Minor speed-up

README.md

@@ -49,13 +49,13 @@ On an Intel Core i7 4790K @ 4.0GHz I'm getting the following performance:
 
 ```
             siglen    keygen   keygen/s      sign     sign/s    verify   verify/s
-  NIST192p:     48   0.03183s     31.42   0.01127s     88.70   0.02253s     44.39
-  NIST224p:     56   0.04304s     23.24   0.01548s     64.59   0.03122s     32.03
-  NIST256p:     64   0.05720s     17.48   0.02055s     48.67   0.04075s     24.54
-  NIST384p:     96   0.13216s      7.57   0.04696s     21.29   0.09400s     10.64
-  NIST521p:    132   0.25805s      3.88   0.09329s     10.72   0.18841s      5.31
- SECP256k1:     64   0.05677s     17.61   0.02073s     48.23   0.04067s     24.59
-```
+  NIST192p:     48   0.01586s     63.05   0.00853s    117.26   0.01624s     61.58
+  NIST224p:     56   0.02153s     46.46   0.01145s     87.36   0.02307s     43.35
+  NIST256p:     64   0.02850s     35.09   0.01500s     66.65   0.02925s     34.19
+  NIST384p:     96   0.06664s     15.01   0.03512s     28.48   0.06887s     14.52
+  NIST521p:    132   0.13048s      7.66   0.07050s     14.18   0.13673s      7.31
+ SECP256k1:     64   0.02809s     35.60   0.01531s     65.32   0.03113s     32.12
+ ```
 
 For comparison, a highly optimised implementation (including curve-specific
 assemply) like OpenSSL provides following performance numbers on the same

src/ecdsa/keys.py

@@ -708,10 +708,10 @@ def from_secret_exponent(cls, secexp, curve=NIST192p, hashfunc=sha1):
                 "Invalid value for secexp, expected integer between 1 and {0}"
                 .format(n))
         pubkey_point = curve.generator * secexp
-        pubkey = ecdsa.Public_key(curve.generator, pubkey_point)
-        pubkey.order = n
-        self.verifying_key = VerifyingKey.from_public_point(pubkey_point, curve,
+        self.verifying_key = VerifyingKey.from_public_point(pubkey_point,
+                                                            curve,
                                                             hashfunc)
+        pubkey = self.verifying_key.pubkey
         self.privkey = ecdsa.Private_key(pubkey, secexp)
         self.privkey.order = n
         return self

src/ecdsa/numbertheory.py

@@ -202,27 +202,18 @@ def square_root_mod_prime(a, p):
 
 
 def inverse_mod(a, m):
-  """Inverse of a mod m."""
+    """Inverse of a mod m."""
 
-  if a < 0 or m <= a:
-    a = a % m
+    if a == 0:
+        return 0
 
-  # From Ferguson and Schneier, roughly:
+    lm, hm = 1, 0
+    low, high = a % m, m
+    while low > 1:
+        r = high // low
+        lm, low, hm, high = hm - lm * r, high - low * r, lm, low
 
-  c, d = a, m
-  uc, vc, ud, vd = 1, 0, 0, 1
-  while c != 0:
-    q, c, d = divmod(d, c) + (c,)
-    uc, vc, ud, vd = ud - q * uc, vd - q * vc, uc, vc
-
-  # At this point, d is the GCD, and ud*a+vd*m = d.
-  # If d == 1, this means that ud is a inverse.
-
-  assert d == 1
-  if ud > 0:
-    return ud
-  else:
-    return ud + m
+    return lm % m
 
 
 def gcd2(a, b):

src/ecdsa/test_numbertheory.py

@@ -259,3 +259,6 @@ def test_inverse_mod(self, nums):
 
         assert 0 < inv < mod
         assert num * inv % mod == 1
+
+    def test_inverse_mod_with_zero(self):
+        assert 0 == inverse_mod(0, 11)