ecpy

Elliptic-Curve Cryptography Library (Implemented by Python)

Features

• Calculation between elliptic curve points
  • Elliptic curve: y^2 = x^3 + ax + b over Field K (char(K) != 2, 3).
  • You can choose K from below:
    • Complex Field, Rational Field, FiniteField and Extended Finite Field(Irreducible polynomial: x^2 + 1 or x^2 + x + 1)
• Weil/Tate Pairing
  • Distortion Map, symmetric-pairing functions
• SSSA-Attack Implementation
  • Sample (CTF Challenge Writeup)
• Example Applications
  • example/id_based_encryption.py: Implementation of Boneh-Franklin's Identity-based Encryption Scheme
  • example/boneh_lynn_shacham_short_signature.py: Implementation of Boneh-Lynn-Shacham's Short Signature Scheme
  • example/ecdsa.py: Implementation of ECDSA Signature Scheme

Setup

> git clone https://github.com/elliptic-shiho/ecpy && cd ecpy
> pip install --upgrade .

Require modules:

• six

If installed following modules, ecpy uses that.

• gmpy2
• primefac or primefac-fork

Setup with Native modules

ecpy has a native module. If you want to speed-up ecpy, you can use that.

> cd ecpy/cpp
> make
> sudo make install

The description is here: cpp/README.md

Speed

See bench_pairing.py .

Sat Jan 28 03:55:47 JST 2017 ~/prog/lab/mathematics/ecpy 100%
> time python scripts/bench_pairing.py
[+] found gmpy! use gmpy.is_prime
[+] Found native module!
Point (25 : 5635866983L + 11271733966Lw : 1) on Elliptic Curve y^2 = x^3 + 1 over ExtendedFiniteField(13208557577, "x^2+x+1")
[+] Weil Pairing: 
weil: 14744.50 usec/pass
weil: 14842.80 usec/pass
weil: 14626.05 usec/pass
weil: 14773.50 usec/pass
weil: 14582.25 usec/pass
weil: 14560.95 usec/pass
weil: 14622.40 usec/pass
weil: 15073.19 usec/pass
weil: 14874.60 usec/pass
weil: 14695.20 usec/pass
[+] Tate Pairing: 
tate: 3079.89 usec/pass
tate: 3083.21 usec/pass
tate: 3079.10 usec/pass
tate: 3072.70 usec/pass
tate: 3069.81 usec/pass
tate: 3089.30 usec/pass
tate: 3077.90 usec/pass
tate: 3116.00 usec/pass
tate: 3095.35 usec/pass
tate: 3193.65 usec/pass
================================================================
weil: 14739.54 usec/pass
tate: 3095.69 usec/pass

real    0m4.293s
user    0m4.256s
sys     0m0.012s

Special Thanks

Cybozu Labs Youth (5th, 6th) - http://labs.cybozu.co.jp/youth.html

License

This software released under MIT License. Please see /LICENSE.