A new class of codes for Boolean masking of cryptographic computations

TL;DR

This paper introduces a new class of binary codes called complementary information set codes (CIS codes), which enhance cryptographic masking techniques against side channel attacks by leveraging their structural properties.

Contribution

The paper defines CIS codes, explores their properties, provides optimal constructions for lengths under 132, and establishes bounds and classification methods for these codes.

Findings

Optimal or best known CIS codes for length < 132.

Derived a Varshamov-Gilbert bound for long CIS codes.

Classified small length CIS codes (≤12) using the building up construction.

Abstract

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.