Turbocharge by using Jacobi representation, 2-ary NAF and precomputation #127

tomato42 · 2019-10-06T23:07:23Z

Use Jacobi representation for internal calculations. Precompute point doublings for curve generators and public keys. Use 2-ary Non-Adjacent Form for multiplication (both for regular and precomputed points).

ver 0.14.1:

                  siglen    keygen   keygen/s      sign     sign/s    verify   verify/s
        NIST192p:     48   0.01550s     64.50   0.00826s    121.04   0.01605s     62.32
        NIST224p:     56   0.02100s     47.61   0.01131s     88.44   0.02281s     43.85
        NIST256p:     64   0.02828s     35.36   0.01514s     66.04   0.02988s     33.47
        NIST384p:     96   0.06678s     14.97   0.03536s     28.28   0.07114s     14.06
        NIST521p:    132   0.13108s      7.63   0.07089s     14.11   0.13921s      7.18
       SECP256k1:     64   0.02723s     36.72   0.01472s     67.93   0.02901s     34.47

this branch:

                  siglen    keygen   keygen/s      sign     sign/s    verify   verify/s
        NIST192p:     48   0.00033s   3062.43   0.00036s   2748.08   0.00062s   1605.66
        NIST224p:     56   0.00041s   2424.07   0.00046s   2196.71   0.00083s   1205.81
        NIST256p:     64   0.00053s   1892.05   0.00058s   1735.23   0.00106s    944.82
        NIST384p:     96   0.00110s    904.98   0.00118s    847.82   0.00217s    460.26
        NIST521p:    132   0.00234s    428.24   0.00245s    408.54   0.00443s    225.95
       SECP256k1:     64   0.00053s   1891.93   0.00058s   1734.46   0.00109s    913.35
 BRAINPOOLP160r1:     40   0.00025s   3982.49   0.00029s   3490.15   0.00053s   1878.51
 BRAINPOOLP192r1:     48   0.00032s   3086.07   0.00036s   2761.68   0.00063s   1578.22
 BRAINPOOLP224r1:     56   0.00041s   2412.41   0.00046s   2185.52   0.00076s   1311.65
 BRAINPOOLP256r1:     64   0.00054s   1866.84   0.00058s   1719.45   0.00110s    906.85
 BRAINPOOLP320r1:     80   0.00077s   1306.97   0.00083s   1201.59   0.00158s    632.82
 BRAINPOOLP384r1:     96   0.00112s    892.44   0.00119s    841.48   0.00229s    436.71
 BRAINPOOLP512r1:    128   0.00214s    467.05   0.00226s    441.64   0.00422s    237.13

for comparison, OpenSSL on same machine achieves:

                              sign    verify    sign/s verify/s
 256 bits ecdsa (nistp256)   0.0000s   0.0001s  45320.1  14171.3
 384 bits ecdsa (nistp384)   0.0008s   0.0006s   1259.5   1653.3
 256 bits ecdsa (brainpoolP256r1)   0.0003s   0.0003s   2983.5   3333.2
 384 bits ecdsa (brainpoolP384r1)   0.0008s   0.0007s   1258.8   1528.1
 512 bits ecdsa (brainpoolP512r1)   0.0015s   0.0012s    675.1    860.1

(OpenSSL has hand-optimised assembly with AVX for nistp256/NIST256p curve)

depends on #126, fixes #94 (while there are more efficient algorithms still, being 3.6 times slower than generic C implementation for verification and 33% slower for signing is acceptable to me 😄 )

or when gmpy2 is used, being like 7% slower for verify and more than 2 times faster for signing 😁

