Higher-order CIS codes
Claude Carlet, Finley Freibert, Sylvain Guilley, Michael Kiermaier,, Jon-Lark Kim, Patrick Sol\'e

TL;DR
This paper introduces higher-order complementary information set (CIS) codes, explores their properties, constructions, and classifications, and develops algorithms to identify optimal codes useful for cryptographic masking against side-channel attacks.
Contribution
It defines and investigates higher-order CIS codes, provides new constructions, classifications, and an algorithm to identify such codes in binary linear codes.
Findings
Existence of good long 3-CIS codes established by counting arguments.
Constructed new classes of CIS codes using cyclic and quasi-cyclic codes.
Developed an algorithm that identifies t-CIS codes among optimal or best known codes.
Abstract
We introduce {\bf complementary information set codes} of higher-order. A binary linear code of length and dimension is called a complementary information set code of order (-CIS code for short) if it has 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 -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 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 is given. Nonlinear codes…
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Taxonomy
TopicsCoding theory and cryptography · Cryptographic Implementations and Security · Chaos-based Image/Signal Encryption
