Characterizing the structures of cryptographic functions satisfying the propagation criterion for almost all vectors

Designs, Codes, and Cryptography

Volumn 7, Issue 1-2, 1996, Pages 111-134

  Zhang, Xian Mo ^a   Zheng, Yuliang ^b  

^a UNIVERSITY OF WOLLONGONG   (Australia)

^b MONASH UNIVERSITY   (Australia)

Author keywords

Authentication; Boolean functions; Cryptography; Data security; Nonlinearity; Propagation criterion

Indexed keywords

EID: 0001331280     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00125079     Document Type: Article

References (18)

1. C. M. Adams and S. E. Tavares, Generating and counting binary bent sequences, IEEE Transactions on Information Theory, Vol. IT-36 No. 5 (1990) pp. 1170-1173.
2. Claude Carlei, Partially-bent functions, Designs, Codes and Cryptography. Vol 3 (1993) pp 135-145
3. J. F. Dillon, A survey of bent function, The NSA Technical Journal, (1972) pp. 191-215. (unclassified).
4. J. -H. Evertse, Linear structures in blockciphers, Advances in Cryptology - EUROCEYPT'87, Lecture Notes in Computer Science, Springer-Verlag, Berlin, Heidelberg, New York, 304 (1988) pp. 249-266.
5. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, New York, Oxford, (1977).
6. W. Meier and O. Staffelbach, Nonlinearity criteria for cryptographic functions, Advances in Cryptology - EUROCRYPT'89, Lecture Notes in Computer Science, Springer-Verlag, Berlin, Heidelberg, New York, 434 (1990) pp. 549-562.
7. K. Nyberg, On the construction of highly nonlinear permutations, Advances in Cryptology - EUROCRYPT'92 , Lecture Notes in Computer Science, Springer-Verlag, Berlin, Heidelberg, New York, 658 (1993) pp. 92-98.
8. K. Nyberg, Differentially uniform mappings for cryptography. Advances in Cryptology - EUROCRYPT'93 , Lecture Notes in Computer Science, Springer Verlag, Berlin, Heidelberg, New York, 765 (1994) pp. 55-65.
9. B. Preneel, R. Govaerts, and J. Vandewalle, Boolean functions satisfying higher order propagation criteria, Advances in Cryptology - EUROCRYPT'91, Lecture Notes in Computer Science, Springer-Verlag, Berlin, Heidelberg, New York, 547 (1991) pp. 141-152.
10. B. Preneel, W. V. Leekwijck, L. V. Linden, R. Govaerts, and J. Vandewalle, Propagation characteristics of boolean functions, Advances in Cryptology - EUROCRYPT'90, Lecture Notes in Computer Science, Springer-Verlag, Berlin, Heidelberg, New York, 437 (1991) pp. 155-165.
11. O. S. Rothaus, On "bent" functions, Journal of Combinatorial Theory, Ser. A, No. 20 (1976) pp. 300-305.
12. J. Seberry, X. M. Zhang, and Y. Zheng, Relationships among nonlinearity criteria, Presented at EUROCRYPT'94 (1994).
13. J. Seberry, X. M. Zhang, and Y. Zheng, Nonlinearity and propagation characteristics of balanced boolean functions, Information and Computation, Vol. 119, No, 1 (1995) pp. 1-13.
14. J. Seberry, X. M. Zhang, and Y. Zheng, The relationship between propagation characteristics and nonlinearity of cryptographic funtions, Journal of Universal Computer Science, Vol. 1, No. 2 (1995) pp. 136-150. (available at http://hgiicm.tu-graz.ac.at./).
15. A. F. Webster, Plaintext/ciphertext bit dependencies in cryptographic system, Master's Thesis, Department of Electrical Engineering, Queen's University, Ontario(1985).
16. A. F. Webster and S. E. Tavares, On the design of S-boxes, Advances in Cryptology - CRYPTO'85, Lecture Notes in Computer Science, Springer-Verlag, Berlin, Heidelberg, New York, 219 (1986) pp. 523-534.
17. R. Yarlagadda and J. E. Hershey, Analysis and synthesis of bent sequences, IEE Proceedings (Part E), Vol. 136 (1989) pp. 112-123.
18. X. M. Zhang and Y. Zheng, Gac - the criterion for global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science, Vol 1, No. 5 (1995) pp. 316-333. (available at http://hgiicm.tu-graz.ac.at./).