1,201 research outputs found
A new class of codes for Boolean masking of cryptographic computations
We introduce a new class of rate one-half binary codes: {\bf complementary
information set codes.} A binary linear code of length and dimension
is called a complementary information set code (CIS code for short) if it has
two disjoint information sets. This class of codes contains self-dual codes as
a subclass. It is connected to graph correlation immune Boolean functions of
use in the security of hardware implementations of cryptographic primitives.
Such codes permit to improve the cost of masking cryptographic algorithms
against side channel attacks. In this paper we investigate this new class of
codes: we give optimal or best known CIS codes of length We derive
general constructions based on cyclic codes and on double circulant codes. We
derive a Varshamov-Gilbert bound for long CIS codes, and show that they can all
be classified in small lengths by the building up construction. Some
nonlinear permutations are constructed by using -codes, based on the
notion of dual distance of an unrestricted code.Comment: 19 pages. IEEE Trans. on Information Theory, to appea
2^n Bordered Constructions of Self-Dual codes from Group Rings
Self-dual codes, which are codes that are equal to their orthogonal, are a widely studied family of codes.
Various techniques involving circulant matrices and matrices from group rings have been used to construct
such codes. Moreover, families of rings have been used, together with a Gray map, to construct binary
self-dual codes. In this paper, we introduce a new bordered construction over group rings for self-dual
codes by combining many of the previously used techniques. The purpose of this is to construct self-dual
codes that were missed using classical construction techniques by constructing self-dual codes with different
automorphism groups. We apply the technique to codes over finite commutative Frobenius rings of characteristic
2 and several group rings and use these to construct interesting binary self-dual codes. In particular, we construct
some extremal self-dual codes length 64 and 68, constructing 30 new extremal self-dual codes of length 68
Construction of isodual codes from polycirculant matrices
Double polycirculant codes are introduced here as a generalization of double
circulant codes. When the matrix of the polyshift is a companion matrix of a
trinomial, we show that such a code is isodual, hence formally self-dual.
Numerical examples show that the codes constructed have optimal or
quasi-optimal parameters amongst formally self-dual codes. Self-duality, the
trivial case of isoduality, can only occur over \F_2 in the double circulant
case. Building on an explicit infinite sequence of irreducible trinomials over
\F_2, we show that binary double polycirculant codes are asymptotically good
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