Paper 2014/274
A note on the construction of pairing-friendly elliptic curves for composite order protocols
Sorina Ionica and Malika Izabachène
Abstract
In pairing-based cryptography, the security of protocols using composite order groups relies on the difficulty of factoring a composite number $N$. Boneh~\etal~proposed the Cocks-Pinch method to construct ordinary pairing-friendly elliptic curves having a subgroup of composite order $N$. Displaying such a curve as a public parameter implies revealing a square root $s$ of the complex multiplication discriminant $-D$ modulo $N$. We exploit this information leak and the structure of the endomorphism ring of the curve to factor the RSA modulus, under certain conditions. Our conclusion is that the values of $s$ modulo each prime in the factorization of $N$ should be chosen as high entropy input parameters when running the Cocks-Pinch algorithm.
Metadata
- Available format(s)
-
PDF
- Publication info
- Published elsewhere. Minor revision. Balkan Cryptsec 2018
- Keywords
- composite order groupinteger factorizationelliptic curveendomorphismCoppersmith's algorithm
- Contact author(s)
- sorina ionica @ m4x org
- History
- 2019-08-11: last of 4 revisions
- 2014-04-21: received
- See all versions
- Short URL
- https://ia.cr/2014/274
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2014/274,
author = {Sorina Ionica and Malika Izabachène},
title = {A note on the construction of pairing-friendly elliptic curves for composite order protocols},
howpublished = {Cryptology ePrint Archive, Paper 2014/274},
year = {2014},
note = {\url{https://eprint.iacr.org/2014/274}},
url = {https://eprint.iacr.org/2014/274}
}
