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    Wyświetlanie 1-5 z 5
    Tytuł:
    Combined small subgroups and side-channel attack on elliptic curves with cofactor divisible by 2m
    Autorzy:
    Wroński, Michał
    Powiązania:
    https://bibliotekanauki.pl/articles/227051.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    small subgroups attack
    side-channel attack
    alternative models of elliptic curves
    Opis:
    Nowadays, alternative models of elliptic curves like Montgomery, Edwards, twisted Edwards, Hessian, twisted Hessian, Huff's curves and many others are very popular and many people use them in cryptosystems which are based on elliptic curve cryptography. Most of these models allow to use fast and complete arithmetic which is especially convenient in fast implementations that are side-channel attacks resistant. Montgomery, Edwards and twisted Edwards curves have always order of group of rational points divisible by 4. Huff's curves have always order of rational points divisible by 8. Moreover, sometimes to get fast and efficient implementations one can choose elliptic curve with even bigger cofactor, for example 16. Of course the bigger cofactor is, the smaller is the security of cryptosystem which uses such elliptic curve. In this article will be checked what influence on the security has form of cofactor of elliptic curve and will be showed that in some situations elliptic curves with cofactor divisible by 2m are vulnerable for combined small subgroups and side-channel attacks.
    Źródło:
    International Journal of Electronics and Telecommunications; 2019, 65, 2; 203-209
    2300-1933
    Pojawia się w:
    International Journal of Electronics and Telecommunications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal Strategies for Computation of Degree `n Isogenies for SIDH
    Autorzy:
    Wroński, Michał
    Chojnacki, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/227069.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    SIDH
    optimal strategies
    generating functions
    Opis:
    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.
    Źródło:
    International Journal of Electronics and Telecommunications; 2020, 66, 3; 465-472
    2300-1933
    Pojawia się w:
    International Journal of Electronics and Telecommunications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    How to compute an isogeny on the extended Jacobi quartic curves?
    Autorzy:
    Dzierzkowski, Łukasz
    Wroński, Michał
    Powiązania:
    https://bibliotekanauki.pl/articles/2124751.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    cryptology
    post-quantum
    elliptic curves
    Jacobi quartics
    isogenies
    Opis:
    Computing isogenies between elliptic curves is a significant part of post-quantum cryptography with many practical applications (for example, in SIDH, SIKE, B-SIDH, or CSIDH algorithms). Comparing to other post-quantum algorithms, the main advantages of these protocols are smaller keys, the similar idea as in the ECDH, and a large basis of expertise about elliptic curves. The main disadvantage of the isogeny-based cryptosystems is their computational efficiency - they are slower than other post-quantum algorithms (e.g., lattice-based). That is why so much effort has been put into improving the hitherto known methods of computing isogenies between elliptic curves. In this paper, we present new formulas for computing isogenies between elliptic curves in the extended Jacobi quartic form with two methods: by transforming such curves into the short Weierstrass model, computing an isogeny in this form and then transforming back into an initial model or by computing an isogeny directly between two extended Jacobi quartics.
    Źródło:
    International Journal of Electronics and Telecommunications; 2022, 68, 3; 463--468
    2300-1933
    Pojawia się w:
    International Journal of Electronics and Telecommunications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    SIDH Hybrid Schemes with Classical Component Based on the Discrete Logarithm Problem over Finite Field Extension
    Autorzy:
    Wroński, Michał
    Burek, Elżbieta
    Dzierzkowski, Łukasz
    Powiązania:
    https://bibliotekanauki.pl/articles/226917.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    SIDH
    Diffie-Hellman algorithm
    hybrid schemes
    Opis:
    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.
    Źródło:
    International Journal of Electronics and Telecommunications; 2020, 66, 3; 431-441
    2300-1933
    Pojawia się w:
    International Journal of Electronics and Telecommunications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Arithmetic Using Compression on Elliptic Curves in Huff’s Form and Its Applications
    Autorzy:
    Dryło, Robert
    Kijko, Tomasz
    Wroński, Michał
    Powiązania:
    https://bibliotekanauki.pl/articles/1844692.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Huff's curves
    isogeny-based cryptography
    compression functions on elliptic curves
    Opis:
    In this paper for elliptic curves provided by Huff’s equation H a,b : ax(y² − 1) = by(x² − 1) and general Huff’s equation G a,b : x(ay² − 1) = y(bx² − 1) and degree 2 compression function f(x, y) = xy on these curves, herein we provide formulas for doubling and differential addition after compression, which for Huff’s curves are as efficient as Montgomery’s formulas for Montgomery’s curves By² = x³ + Ax² + x. For these curves we also provided point recovery formulas after compression, which for a point P on these curves allows to compute [n]f(P) after compression using the Montgomery ladder algorithm, and then recover [n]P. Using formulas of Moody and Shumow for computing odd degree isogenies on general Huff’s curves, we have also provide formulas for computing odd degree isogenies after compression for these curves. Moreover, it is shown herein how to apply obtained formulas using compression to the ECM algorithm.
    Źródło:
    International Journal of Electronics and Telecommunications; 2021, 67, 2; 193-200
    2300-1933
    Pojawia się w:
    International Journal of Electronics and Telecommunications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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