TY - GEN
T1 - Relationships among nonlinearity criteria
AU - Seberry, Jennifer
AU - Zhang, Xian Mo
AU - Zheng, Yuliang
PY - 1995
Y1 - 1995
N2 - An important question in designing cryptographic functions including substitution boxes (S-boxes) is the relationships among the various nonlinearity criteria each of which indicates the strength or weakness of a cryptographic function against a particular type of cryptanalytic attacks. In this paper we reveal, for the first time, interesting connections among the strict avalanche characteristics, differential characteristics, linear structures and nonlinearity of quadratic S-boxes. In addition, we show that our proof techniques allow us to treat in a unified fashion all quadratic permutations, regardless of the underlying construction methods. This greatly simplifies the proofs for a number of known results on nonlinearity characteristics of quadratic permutations. As a by-product, we obtain a negative answer to an open problem regarding the existence of differentially 2-uniform quadratic permutations on an even dimensional vector space.
AB - An important question in designing cryptographic functions including substitution boxes (S-boxes) is the relationships among the various nonlinearity criteria each of which indicates the strength or weakness of a cryptographic function against a particular type of cryptanalytic attacks. In this paper we reveal, for the first time, interesting connections among the strict avalanche characteristics, differential characteristics, linear structures and nonlinearity of quadratic S-boxes. In addition, we show that our proof techniques allow us to treat in a unified fashion all quadratic permutations, regardless of the underlying construction methods. This greatly simplifies the proofs for a number of known results on nonlinearity characteristics of quadratic permutations. As a by-product, we obtain a negative answer to an open problem regarding the existence of differentially 2-uniform quadratic permutations on an even dimensional vector space.
UR - http://www.scopus.com/inward/record.url?scp=84948966990&partnerID=8YFLogxK
M3 - Conference proceeding contribution
AN - SCOPUS:84948966990
SN - 3540601767
SN - 9783540601760
VL - 950
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 376
EP - 388
BT - Advances in Cryptology - EUROCRYPT 1994 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings
PB - Springer, Springer Nature
T2 - Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1994
Y2 - 9 May 1994 through 12 May 1994
ER -