Kasami

Kasami is a surname of Japanese origin and appears in several scientific terms in coding theory and cryptography. In those contexts, Kasami is associated with two notable concepts: Kasami sequences and Kasami functions.

Kasami sequences are a family of binary pseudorandom sequences with favorable cross-correlation properties, introduced for use in code-division multiple access (CDMA) systems. They are constructed from one or more maximum-length sequences (m-sequences) over GF(2) using a Kasami construction. The original approach yields two principal families: small Kasami sets and large Kasami sets, both of length 2^m − 1, designed to achieve low cross-correlation between distinct sequences. These properties make Kasami sequences useful in spread-spectrum communications, radar, and synchronization, where multiple users require near-orthogonal codes. They are related to, but distinct from, Gold codes and have seen use in various legacy CDMA standards and research.

Kasami function refers to a class of almost perfect nonlinear (APN) power functions over finite fields GF(2^m) used in cryptography. Named after Kasami, these functions exhibit high nonlinearity, making them resistant to differential cryptanalysis, and are employed in the design of S-boxes and other nonlinear components of some symmetric ciphers. The Kasami constructions often involve specific exponents in powers of two, chosen to ensure APN properties for particular field sizes.

Notable individuals bearing the Kasami name have contributed to coding theory, cryptography, and related areas. The terms Kasami sequences and Kasami functions commemorate those researchers' work.

See also: m-sequences, CDMA, Gold codes, APN functions, S-box.