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Journals and Conferences
Recently, Gligoroski et al. proposed code-based encryption and signature schemes using list decoding, blockwise triangular private keys, and a nonuniform error pattern based on “generalized error sets.” The general approach was referred to as McEliece in the World of Escher. This paper demonstrates attacks which are significantly cheaper than the claimed… (More)
We look at arithmetic progressions on elliptic curves known as Huff curves. By an arithmetic progression on an elliptic curve, we mean that either the x or y-coordinates of a sequence of rational points on the curve form an arithmetic progression. Previous work has found arithmetic progressions on Weierstrass curves, quartic curves, Edwards curves, and… (More)
The JH hash function is one of the five finalists of the ongoing NIST SHA3 hash function competition. Despite several earlier attempts, and years of analysis, the indifferentiability security bound of the JH mode has so far remained remarkably low, only up to n/3 bits . Using a recent technique introduced by Moody, Paul, and Smith-Tone in , we… (More)
A hash function secure in the indifferentiability framework (TCC 2004) is able to resist all meaningful generic attacks. Such hash functions also play a crucial role in establishing the security of protocols that use them as random functions. To eliminate multi-collision type attacks on the Merkle-Damgård mode (Crypto 1989), Lucks proposed widening the size… (More)
Bilinear pairings on elliptic curves have been of much interest in cryptography recently. Most of the protocols involving pairings rely on the hardness of the bilinear Diffie-Hellman problem. In contrast to the discrete log (or Diffie-Hellman) problem in a finite field, the difficulty of this problem has not yet been much studied. In 2001, Verheul … (More)
Edwards curves are an alternate model for elliptic curves, which have attracted notice in cryptography. We give exact formulas for the number of Fq-isomorphism classes of Edwards curves and twisted Edwards curves. This answers a question recently asked by R. Farashahi and I. Shparlinski.
Historically, multivariate public key cryptography has been less than successful at offering encryption schemes which are both secure and efficient. At PQCRYPTO ’13 in Limoges, Tao, Diene, Tang, and Ding introduced a promising new multivariate encryption algorithm based on a fundamentally new idea: hiding the structure of a large matrix algebra over a… (More)
R. Feng, and H. Wu recently established a certain mean-value formula for the x-coordinates of the n-division points on an elliptic curve given in Weierstrass form (A mean value formula for elliptic curves, 2010, available at http://eprint.iacr.org/2009/586.pdf ). We prove a similar result for both the x and y-coordinates on a twisted Edwards elliptic curve.
In this paper we find division polynomials for Huff curves, Jacobi quartics, and Jacobi intersections. These curves are alternate models for elliptic curves to the more common Weierstrass curve. Division polynomials for Weierstrass curves are well known, and the division polynomials we find are analogues for these alternate models. Using the division… (More)