Skip to main content

A tiny library to perform arithmetic operations on elliptic curves in pure python

Project description

tinyec

A tiny library to perform arithmetic operations on elliptic curves in pure python. No dependencies.

This is not a library suitable for production. It is useful for security professionals to understand the inner workings of EC, and be able to play with pre-defined curves.

installation

pip install tinyec

usage

There are 2 main classes:

  • Curve(), which describes an elliptic curve in a finite field
  • Point(), which describes a point belonging to an EC

Warning Calculation on points outside the curve are allowed. They will only raise a warning.

working on existing curves

Example use on the NIST routine samples => https://www.nsa.gov/ia/_files/nist-routines.pdf:

>>> import tinyec.ec as ec
>>> import tinyec.registry as reg
>>> c = reg.get_curve("secp192r1")
>>> s = ec.Point(c, 0xd458e7d127ae671b0c330266d246769353a012073e97acf8, 0x325930500d851f336bddc050cf7fb11b5673a1645086df3b)
>>> t = ec.Point(c, 0xf22c4395213e9ebe67ddecdd87fdbd01be16fb059b9753a4, 0x264424096af2b3597796db48f8dfb41fa9cecc97691a9c79)
>>> r = s + t
>>> r
(1787070900316344022479363585363935252075532448940096815760, 1583034776780933252095415958625802984888372377603917916747) on secp192r1 => y^2 = x^3 + 6277101735386680763835789423207666416083908700390324961276x + 2455155546008943817740293915197451784769108058161191238065 
(mod 6277101735386680763835789423207666416083908700390324961279)
>>> hex(r.x)
'0x48e1e4096b9b8e5ca9d0f1f077b8abf58e843894de4d0290L'
>>> hex(r.y)
'0x408fa77c797cd7dbfb16aa48a3648d3d63c94117d7b6aa4bL'
>>> r = s - t
>>> r
(6193438478050209507979672067809269724375390027440522152494, 226636415264149817017346905052752138772359775362461041003) on secp192r1 => y^2 = x^3 + 6277101735386680763835789423207666416083908700390324961276x + 2455155546008943817740293915197451784769108058161191238065 (
mod 6277101735386680763835789423207666416083908700390324961279)
>>> hex(r.x)
'0xfc9683cc5abfb4fe0cc8cc3bc9f61eabc4688f11e9f64a2eL'
>>> hex(r.y)
'0x93e31d00fb78269732b1bd2a73c23cdd31745d0523d816bL'
>>> r = 2 * s
>>> r
(1195895923065450997501505402941681398272052708885411031394, 340030206158745947396451508065335698335058477174385838543) on secp192r1 => y^2 = x^3 + 6277101735386680763835789423207666416083908700390324961276x + 2455155546008943817740293915197451784769108058161191238065 (
mod 6277101735386680763835789423207666416083908700390324961279)
>>> hex(r.x)
'0x30c5bc6b8c7da25354b373dc14dd8a0eba42d25a3f6e6962L'
>>> hex(r.y)
'0xdde14bc4249a721c407aedbf011e2ddbbcb2968c9d889cfL'
>>> d = 0xa78a236d60baec0c5dd41b33a542463a8255391af64c74ee
>>> r = d * s
>>> hex(r.x)
'0x1faee4205a4f669d2d0a8f25e3bcec9a62a6952965bf6d31L'
>>> hex(r.y)
'0x5ff2cdfa508a2581892367087c696f179e7a4d7e8260fb06L'
>>> e = 0xc4be3d53ec3089e71e4de8ceab7cce889bc393cd85b972bc
>>> r = d * s + e * t
>>> r
(39786866609245082371772779541859439402855864496422607838, 547967566579883709478937502153554894699060378424501614148) on secp192r1 => y^2 = x^3 + 6277101735386680763835789423207666416083908700390324961276x + 2455155546008943817740293915197451784769108058161191238065 (mo
d 6277101735386680763835789423207666416083908700390324961279)
>>> hex(r.x)
'0x19f64eed8fa9b72b7dfea82c17c9bfa60ecb9e1778b5bdeL'
>>> hex(r.y)
'0x16590c5fcd8655fa4ced33fb800e2a7e3c61f35d83503644L'

working on custom curves

If needed, you can also work on your own curves. Here we take a a prime field 97, with a generator point (1, 2), an order 5 and a cofactor of 1:

>>> import tinyec.ec as ec
>>> field = ec.SubGroup(97, (1, 2), 5, 1)
>>> curve = ec.Curve(2, 3, field)
tinyec/ec.py:115: UserWarning: Point (1, 2) is not on curve "undefined" => y^2 = x^3 + 2x + 3 (mod 97)
  warnings.warn("Point (%d, %d) is not on curve %s" % (self.x, self.y, self.curve))
>>> # Warning is generated because the generator point does not belong to the curve
>>> p1 = ec.Point(curve, -5, 3)
>>> p1.on_curve
False
>>> p2 = ec.Point(curve, 22, 5)
>>> p2.on_curve
True
>>> print(p1 + p2)
(18, 42) off "undefined" => y^2 = x^3 + 2x + 3 (mod 97)

Project details


Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

tinyec-0.4.0.tar.gz (24.1 kB view hashes)

Uploaded Source

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page