(void) {
         {0x9b, 0x09, 0xff, 0xa7, 0x1b, 0x94, 0x2f, 0xcb, 0x27, 0x63, 0x5f, 0xbc, 0xd5, 0xb0, 0xe9, 0x44, 0xbf, 0xdc, 0x63, 0x64, 0x4f, 0x07, 0x13, 0x93, 0x8a, 0x7f, 0x51, 0x53, 0x5c, 0x3a, 0x35, 0xe2}
     };
     int i;
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
     for (i = 0; i < 6; i++) {
         secp256k1_hmac_sha256 hasher;
         unsigned char out[32];
-        secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
-        secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
-        secp256k1_hmac_sha256_finalize(&hasher, out);
+        secp256k1_hmac_sha256_initialize(hash_ctx, &hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
+        secp256k1_hmac_sha256_write(hash_ctx, &hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
+        secp256k1_hmac_sha256_finalize(hash_ctx, &hasher, out);
         CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
         if (strlen(inputs[i]) > 0) {
             int split = testrand_int(strlen(inputs[i]));
-            secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
-            secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
-            secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
-            secp256k1_hmac_sha256_finalize(&hasher, out);
+            secp256k1_hmac_sha256_initialize(hash_ctx, &hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
+            secp256k1_hmac_sha256_write(hash_ctx, &hasher, (const unsigned char*)(inputs[i]), split);
+            secp256k1_hmac_sha256_write(hash_ctx, &hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
+            secp256k1_hmac_sha256_finalize(hash_ctx, &hasher, out);
             CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
         }
     }
@@ -689,27 +833,28 @@ static void run_rfc6979_hmac_sha256_tests(void) {
         {0x75, 0x97, 0x88, 0x7c, 0xbd, 0x76, 0x32, 0x1f, 0x32, 0xe3, 0x04, 0x40, 0x67, 0x9a, 0x22, 0xcf, 0x7f, 0x8d, 0x9d, 0x2e, 0xac, 0x39, 0x0e, 0x58, 0x1f, 0xea, 0x09, 0x1c, 0xe2, 0x02, 0xba, 0x94}
     };
 
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
     secp256k1_rfc6979_hmac_sha256 rng;
     unsigned char out[32];
     int i;
 
-    secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 64);
+    secp256k1_rfc6979_hmac_sha256_initialize(hash_ctx, &rng, key1, 64);
     for (i = 0; i < 3; i++) {
-        secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
+        secp256k1_rfc6979_hmac_sha256_generate(hash_ctx, &rng, out, 32);
         CHECK(secp256k1_memcmp_var(out, out1[i], 32) == 0);
     }
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 
-    secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 65);
+    secp256k1_rfc6979_hmac_sha256_initialize(hash_ctx, &rng, key1, 65);
     for (i = 0; i < 3; i++) {
-        secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
+        secp256k1_rfc6979_hmac_sha256_generate(hash_ctx, &rng, out, 32);
         CHECK(secp256k1_memcmp_var(out, out1[i], 32) != 0);
     }
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 
-    secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 64);
+    secp256k1_rfc6979_hmac_sha256_initialize(hash_ctx, &rng, key2, 64);
     for (i = 0; i < 3; i++) {
-        secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
+        secp256k1_rfc6979_hmac_sha256_generate(hash_ctx, &rng, out, 32);
         CHECK(secp256k1_memcmp_var(out, out2[i], 32) == 0);
     }
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
@@ -746,10 +891,11 @@ static void run_sha256_initialize_midstate_tests(void) {
         0xa9ec59eaul, 0x9b4c2ffful, 0x400821e2ul, 0x0dcf3847ul,
         0xbe7ea179ul, 0xa5772bdcul, 0x7d29bfe3ul, 0xa486b855ul
     };
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
     secp256k1_sha256 sha;
 
     secp256k1_sha256_initialize_midstate(&sha, 64, midstate);
-    test_sha256_tag_midstate(&sha, tag, sizeof(tag) - 1);
+    test_sha256_tag_midstate(hash_ctx, &sha, tag, sizeof(tag) - 1);
 }
 
