TY - JOUR

T1 - S-Blocks of Special Type with Few Variables

AU - Zyubina, D. A.

AU - Tokareva, N. N.

N1 - This research was carried out within the framework of the state contract for the Sobolev Institute of Mathematics, project no. FWNF–2022–0018.

PY - 2023/6

Y1 - 2023/6

N2 - When constructing block ciphers, it is necessary to use vector Boolean functions withspecial cryptographic properties as S-blocks for the cipher’s resistance to various types ofcryptanalysis. In this paper, we investigate the following S-block construction: let (Formula presented.) be a permutation on n elements, let (Formula presented.) be the i-fold application of the permutation (Formula presented.), and let f be a Boolean function of n variables. Define a vector Boolean function (Formula presented.) as (Formula presented.). We study the cryptographic properties of (Formula presented.) such as high nonlinearity, balancedness, and low differential δ-uniformity in the dependence on the properties of f and (Formula presented.) for small n. Complete sets of Boolean functions f and vector Boolean functions (Formula presented.) of few variables with maximum algebraic immunity are also obtained.

AB - When constructing block ciphers, it is necessary to use vector Boolean functions withspecial cryptographic properties as S-blocks for the cipher’s resistance to various types ofcryptanalysis. In this paper, we investigate the following S-block construction: let (Formula presented.) be a permutation on n elements, let (Formula presented.) be the i-fold application of the permutation (Formula presented.), and let f be a Boolean function of n variables. Define a vector Boolean function (Formula presented.) as (Formula presented.). We study the cryptographic properties of (Formula presented.) such as high nonlinearity, balancedness, and low differential δ-uniformity in the dependence on the properties of f and (Formula presented.) for small n. Complete sets of Boolean functions f and vector Boolean functions (Formula presented.) of few variables with maximum algebraic immunity are also obtained.

KW - Boolean function

KW - balancedness

KW - high algebraic degree

KW - high algebraic immunity

KW - high nonlinearity

KW - low differential δ-uniformity

KW - vectorial Boolean function

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85168145123&origin=inward&txGid=7a4e02c095dcd82746c464af1dc6c136

UR - https://www.mendeley.com/catalogue/4b954398-f3fc-3863-adbc-791b8ee92015/

U2 - 10.1134/S1990478923020229

DO - 10.1134/S1990478923020229

M3 - Article

VL - 17

SP - 451

EP - 457

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 2

ER -