Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 International Journal of Electronics and Telecommunications

2 2020

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: SIDH

Sortuj według:

Ogranicz wyniki do:

SIDH Hybrid Schemes with Classical Component Based on the Discrete Logarithm Problem over Finite Field Extension

Wroński Michał, Burek Elżbieta, Dzierzkowski Łukasz

International Journal of Electronics and Telecommunications

2020

Vol. 66, No. 3

431--441

The concept of a hybrid scheme with connection of SIDH and ECDH is nowadays very popular. In hardware implementations it is convenient to use a classical key exchange algorithm, which is based on the same finite field as SIDH. Most frequently used hybrid scheme is SIDH-ECDH. On the other hand, using the same field as in SIDH, one can construct schemes over Fpn, like Diffie-Hellman or XTR scheme, whose security is based on the discrete logarithm problem. In this paper, idea of such schemes will be presented. The security of schemes, which are based on the discrete logarithm problem over fields Fp; Fp2 ; Fp4 ; Fp6 and Fp8 , for primes p used in SIDH, will be analyzed. At the end, the propositions of practical applications of these schemes will be presented.

Optimal Strategies for Computation of Degree degree ℓⁿ Isogenies for SIDH

Wroński Michał, Chojnacki Andrzej

International Journal of Electronics and Telecommunications

2020

Vol. 66, No. 3

465--472

This article presents methods and algorithms for the computation of isogenies of degree ℓⁿ. Some of these methods are obtained using recurrence equations and generating functions. A standard multiplication based algorithm for computation of isogeny of degree ℓⁿ has time complexity equal to O(n²M (n log n)), where M (N) denotes the cost of integers of size N multiplication. The memory complexity of this algorithm is equal to O (n log (n log (n))). In this article are presented algorithms for: - determination of optimal strategy for computation of degree ℓⁿ isogeny, - determination of cost of optimal strategy of computation of ℓⁿ isogeny using solutions of recurrence equations, - determination of cost of optimal strategy of computation of ℓⁿ isogeny using recurrence equations, where optimality in this context means that, for the given parameters, no other strategy exists that requires fewer operations for computation of isogeny. Also this article presents a method using generating functions for obtaining the solutions of sequences (սₘ) and (cₘ) where cₘ denotes the cost of computations of isogeny of degree ℓᵘᵐum for given costs p, q of ℓ-isogeny computation and ℓ-isogeny evaluation. These solutions are also used in the construction of the algorithms presented in this article.