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Attacking the linear congruential generator on elliptic curves via lattice techniques

Abstract: In this paper we study the linear congruential generator on elliptic curves from the cryptographic point of view. We show that if sufficiently many of the most significant bits of the composer and of three consecutive values of the sequence are given, then one can recover the seed and the composer (even in the case where the elliptic curve is private). The results are based on lattice reduction techniques and improve some recent approaches of the same security problem. We also estimate limits of some heuristic approaches, which still remain much weaker than those known for nonlinear congruential generators. Several examples are tested using implementations of ours algorithms.

 Authorship: Gutierrez J.,

 Fuente: Cryptography and Communications, 2022, 14(3), 505-525

 Publisher: Springer

 Publication date: 12/09/2022

 No. of pages: 21

 Publication type: Article

 DOI: 10.1007/s12095-021-00535-6

 ISSN: 1936-2447,1936-2455

 Publication Url: https://doi.org/10.1007/s12095-021-00535-6