Abstract
In [6] higher order derivatives of discrete functions were considered and the concept of higher order differentials was introduced. We introduce the concept of truncated differentials and present attacks on ciphers presumably secure against differential attacks, but vulnerable to attacks using higher order and truncated differentials. Also we give a differential attack using truncated differentials on DES reduced to 6 rounds using only 46 chosen plaintexts with an expected running time of about the time of 3,500 encryptions. Finally it is shown how to find a minimum nonlinear order of a block cipher using higher order differentials.
Chapter PDF
Similar content being viewed by others
References
E. Biham and A. Shamir. Differential cryptanalysis of DES-like cryptosystems. Journal of Cryptology, 4(1):3–72, 1991.
E. Biham and A. Shamir. Differential Cryptanalysis of the Data Encryption Standard. Springer Verlag, 1993.
M.E. Hellman, R. Merkle, R. Schroeppel, L. Washington, W. Diffie, S. Pohlig, and P. Schweitzer. Results of an initial attempt to cryptanalyze the NBS Data Encryption Standard. Technical report, Stanford University, U.S.A., September 1976.
M. E. Hellman and S. K. Langford. Differential-linear cryptanalysis. In Y. G. Desmedt, editor, Advances in Cryptology — Proc. Crypto'94, LNCS 839, pages 26–39. Springer Verlag, 1994.
L.R. Knudsen. Block Ciphers — Analysis, Design and Applications. PhD thesis, Aarhus University, Denmark, 1994, DAIMI PB — 485.
X. Lai. Higher order derivatives and differential cryptanalysis. In Proc. ”Symposium on Communication, Coding and Cryptography”, in honor of James L. Massey on the occasion of his 60'th birthday, Feb. 10–13, 1994, Monte-Verita, Ascona, Switzerland, 1994. To appear.
K. Nyberg. Differentially uniform mappings for cryptography. In T. Helleseth, editor, Advances in Cryptology — Proc. Eurocrypt'93, LNCS 765, pages 55–64. Springer Verlag, 1993.
K. Nyberg and L.R. Knudsen. Provable security against differential cryptanalysis. In E.F. Brickell, editor, Advances in Cryptology — Proc. Crypto'92, LNCS 740, pages 566–574. Springer Verlag, 1993.
National Bureau of Standards. Data encryption standard. Federal Information Processing Standard (FIPS), Publication 46, National Bureau of Standards, U.S. Department of Commerce, Washington D.C., January 1977.
B. Preneel, M. Nuttin, Y. Rijmen, and J. Buelens. Differential cryptanalysis of the CFB mode. In D.R. Stinson, editor, Advances in Cryptology — Proc. Crypto'93, LNCS 773, pages 212–223. Springer Verlag, 1993.
I. Schaumüller-Bichl. The method of formal coding. In Cryptography — Proc., Burg Feuerstein, 1992, LNCS 149, pages 235–255. Springer Verlag, 1982.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Knudsen, L.R. (1995). Truncated and higher order differentials. In: Preneel, B. (eds) Fast Software Encryption. FSE 1994. Lecture Notes in Computer Science, vol 1008. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60590-8_16
Download citation
DOI: https://doi.org/10.1007/3-540-60590-8_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60590-4
Online ISBN: 978-3-540-47809-6
eBook Packages: Springer Book Archive