Advances in Alternative Non-adjacent Form Representations

Abstract. From several decades, non-adjacent form (NAF) representations for integers have been extensively studied as an alternative to the usual binary number system where digits are in {0, 1}. In cryptography, the non-adjacent digit set (NADS) {−1, 0, 1} is used for optimization of arithmetic operations in elliptic curves. At SAC 2003, Muir and Stinson published new results on alternative digit sets: they proposed infinite families of integers x such that {0, 1, x} is a NADS as well as infinite families of integers x such that {0, 1, x} is not a NADS, so called a NONNADS. Muir and Stinson also provided an algorithm that determines whether x leads to a NADS by checking if every integer n ∈ [0, −x 3 ] has a {0, 1, x}-NAF. In this paper, we extend these results by providing generators of NON-NADS infinite families. Furthermore, we reduce the search bound from −x 3 to −x 12 . We introduce the notion of worst NON-NADS and give the complete characterization of such sets. Beyon...

• Type: Conference
• Year: 2004
• Where: INDOCRYPT
• Authors: Gildas Avoine, Jean Monnerat, Thomas Peyrin
• Keywords: Digit Sets, INDOCRYPT 2004, Infinite Families, NADS