The Classification of Complementary Information Set Codes of Lengths 14 and 16

TL;DR

This paper classifies complementary information set (CIS) codes of lengths 14 and 16, expanding the understanding of their structure and potential cryptographic applications, including classifications of related optimal codes.

Contribution

It provides a complete classification of length 14 CIS codes and new classifications for certain length 16 codes, advancing the theoretical understanding of CIS codes.

Findings

Complete classification of length 14 CIS codes.

New classifications for binary [16,8,3] and [16,8,4] codes.

Additional classifications for optimal CIS codes of lengths 20 and 26.

Abstract

In the paper "A new class of codes for Boolean masking of cryptographic computations," Carlet, Gaborit, Kim, and Sol\'{e} defined a new class of rate one-half binary codes called \emph{complementary information set} (or CIS) codes. The authors then classified all CIS codes of length less than or equal to 12. CIS codes have relations to classical Coding Theory as they are a generalization of self-dual codes. As stated in the paper, CIS codes also have important practical applications as they may improve the cost of masking cryptographic algorithms against side channel attacks. In this paper, we give a complete classification result for length 14 CIS codes using an equivalence relation on $GL(n,\FF_2)$. We also give a new classification for all binary $[16,8,3]$ and $[16,8,4]$ codes. We then complete the classification for length 16 CIS codes and give additional classifications for optimal CIS codes of lengths 20 and 26.