منابع مشابه
Analysis of Low Hamming Weight Products
Hoffstein and Silverman suggested a use of Low Hamming Weight Product (LHWP) to compute a random power in a group or a multiple of an element in a ring. It reduces the computation of powers in a group with fast endomorphisms such as the Galois field F2n and Koblitz elliptic curves. In this paper, we introduce a reduced representation of LHWP and apply them to attack the relevant cryptosystems.
متن کاملRandom small Hamming weight products with applications to cryptography
There are many cryptographic constructions in which one uses a random power or multiple of an element in a group or a ring. We describe a fast method to compute random powers and multiples in certain important situations including powers in the Galois field F2n , multiples on Koblitz elliptic curves, and multiples in NTRU convolution polynomial rings. The underlying idea is to form a random exp...
متن کاملComputation of Minimum Hamming Weight for Linear Codes
In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$ which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...
متن کاملAnalysis of the Hamming Weight of the Extended wmbNAF
Scalar multiplication is an important operation in elliptic curve cryptosystems(ECC). The algorithms for computing scalar multiplication are mostly based on the binary expansions of scalars, such as the non-adjacent form (NAF) and wNAF(sliding window method). Representing scalars using more bases can speed up the scalar multiplication, such as mbNAF, wmbNAF and extended wmbNAF, which was propos...
متن کاملWeight Distributions of Hamming Codes
We derive a recursive formula determining the weight distribution of the [n = (qm − 1)/(q − 1), n − m, 3] Hamming code H(m, q), when (m, q−1) = 1. Here q is a prime power. The proof is based on Moisio’s idea of using Pless power moment identity together with exponential sum techniques.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2008
ISSN: 0166-218X
DOI: 10.1016/j.dam.2007.09.018