Higher-Order CIS Codes

• Published in: IEEE transactions on information theory Vol. 60; no. 9; pp. 5283 - 5295
• Main Authors: Carlet, Claude, Freibert, Finley, Guilley, Sylvain, Kiermaier, Michael, Jon-Lark Kim, Solé, Patrick
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Boolean functions; Coding, codes; Cryptography; Educational institutions; Exact sciences and technology; Information Theory; Information, signal and communications theory; Linear codes; Mathematics; Partitioning algorithms; Registers; Security; Signal and communications theory; Silicon; Telecommunications and information theory; Dual distance; ( {\mathbb Z}_{4}\) -linear codes; Boolean functions; quasi-cyclic codes; Side channel attack; Nonlinear codes; Cyclic code; linear codes; ℤ; Matroid; Golay codes; Boolean function; Algorithm; Binary code; Linear code; Security of data; Binary image; Minimal distance; Masking; Error correction; Cryptography; Dual codes; (Z_4) -linear codes
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2014.2332468

We introduce complementary information set codes of higher order. A binary linear code of length tk and dimension k is called a complementary information set code of order t (t-CIS code for short) if it has t pairwise disjoint information sets. The duals of such codes permit to reduce the cost of masking cryptographic algorithms against side-channel attacks. As in the case of codes for error correction, given the length and the dimension of a t-CIS code, we look for the highest possible minimum distance. In this paper, this new class of codes is investigated. The existence of good long CIS codes of order 3 is derived by a counting argument. General constructions based on cyclic and quasi-cyclic codes and on the building up construction are given. A formula similar to a mass formula is given. A classification of 3-CIS codes of length ≤ 12 is given. Nonlinear codes better than linear codes are derived by taking binary images of Z 4 -codes. A general algorithm based on Edmonds' basis packing algorithm from matroid theory is developed with the following property: given a binary linear code of rate 1/t, it either provides t disjoint information sets or proves that the code is not t-CIS. Using this algorithm, all optimal or best known [tk, k] codes, where t = 3, 4, . . . , 256 and 1≤ k ≤⌊256/t⌋ are shown to be t-CIS for all such k and t, except for t = 3 with k = 44 and t = 4 with k = 37.