7 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
Formally Unimodular Packings for the Gaussian Wiretap Channel
This paper introduces the family of lattice-like packings, which generalizes
lattices, consisting of packings possessing periodicity and geometric
uniformity. The subfamily of formally unimodular (lattice-like) packings is
further investigated. It can be seen as a generalization of the unimodular and
isodual lattices, and the Construction A formally unimodular packings obtained
from formally self-dual codes are presented. Recently, lattice coding for the
Gaussian wiretap channel has been considered. A measure called secrecy function
was proposed to characterize the eavesdropper's probability of correctly
decoding. The aim is to determine the global maximum value of the secrecy
function, called (strong) secrecy gain.
We further apply lattice-like packings to coset coding for the Gaussian
wiretap channel and show that the family of formally unimodular packings shares
the same secrecy function behavior as unimodular and isodual lattices. We
propose a universal approach to determine the secrecy gain of a Construction A
formally unimodular packing obtained from a formally self-dual code. From the
weight distribution of a code, we provide a necessary condition for a formally
self-dual code such that its Construction A formally unimodular packing is
secrecy-optimal. Finally, we demonstrate that formally unimodular
packings/lattices can achieve higher secrecy gain than the best-known
unimodular lattices.Comment: Accepted for publication in IEEE Transactions on Information Theory.
arXiv admin note: text overlap with arXiv:2111.0143
Self-dual codes, subcode structures, and applications.
The classification of self-dual codes has been an extremely active area in coding theory since 1972 [33]. A particularly interesting class of self-dual codes is those of Type II which have high minimum distance (called extremal or near-extremal). It is notable that this class of codes contains famous unique codes: the extended Hamming [8,4,4] code, the extended Golay [24,12,8] code, and the extended quadratic residue [48,24,12] code. We examine the subcode structures of Type II codes for lengths up to 24, extremal Type II codes of length 32, and give partial results on the extended quadratic residue [48,24,12] code. We also develop a generalization of self-dual codes to Network Coding Theory and give some results on existence of self-dual network codes with largest minimum distance for lengths up to 10. Complementary Information Set (CIS for short) codes, a class of classical codes recently developed in [7], have important applications to Cryptography. CIS codes contain self-dual codes as a subclass. We give a new classification result for CIS codes of length 14 and a partial result for length 16
Binary Optimal Linear Rate 1/2 Codes
In this paper, we complete the classi cation of optimal linear [n; n/2] codes up to length 28. We have determined that there are 1535 inequivalent [14,7,4] codes, 1682 inequivalent [20,10,6] codes, and 3 inequivalent [26,13,7] codes. In addition, we show that the smallest length for which an optimal rate 1/2 code has a trivial automorphism group is 14. Double circulant codes which attain the highest known minimum distance are given for lengths up to 64