Results 31 to 40 of about 2,050 (182)
The Q-curve construction for endomorphism-accelerated elliptic curves [PDF]
, 2014 We give a detailed account of the use of $\mathbb{Q}$-curve reductions to construct elliptic curves over $\mathbb{F}\_{p^2}$ with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way as ...
Smith, Benjamin
core +13 more sources
Constructing elliptic curve isogenies in quantum subexponential time
Journal of Mathematical Cryptology, 2014 Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but finding such an isogeny is believed to be computationally difficult.
Childs Andrew +2 more
doaj +1 more source
IEEE Access, 2021 Since the introduction of the Supersingular isogeny Diffie–Hellman (SIDH) key exchange protocol by Jao and de Feo in 2011, it and its variation (SIKE) have gained significant attention as a promising candidate for post-quantum cryptography (PQC ...
Seog Chung Seo
doaj +1 more source
Isogeny-based post-quantum key exchange protocols [PDF]
, 2020 The goal of this project is to understand and analyze the supersingular isogeny Diffie Hellman (SIDH), a post-quantum key exchange protocol which security lies on the isogeny-finding problem between supersingular elliptic curves.
Sorinas Capdevila, Ernest
core
Ramanujan graphs in cryptography [PDF]
, 2018 In this paper we study the security of a proposal for Post-Quantum Cryptography from both a number theoretic and cryptographic perspective. Charles-Goren-Lauter in 2006 [CGL06] proposed two hash functions based on the hardness of finding paths in ...
Costache, Anamaria +4 more
core +2 more sources
The Role of Non-Positional Arithmetic on Efficient Emerging Cryptographic Algorithms
IEEE Access, 2020 Number representation systems establish ways in which numbers are mapped to computer architectures, and how operations over the numbers are translated into computer instructions.
Paulo Martins, Leonel Sousa
doaj +1 more source
Heuristics on pairing-friendly abelian varieties [PDF]
, 2013 We discuss heuristic asymptotic formulae for the number of pairing-friendly abelian varieties over prime fields, generalizing previous work of one of the authors arXiv:math1107.0307Comment: Pages 6-7 rewritten, other minor changes ...
Boxall, John, Gruenewald, David
core +2 more sources
A Subexponential Algorithm for Evaluating Large Degree Isogenies
, 2010 An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between elliptic curves efficiently. For ordinary curves of the same endomorphism ring,
Jao, David, Soukharev, Vladimir
core +1 more source
On the Distribution of Atkin and Elkies Primes [PDF]
, 2011 Given an elliptic curve E over a finite field F_q of q elements, we say that an odd prime ell not dividing q is an Elkies prime for E if t_E^2 - 4q is a square modulo ell, where t_E = q+1 - #E(F_q) and #E(F_q) is the number of F_q-rational points on E ...
Shparlinski, Igor E. +1 more
core +2 more sources
Computing Hilbert class polynomials with the Chinese Remainder Theorem [PDF]
, 2009 We present a space-efficient algorithm to compute the Hilbert class polynomial H_D(X) modulo a positive integer P, based on an explicit form of the Chinese Remainder Theorem.
Sutherland, Andrew V.
core +5 more sources