                  siglen    keygen   keygen/s      sign     sign/s    verify   verify/s
        NIST192p:     48   0.00016s   6180.12   0.00017s   5846.30   0.00033s   3029.51
        NIST224p:     56   0.00021s   4861.86   0.00021s   4662.63   0.00042s   2366.47
        NIST256p:     64   0.00023s   4343.93   0.00024s   4152.79   0.00047s   2148.83
        NIST384p:     96   0.00040s   2507.97   0.00041s   2435.99   0.00079s   1260.01
        NIST521p:    132   0.00088s   1135.13   0.00089s   1121.94   0.00139s    721.07
       SECP256k1:     64   0.00023s   4360.83   0.00024s   4147.61   0.00044s   2254.53
 BRAINPOOLP160r1:     40   0.00014s   7261.37   0.00015s   6824.47   0.00031s   3248.21
 BRAINPOOLP192r1:     48   0.00016s   6219.18   0.00017s   5862.93   0.00034s   2933.74
 BRAINPOOLP224r1:     56   0.00021s   4876.48   0.00022s   4640.40   0.00041s   2413.48
 BRAINPOOLP256r1:     64   0.00023s   4397.89   0.00024s   4178.48   0.00044s   2272.76
 BRAINPOOLP320r1:     80   0.00031s   3246.64   0.00032s   3138.38   0.00063s   1593.14
 BRAINPOOLP384r1:     96   0.00040s   2491.04   0.00041s   2421.67   0.00079s   1262.64
 BRAINPOOLP512r1:    128   0.00062s   1618.30   0.00063s   1577.42   0.00125s    799.29

To do:

rename the "classical" representation to "affine"
merge fixup commits to earlier ones
add documentation
test coverage
make sure that all the expensive test cases use the new PointJacobi implementation
use jacobi representation for Brainpool curves too
avoid constructing PointJacobi objects over and over when multiplying
add to travis tests with oldest gmpy and gmpy2 that work for us, specify them in setup.py

coveralls · 2019-10-06T23:16:29Z

Coverage increased (+1.5%) to 96.233% when pulling a67da69 on tomato42:jacobi into 34864b1 on warner:master.

since inverse_mod is very computationally expensive (around 100 multiplications) it's cheaper to just bring the fractions to the same denominator

when loading public keys, perform the point verification just once when loading private keys, do not verify the derived public point

make all test cases execute in less than 0.3s on i7 4790K

don't treat the universal code for point addition specially

since this avoids creating new PointJacobi after every addition it makes the signing about 20% faster

looks like few merges/rebases didn't go exactly as planned and ended up duplicating test code, remove it

since some branching in hypothesis strategies and in handling different python, hypothesis, openssl and unittest versions is necessary, ignore them for branch coverage remove benchmarking code and dead code from test_pyecdsa.py (we have speed.py now) and exclude a disabled test case from coverage

the x and y needs to be on curve, so they need to be smaller than the curve's prime, not the base point order See Section 3.2.2.1 of SEC 1 v2

since multiplying a point by the order is farily expensive, skipping it (when safe to do so) greatly increases performance does not increase the speed.py numbers as point verification happens outside the signing and verifying operations

since on older distros like CentOS 6 there is python-gmpy but not python-gmpy2, support gmpy too

tomato42 added the feature functionality to be implemented label Oct 6, 2019

tomato42 self-assigned this Oct 6, 2019

tomato42 force-pushed the jacobi branch from 85574d5 to 7db74ba Compare October 6, 2019 23:16

tomato42 force-pushed the jacobi branch 2 times, most recently from cce7792 to ee9775b Compare October 10, 2019 23:31

tomato42 changed the title ~~Turbocharge by using Jacobi representation internally~~ Turbocharge by using Jacobi representation, 2-ary NAF and precomputation Oct 12, 2019

tomato42 added this to the someday/future milestone Oct 13, 2019

tomato42 force-pushed the jacobi branch from e8b709a to 7755356 Compare October 18, 2019 21:43

tomato42 changed the title ~~Turbocharge by using Jacobi representation, 2-ary NAF and precomputation~~ [WIP] Turbocharge by using Jacobi representation, 2-ary NAF and precomputation Oct 19, 2019

This was referenced Oct 27, 2019

better test coverage for internal modules #146

Merged

Minor speed-up #147

Merged

Add mutation testing to CI #156

Merged

Verify quality of test coverage #131

Open

tomato42 force-pushed the jacobi branch 3 times, most recently from e29976c to a8466ca Compare November 9, 2019 22:57

tomato42 force-pushed the jacobi branch 5 times, most recently from 77e7e69 to d3d9f07 Compare November 13, 2019 01:45

tomato42 changed the title ~~[WIP] Turbocharge by using Jacobi representation, 2-ary NAF and precomputation~~ Turbocharge by using Jacobi representation, 2-ary NAF and precomputation Nov 13, 2019

tomato42 modified the milestones: someday/future, v0.15 Nov 13, 2019

tomato42 force-pushed the jacobi branch 5 times, most recently from 072980a to c0eafc9 Compare November 23, 2019 15:30

tomato42 and others added 25 commits December 2, 2019 18:04

implement equality without inverse_mod

dae2f33

since inverse_mod is very computationally expensive (around 100 multiplications) it's cheaper to just bring the fractions to the same denominator

add ability to precompute for verification

08e3576

verify in one place, skip for self-created points

6c7099d

when loading public keys, perform the point verification just once when loading private keys, do not verify the derived public point

add method that does multiplication and addition of two points

191898c

use combined multiplication and addition in verification

304c522

use 2-ary NAF for multiplication with precomputation

90b3564

use 2-ary NAF for regular multiplication too

d60ec5e

point_is_valid: speed up with Jacobi

a96af14

speed up test suite

19962f1

make all test cases execute in less than 0.3s on i7 4790K

complete doc for PointJacobi

48040d7

faster double for scaled points

58eef88

move numeric code out of __add__

ab07a0c

don't treat the universal code for point addition specially

use tuples for calculation of double

d4c2387

use tuples for calculation of addition

b0084d9

use tuples for calculation of multiplication

272349f

since this avoids creating new PointJacobi after every addition it makes the signing about 20% faster

update README with info about the Jacobi code performance

6469c2e

remove duplicated test cases

7d9c556

looks like few merges/rebases didn't go exactly as planned and ended up duplicating test code, remove it

test_keys.py: fix typo in test case name

8aac4a4

Public_key: fix check for x and y size

b8fdfbe

the x and y needs to be on curve, so they need to be smaller than the curve's prime, not the base point order See Section 3.2.2.1 of SEC 1 v2

use curve cofactor for point verification

8ab416b

since multiplying a point by the order is farily expensive, skipping it (when safe to do so) greatly increases performance does not increase the speed.py numbers as point verification happens outside the signing and verifying operations

use gmp2 for faster arithmetic

f7910cf

be explicit about the optional dependency on gmpy2

4403ec3

also allow the older gmpy

b1568d4

since on older distros like CentOS 6 there is python-gmpy but not python-gmpy2, support gmpy too

ensure old versions of gmpy(2) work

a67da69

tomato42 force-pushed the jacobi branch from d884156 to a67da69 Compare December 2, 2019 19:11

tomato42 merged commit feecedd into tlsfuzzer:master Dec 2, 2019

tomato42 deleted the jacobi branch December 2, 2019 19:29

tomato42 mentioned this pull request Dec 2, 2019

Speed compare with python-ecdsa? AntonKueltz/fastecdsa#45

Open

tomato42 mentioned this pull request Dec 6, 2020

speed up instrumental, reenable test_malformed_sigs.py under it #222

Merged

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Turbocharge by using Jacobi representation, 2-ary NAF and precomputation #127

Turbocharge by using Jacobi representation, 2-ary NAF and precomputation #127

tomato42 commented Oct 6, 2019 •

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coveralls commented Oct 6, 2019 •

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Turbocharge by using Jacobi representation, 2-ary NAF and precomputation #127

Turbocharge by using Jacobi representation, 2-ary NAF and precomputation #127

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tomato42 commented Oct 6, 2019 • edited Loading

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