1,081 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
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
An Iteratively Decodable Tensor Product Code with Application to Data Storage
The error pattern correcting code (EPCC) can be constructed to provide a
syndrome decoding table targeting the dominant error events of an inter-symbol
interference channel at the output of the Viterbi detector. For the size of the
syndrome table to be manageable and the list of possible error events to be
reasonable in size, the codeword length of EPCC needs to be short enough.
However, the rate of such a short length code will be too low for hard drive
applications. To accommodate the required large redundancy, it is possible to
record only a highly compressed function of the parity bits of EPCC's tensor
product with a symbol correcting code. In this paper, we show that the proposed
tensor error-pattern correcting code (T-EPCC) is linear time encodable and also
devise a low-complexity soft iterative decoding algorithm for EPCC's tensor
product with q-ary LDPC (T-EPCC-qLDPC). Simulation results show that
T-EPCC-qLDPC achieves almost similar performance to single-level qLDPC with a
1/2 KB sector at 50% reduction in decoding complexity. Moreover, 1 KB
T-EPCC-qLDPC surpasses the performance of 1/2 KB single-level qLDPC at the same
decoder complexity.Comment: Hakim Alhussien, Jaekyun Moon, "An Iteratively Decodable Tensor
Product Code with Application to Data Storage
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