Description of the sage-code implementation

This sage code implements the SwiftEC and ElligatorSwift algorithms and contains scripts for generating the required precomputation parameters.

Example runs

Compute and benchmark a single encoding-decoding test with curve P256 sage enc_test.py -p P256

Compute and benchmark a single projective X-only encoding-decoding test with curve P256 sage Xenc_test.py -p P256

For curves with a=0, you must call enc_test_0.py and Xenc_test_0.py instead sage enc_test_0.py -p secp256k1 sage Xenc_test_0.py -p secp256k1

Compute and benchmark a single encoding-decoding test with a curve that requires the isogeny trick (never needed for a=0) sage encisog_test.py -p P25519

Generate the precomputation parameters for a new curve (both for a=0 and a!=0) sage generate_parameters.py -p P256 sage generate_parameters.py -p secp256k1

Test precomputation parameters (not implemented for a=0) sage param_test.py -p P256

Script for exhaustively counting the number of encoding preimages (only run this for less-than-15-bit primes) (not implemented for a=0) sage preimage_test.py -p P15

Adding new curves

To add a new curve E: x^3 + a*x + b over a prime field F_p, give it a name and enter p,a,b (one per line in this order, in decimal form) to the file curves/PRIME_NAME

You must then run sage generate_parameters -p PRIME_NAME.

Example for curve E: x^3 + 2*x + 7 over F_13,

echo 13\n2\n7 > curves/MyCurve
sage generate_parameters -p MyCurve
sage enc_test -p MyCurve

Additionally, when using the isogeny trick, add the corresponding objects to isogenies.py

Authors

1. Jorge Chávez-Saab jorge.saab@tii.ae,
2. Francisco Rodríguez-Henríquez francisco.rodriguez@tii.ae,
3. Mehdi Tibouchi mehdi.tibouchi@normalesup.org,