Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies
Copyright 2011-2016 Luca De Feo http://defeo.lu/.
This software implements the cryptosystem described in
D. Jao and L. De Feo, Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. Post-Quantum Cryptography, Nov 2011, Taipei, Taiwan. Springer, LNCS 7071, pp. 19-34, 2011.
L. De Feo, D. Jao and J. Plût, Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. Journal of Mathematical Cryptology, 8(3), pp. 209-247. De Gruyter, 2014.
Just clone or download this repo.
You will need a recent version of Sage and a C compiler. This version has been tested with Sage 6.10 and gcc 5.2.1.
In a Sage shell type
Some predefined key sizes are stored in a string-indexed dictionary
called 'parameters'. Read
pqcrypto11.sage to find them out.
Public data for a cryptosystem are generated via a call to
ss_isogeny_gen. For example, to obtain parameters relative to a
40-bit prime, type
sage: set_verbose(1) sage: pdata = ss_isogeny_gen(**parameters['2-3-40'])
The key exchange is performed by
sage: ss_isogeny_exchange(*pdata) sage: set_verbose(0)
ss_isogeny runs both previous functions in one. The
previous sequence of commands is equivalent to
sage: ss_isogeny('2-3-40', verbose=1)
Additional parameters can be passed to these functions, read
NOTE: The file
gfp2.c can be compiled as a standalone program
gcc -lgmp gfp2.c
Then it can be run to gather estimates on the running times of
doublings, triplings, 2 and 3-isogeny evaluations. These data can be
used to tune up (via the dictionary "weights" in
the key exchange algorithm.
Many thanks to those who have helped in testing and fixing this software.
- David Jao,
- Jérôme Plût,
- Erik Nellessen.
- Adarsh Saraf,
- Miha Marolt @miham