컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0504 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Combinatorics / Graph Theory / Cryptography / Coding Theory (SS-05) |
| 영문제목 (Title(Eng.)) |
Higher-order CIS codes |
| 저자(Author(s)) |
Claude Carlet1, Finley Freibert2, Sylvain Guilley3, Michael Kiermaier4, Jon-Lark Kim5, Patrick Sole6 Universities of Paris 8 and Paris 13, LAGA1, Ohio Dominican University, USA2, Telecom-ParisTech, France3, Bayreuth University, Germany4, Sogang University, S. Korea5, Telecom-ParisTech, CNRS and King Abdulaziz University, Saudi Arabia 6 |
| 초록본문(Abstract) | 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. Such codes permit to reduce the cost of masking cryptographic algorithms against side-channel attacks. In this paper, this new class of codes is investigated. The existence of good long CIS codes of order $t$ is derived by a counting argument. General constructions based on cyclic codes and on 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 $\le 12$ 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, some optimal or best known $[tk, k]$ codes where $t=3, 4, \dots, 256$ and $1 \le k \le \lfloor 256/t \rfloor$ are shown to be $t$-CIS for all such $k$ and $t$, except for $t=3$ with $k=44$ and $t=4$ with $k=37$. |
| 분류기호 (MSC number(s)) |
94B05, 11T71, 94A60 |
| 키워드(Keyword(s)) | quasi-cyclic codes, dual distance, Boolean functions, $Z_4$-codes |
| 강연 형태 (Language of Session (Talk)) |
English |