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:
```python
>>> 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:
```python
>>> 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.

Files for tinyec, version 0.3.1
Filename, size File type Python version Upload date Hashes
Filename, size tinyec-0.3.1.tar.gz (23.9 kB) File type Source Python version None Upload date Hashes View

Supported by

Pingdom Pingdom Monitoring Google Google Object Storage and Download Analytics Sentry Sentry Error logging AWS AWS Cloud computing DataDog DataDog Monitoring Fastly Fastly CDN DigiCert DigiCert EV certificate StatusPage StatusPage Status page