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 $2n$ and dimension $n$ 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 $<132.$ 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 $\le 12$ by the building up construction. Some nonlinear permutations are constructed by using $\Z_4$-codes, based on the notion of dual distance of an unrestricted code.Comment: 19 pages. IEEE Trans. on Information Theory, to appea

New extremal binary self-dual codes of length 68 via short kharaghani array over f_2 + uf_2

In this work, new construction methods for self-dual codes are given. The methods use the short Kharaghani array and a variation of it. These are applicable to any commutative Frobenius ring. We apply the constructions over the ring F_2 + uF_2 and self-dual Type I [64, 32, 12]_2-codes with various weight enumerators obtained as Gray images. By the use of an extension theorem for self-dual codes we were able to construct 27 new extremal binary self-dual codes of length 68. The existence of the extremal binary self-dual codes with these weight enumerators was previously unknown.Comment: 10 pages, 5 table

Self-Dual Codes

Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory. Topics covered in this survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems, bounds, mass formulae, enumeration, extremal codes, open problems. There is a comprehensive bibliography.Comment: 136 page