Results 11 to 20 of about 245 (45)
Lattice polytopes in coding theory [PDF]
, 2014 In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also prove a new inductive bound for the minimum distance of generalized toric codes.
Soprunov, Ivan
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The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives [PDF]
, 2017 In this brief note we connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.Comment: 8 ...
Gadiyar, H. Gopalakrishna, Padma, R.
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New Techniques for SIDH-based NIKE
Journal of Mathematical Cryptology, 2020 We consider the problem of producing an efficient, practical, quantum-resistant non-interactive key exchange (NIKE) protocol based on Supersingular Isogeny Diffie-Hellman (SIDH).
Urbanik David, Jao David
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Toric surface codes and Minkowski sums [PDF]
, 2006 Toric codes are evaluation codes obtained from an integral convex polytope $P \subset \R^n$ and finite field $\F_q$. They are, in a sense, a natural extension of Reed-Solomon codes, and have been studied recently by J. Hansen and D. Joyner. In this paper,
Little, John, Schenck, Hal
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Nonlinearities on particular elliptic curves subspaces and applications
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 Researching on mathematical models for cryptography means to, primary, define the optimal spaces and rules for which we can archive the maximum time to find the involved parameters of the keys and, in the same time, to optimise the time for key ...
Alsaedi Ramzi +2 more
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On a relation between GAG codes and AG codes
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this paper, we first give a relationship between generalized algebraic geometry codes (GAG codes) and algebraic geometry codes (AG codes). More precisely, we show that a GAG code is contained (up to isomorphism) in a suitable AG code.
Şenel Engin, Öke Figen
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Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
Journal of Mathematical Cryptology, 2014 We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases
De Feo Luca, Jao David, Plût Jérôme
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Generalization of the Lee-O'Sullivan List Decoding for One-Point AG Codes [PDF]
, 2012 We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan based on Gr\"obner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander.
Adams +23 more
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Algebraic approaches for solving isogeny problems of prime power degrees
Journal of Mathematical Cryptology, 2020 Recently, supersingular isogeny cryptosystems have received attention as a candidate of post-quantum cryptography (PQC). Their security relies on the hardness of solving isogeny problems over supersingular elliptic curves. The meet-in-the-middle approach
Takahashi Yasushi +5 more
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