 /***** MODINV TESTS *****/
@@ -5501,11 +5647,11 @@ static void test_ecmult_accumulate(secp256k1_sha256* acc, const secp256k1_scalar
     if (secp256k1_ge_is_infinity(&r)) {
         /* Store infinity as 0x00 */
         const unsigned char zerobyte[1] = {0};
-        secp256k1_sha256_write(acc, zerobyte, 1);
+        secp256k1_sha256_write(secp256k1_get_hash_context(CTX), acc, zerobyte, 1);
     } else {
         /* Store other points using their uncompressed serialization. */
         secp256k1_eckey_pubkey_serialize65(&r, bytes);
-        secp256k1_sha256_write(acc, bytes, sizeof(bytes));
+        secp256k1_sha256_write(secp256k1_get_hash_context(CTX), acc, bytes, sizeof(bytes));
     }
 }
 
@@ -5547,7 +5693,7 @@ static void test_ecmult_constants_2bit(void) {
             test_ecmult_accumulate(&acc, &x, scratch);
         }
     }
-    secp256k1_sha256_finalize(&acc, b32);
+    secp256k1_sha256_finalize(secp256k1_get_hash_context(CTX), &acc, b32);
     CHECK(secp256k1_memcmp_var(b32, expected32, 32) == 0);
 
     secp256k1_scratch_space_destroy(CTX, scratch);
@@ -5566,6 +5712,7 @@ static void test_ecmult_constants_sha(uint32_t prefix, size_t iter, const unsign
     unsigned char b32[32];
     unsigned char inp[6];
     size_t i;
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
     secp256k1_scratch_space *scratch = secp256k1_scratch_space_create(CTX, 65536);
 
     inp[0] = prefix & 0xFF;
@@ -5585,12 +5732,12 @@ static void test_ecmult_constants_sha(uint32_t prefix, size_t iter, const unsign
         inp[4] = i & 0xff;
         inp[5] = (i >> 8) & 0xff;
         secp256k1_sha256_initialize(&gen);
-        secp256k1_sha256_write(&gen, inp, sizeof(inp));
-        secp256k1_sha256_finalize(&gen, b32);
+        secp256k1_sha256_write(hash_ctx, &gen, inp, sizeof(inp));
+        secp256k1_sha256_finalize(hash_ctx, &gen, b32);
         secp256k1_scalar_set_b32(&x, b32, NULL);
         test_ecmult_accumulate(&acc, &x, scratch);
     }
-    secp256k1_sha256_finalize(&acc, b32);
+    secp256k1_sha256_finalize(hash_ctx, &acc, b32);
     CHECK(secp256k1_memcmp_var(b32, expected32, 32) == 0);
 
     secp256k1_scratch_space_destroy(CTX, scratch);
@@ -5644,7 +5791,7 @@ static void test_ecmult_gen_blind(void) {
     testrand256(seed32);
     b = CTX->ecmult_gen_ctx.scalar_offset;
     p = CTX->ecmult_gen_ctx.ge_offset;
-    secp256k1_ecmult_gen_blind(&CTX->ecmult_gen_ctx, seed32);
+    secp256k1_ecmult_gen_blind(&CTX->ecmult_gen_ctx, secp256k1_get_hash_context(CTX), seed32);
     CHECK(!secp256k1_scalar_eq(&b, &CTX->ecmult_gen_ctx.scalar_offset));
     secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &pgej2, &key);
     CHECK(!gej_xyz_equals_gej(&pgej, &pgej2));
@@ -5657,10 +5804,10 @@ static void test_ecmult_gen_blind_reset(void) {
     /* Test ecmult_gen() blinding reset and confirm that the blinding is consistent. */
     secp256k1_scalar b;
     secp256k1_ge p1, p2;
-    secp256k1_ecmult_gen_blind(&CTX->ecmult_gen_ctx, 0);
+    secp256k1_ecmult_gen_blind(&CTX->ecmult_gen_ctx, secp256k1_get_hash_context(CTX), 0);
     b = CTX->ecmult_gen_ctx.scalar_offset;
     p1 = CTX->ecmult_gen_ctx.ge_offset;
-    secp256k1_ecmult_gen_blind(&CTX->ecmult_gen_ctx, 0);
+    secp256k1_ecmult_gen_blind(&CTX->ecmult_gen_ctx, secp256k1_get_hash_context(CTX), 0);
     CHECK(secp256k1_scalar_eq(&b, &CTX->ecmult_gen_ctx.scalar_offset));
     p2 = CTX->ecmult_gen_ctx.ge_offset;
     CHECK(secp256k1_ge_eq_var(&p1, &p2));
@@ -7122,7 +7269,7 @@ static void run_ecdsa_der_parse(void) {
 }
 
