Design of SAC/PC(l) of Order k Boolean Functions and Three Other Cryptographic Criteria
نویسندگان
چکیده
A Boolean function f satis es PC(l) of order k if f(x) f(x ) is balanced for any such that 1 W ( ) l even if any k input bits are kept constant, where W ( ) denotes the Hamming weight of . This paper shows the rst design method of such functions which provides deg(f) 3. More than that, we show how to design \balanced" such functions. High nonlinearity and large degree are also obtained. Further, we present balanced SAC(k) functions which achieve the maximum degree. Finally, we extend our technique to vector output Boolean functions.
منابع مشابه
Generalization of Higher Order SAC to Vector Output Boolean Functions
S-boxes (vector output Boolean functions) should satisfy cryptographic criteria even if some input bits (say, k bits) are kept constant. However, this kind of security has been studied only for scalar output Boolean functions. SAC(k) is a criterion for scalar output Boolean functions of this type. This paper studies a generalization of SAC(k) to vector output Boolean functions as the rst step t...
متن کاملVectorial Resilient $PC(l)$ of Order $k$ Boolean Functions from AG-Codes
Propagation criteria and resiliency of vectorial Boolean functions are important for cryptographic purpose (see [1], [2], [3], [4], [7], [8], [10], [11] and [16]). Kurosawa , Stoh [8] and Carlet [1] gave a construction of Boolean functions satisfying PC(l) of order k from binary linear or nonlinear codes. In this paper algebraic-geometric codes over GF (2m) are used to modify the Carlet and Kur...
متن کاملBoolean Functions from AG-Codes
Propagation criterion of degree l and order k (PC(l) of order k) and resiliency of vectorial Boolean functions are important for cryptographic purpose (see [1, 2, 3, 6, 7,8,10,11,16]. Kurosawa , Stoh [8] and Carlet [1] gave a construction of Boolean functions satisfying PC(l) of order k from binary linear or nonlinear codes. In this paper, algebraic-geometric codes over GF (2) are used to modif...
متن کاملHighly Nonlinear 0-1 Balanced Boolean Functions Satisfying Strict Avalanche Criterion
Nonlinearity, 0-1 balancedness and strict avalanche criterion (SAC) are important criteria for cryptographic functions. Bent functions have maximum nonlinearity and satisfy SAC however they are not 01 balanced and hence cannot be directly used in many cryptosystems where 0-1 balancedness is needed. In this paper we construct (i) 0-1 balanced boolean functions on V2k+1 (k ≥ 1) having nonlinearit...
متن کاملHighly Nonlinear 0 - 1 Balanced Boolean Functions Satisfying
Nonlinearity, 0-1 balancedness and strict avalanche criterion (SAC) are important criteria for cryptographic functions. Bent functions have maximum nonlinearity and satisfy SAC however they are not 0-1 balanced and hence cannot be directly used in many cryptosystems where 0-1 balancedness is needed. In this paper we construct (i) 0-1 balanced boolean functions on V2k+1 (k > = 1) having nonlinea...
متن کامل