Welcome to the resource topic for 2014/274
Title:
A note on the construction of pairing-friendly elliptic curves for composite order protocols
Authors: Sorina Ionica, 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.
ePrint: https://eprint.iacr.org/2014/274
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