 /* Tests several edge cases. */
-static void test_ecdsa_edge_cases(void) {
+static void run_ecdsa_edge_cases(void) {
     int t;
     secp256k1_ecdsa_signature sig;
 
@@ -7455,8 +7602,25 @@ static void test_ecdsa_edge_cases(void) {
     }
 }
 
-static void run_ecdsa_edge_cases(void) {
-    test_ecdsa_edge_cases();
+DEFINE_SHA256_TRANSFORM_PROBE(sha256_ecdsa)
+static void ecdsa_ctx_sha256(void) {
+    /* Check ctx-provided SHA256 compression override takes effect */
+    secp256k1_context *ctx = secp256k1_context_clone(CTX);
+    secp256k1_ecdsa_signature out_default, out_custom;
+    unsigned char sk[32] = {1}, msg32[32] = {1};
+
+    /* Default behavior. No ctx-provided SHA256 compression */
+    CHECK(secp256k1_ecdsa_sign(ctx, &out_default, msg32, sk, NULL, NULL));
+    CHECK(!sha256_ecdsa_called);
+
+    /* Override SHA256 compression directly, bypassing the ctx setter sanity checks */
+    ctx->hash_ctx.fn_sha256_compression = sha256_ecdsa;
+    CHECK(secp256k1_ecdsa_sign(ctx, &out_custom, msg32, sk, NULL, NULL));
+    CHECK(sha256_ecdsa_called);
+    /* Outputs must differ if custom compression was used */
+    CHECK(secp256k1_memcmp_var(out_default.data, out_custom.data, 64) != 0);
+
+    secp256k1_context_destroy(ctx);
 }
 
 /** Wycheproof tests
@@ -7467,6 +7631,7 @@ static void test_ecdsa_wycheproof(void) {
     #include "wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h"
 
     int t;
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
     for (t = 0; t < SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS; t++) {
         secp256k1_ecdsa_signature signature;
         secp256k1_sha256 hasher;
@@ -7481,8 +7646,8 @@ static void test_ecdsa_wycheproof(void) {
 
         secp256k1_sha256_initialize(&hasher);
         msg = &wycheproof_ecdsa_messages[testvectors[t].msg_offset];
-        secp256k1_sha256_write(&hasher, msg, testvectors[t].msg_len);
-        secp256k1_sha256_finalize(&hasher, out);
+        secp256k1_sha256_write(hash_ctx, &hasher, msg, testvectors[t].msg_len);
+        secp256k1_sha256_finalize(hash_ctx, &hasher, out);
 
         sig = &wycheproof_ecdsa_signatures[testvectors[t].sig_offset];
         if (secp256k1_ecdsa_signature_parse_der(CTX, &signature, sig, testvectors[t].sig_len) == 1) {
@@ -7746,6 +7911,8 @@ static const struct tf_test_entry tests_general[] = {
     CASE(all_static_context_tests),
     CASE(deprecated_context_flags_test),
     CASE(scratch_tests),
+    CASE(plug_sha256_compression_tests),
+    CASE(sha256_multi_block_compression_tests),
 };
 
 static const struct tf_test_entry tests_integer[] = {
@@ -7816,6 +7983,7 @@ static const struct tf_test_entry tests_ecdsa[] = {
     CASE(ecdsa_end_to_end),
     CASE(ecdsa_edge_cases),
     CASE(ecdsa_wycheproof),
+    CASE1(ecdsa_ctx_sha256),
 };
 
 static const struct tf_test_entry tests_utils[] = {
diff --git a/src/testutil.h b/src/testutil.h
index 93ee3d58b5..8fa69a02c9 100644
--- a/src/testutil.h
+++ b/src/testutil.h
@@ -11,6 +11,15 @@
 #include "testrand.h"
 #include "util.h"
 
+/* Helper for when we need to check that the ctx-provided sha256 compression was called */
+#define DEFINE_SHA256_TRANSFORM_PROBE(name)                                     \
+    static int name##_called = 0;                                               \
+    static void name(uint32_t *s, const unsigned char *msg, size_t rounds) {    \
+        name##_called = 1;                                                      \
+        secp256k1_sha256_transform(s, msg, rounds);                             \
+        s[0] ^= 0xdeadbeef; /* intentional perturbation for testing */          \
+    }
+
 /* group order of the secp256k1 curve in 32-byte big endian representation */
 static const unsigned char secp256k1_group_order_bytes[32] = {
     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,