Abstract
We show that some widely accepted criteria for cryptographic functions, including the strict avalanche criterion (SAC) and the propagation criterion, have various limitations in capturing properties of vital importance to cryptographic algorithms, and propose a new criterion called GAC to measure the global avalanche characteristics of cryptographic functions. We also introduce two indicators related to the new criterion, one forecasts the sum-of-squares while the other the absolute avalanche characteristics of a function. Lower and upper bounds on the two indicators are derived, and two methods are presented to construct cryptographic functions that achieve nearly optimal global avalanche characteristics.
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References
C. M. Adams and S. E. Tavares. Generating and counting binary bent sequences. IEEE Transactions on Information Theory, IT-36 No. 5: 1170–1173, 1990.
K. G. Beauchamp. Applications of Walsh and Related Functions with an Introduction to Sequency Functions. Microelectronics and Signal Processing. Academic Press, London, New York, Tokyo, 1984.
L. Brown, M. Kwan, J. Pieprzyk, and J. Seberry. Improving resistance to differential cryptanalysis and the redesign of LOKI. In Advances in Cryptology - ASIACRYPT’91, volume 739, Lecture Notes in Computer Science, pages 36–50. Springer-Verlag, Berlin, Heidelberg, New York, 1993
E. Biham and A. Shamir. Differential Cryptanalysis of the Data Encryption Standard. Springer-Verlag, New York, Heidelberg, Tokyo, 1993.
J. F. Dillon. A survey of bent functions. The NSA Technical Journal, pages 191–215, 1972. (unclassified).
J. Detombe and S. Tavares. Constructing large cryptographically strong S- boxes. In Advances in Cryptology - AUSCRYPT 92, volume 718, Lecture Notes in Computer Science, pages 165–181. Springer-Verlag, Berlin, Heidelberg, New York, 1993.
R. Forre. The strict avalanche criterion: Special properties of boolean functions and extended definition. In Advances in Cryptology - CRYPTO’88, volume 403, Lecture Notes in Computer Science, pages 450–468. Springer- Verlag, Berlin, Heidelberg, New York, 1989.
S. W. Golomb. Shifl Register Sequences. Laguna Hills, CA: Aegean Park, 1982.
S. Lloyd. Counting functions satisfying a higher order strict avalanche criterion. In Advances in Cryptology - EUROCRYPT’89, volume 434, Lecture Notes in Computer Science, pages 64 - 74. Springer-Verlag, Berlin, Heidelberg, New York, 1990.
S. Lloyd. Counting binary functions with certain cryptographic properties. Journal of Cryptology, 5 (2): 107–132, 1992.
C. Mitchell. Enumerating boolean functions of cryptographic significance. Journal of Cryptology, 2 (3): 155–170, 1990.
F. J. MacWilliams and N. J. A. Sloane. The Theory of Error-Correcting Codes. North-Holland, Amsterdam, New York, Oxford, 1977.
K. Nyberg. Perfect nonlinear S-boxes. In Advances in Cryptology - EURO- CRYPT’91, volume 547, Lecture Notes in Computer Science, pages 378–386. Springer-Verlag, Berlin, Heidelberg, New York, 1991.
K. Nyberg. On the construction of highly nonlinear permutations. In Advances in Cryptology - EUROCRYPT’92, volume 658, Lecture Notes in Computer Science, pages 92–98. Springer-Verlag, Berlin, Heidelberg, New York, 1993.
B. Preneel, R. Govaerts, and J. Vandewalle. Boolean functions satisfying higher order propagation criteria. In Advances in Cryptology - EURO- CRYPT’91, volume 547, Lecture Notes in Computer Science, pages 141–152. Springer-Verlag, Berlin, Heidelberg, New York, 1991.
B. Preneel, W. V. Leekwijck, L. V. Linden, R. Govaerts, and J. Vandewalle. Propagation characteristics of boolean functions. In Advances in Cryptology - EUROCRYPT’90, volume 437, Lecture Notes in Computer Science, pages 155 - 165. Springer-Verlag, Berlin, Heidelberg, New York, 1991.
O. S. Rothaus. On “bent” functions. Journal of Combinatorial Theory, Ser. A, 20: 300–305, 1976.
J. Seberry, X. M., and Y. Zhang. Highly nonlinear 0-1 balanced functions satisfying strict avalanche criterion. In Advances in Cryptology - A USCRYPT’92, volume 718, Lecture Notes in Computer Science, pages 145–155. Springer-Verlag, Berlin, Heidelberg, New York, 1993.
J. Seberry, X. M. Zhang, and Y. Zheng. Improving the strict avalanche characteristics of cryptographic functions. Information Processing Letters, 50: 37–41, 1994.
J. Seberry, X. M. Zhang, and Y. Zheng. Nonlinearly balanced boolean func-tions and their propagation characteristics. In Advances in Cryptology - CRYPTO’93, volume 773, Lecture Notes in Computer Science, pages 49–60. Springer-Verlag, Berlin, Heidelberg, New York, 1994.
J. Seberry, X. M. Zhang, and Y. Zheng. Relationships among nonlinearity criteria. Presented at EUROCRYPT’90 1994.
J. Seberry, X. M. Zhang, and Y. Zheng. Structures of cryptographic functions with strong avalanche characteristics. Asiacrypt’94, December 1994.
J. Seberry, X. M. Zhang, and Y. Zheng. Nonlinearity and propagation char-acteristics of balanced boolean functions. To appear in Information and Computation, 1995.
A. F. Webster. Plaintext/ciphertext bit dependencies in cryptographic system. Master’s Thesis, Department of Electrical Engineering, Queen’s University, Ontario, Cannada, 1985.
A. F. Webster and S. E. Tavares. On the design of S-boxes. In Advances in Cryptology - CRYPTO’Sd, volume 219, Lecture Notes in Computer Science, pages 523–534. Springer-Verlag, Berlin, Heidelberg, New York, 1986.
R. Yarlagadda and J. E. Hershey. Analysis and synthesis of bent sequences. IEE Proceedings (Part E), 136: 112–123, 1989.
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Zhang, XM., Zheng, Y. (1996). GAC — the Criterion for Global Avalanche Characteristics of Cryptographic Functions. In: Maurer, H., Calude, C., Salomaa, A. (eds) J.UCS The Journal of Universal Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80350-5_30
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DOI: https://doi.org/10.1007/978-3-642-80350-5_30
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