Welcome to the resource topic for 2020/021
Title:
eSIDH: the revenge of the SIDH
Authors: Daniel Cervantes-Vázquez, Eduardo Ochoa-Jiménez, Francisco Rodríguez-Henríquez
Abstract:The Supersingular Isogeny-based Diffie-Hellman key exchange protocol (SIDH) was introduced by Jao an De Feo in 2011. SIDH operates on supersingular elliptic curves defined over quadratic extension fields of the form GF(p^2), where p is a large prime number of the form p = 4^{e_A} 3^{e_B} - 1, where e_A, e_B are positive integers such that 4^{e_A} \approx 3^{e_B}. In this paper, a variant of the SIDH protocol that we dubbed extended SIDH (eSIDH) is presented. The eSIDH variant makes use of primes of the form, p = 4^{e_A} \ell_B^{e_B}\ell_C^{e_C} f - 1. Here \ell_B, \ell_C are two small prime numbers; f is a cofactor; and e_A, e_B and e_C are positive integers such that 4^{e_A} \approx \ell_B^{e_B}\ell_C^{e_C}. We show that for many relevant instantiations of the SIDH protocol, this new family of primes enjoys a faster field arithmetic than the one associated to traditional SIDH primes. Furthermore, the proposed eSIDH protocol preserves the length and format of SIDH private/public keys, and its richer opportunities for parallelism yields a noticeable speedup factor when implemented on multi-core platforms. Using a single-core SIDH p_{751} implementation as a baseline, a parallel eSIDH p_{765} instantiation yields an acceleration factor of 1.05, 1.30 and 1.41, when implemented on k = \{1, 2, 3\}-core processors. In addition, eSIDH p_{765} yields an acceleration factor of 1.050, 1.160 and 1.162. when both protocols are implemented on k = \{1, 2, 3\}-core processors. To our knowledge, this work reports the first multi-core implementation of SIDH.
ePrint: https://eprint.iacr.org/2020/021
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .