Abstract
In this paper, we describe how to construct a 32 ×32 binary matrix of branch number 10, and use some mathematical techniques to find a form in product of matrices for increasing efficiency in software implementations of the binary matrix. We estimate a security against cryptanlysis when the binary matrix is used as a diffusion layer of a 256-bit SPN block cipher with an 8-bit s-box as a substitution layer in a round function. Also we describe the cryptanalytic properties such as the resistances to differential, linear, impossible differential, and truncated differential cryptanalysis. The number of operations to be required for implementing the binary matrix as a diffusion layer of a 256-bit SPN block cipher are given in this paper. We have a result that the binary matrix A is more efficient than the diffusion layer used Rijndael-256 on low bit platforms, such as 8-bit processors.
This research is supported by National Security Research Institute(NSRI), Korea.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Koo, B.-W., Jang, H.S., Song, J.H.: Constructing and Cryptanalysis of a 16 × 16 Binary Matrix as a Diffusion Layer. In: Chae, K.-J., Yung, M. (eds.) WISA 2003. LNCS, vol. 2908, pp. 489–503. Springer, Heidelberg (2004)
Kwon, D., Kim, J., Park, S., Sung, S.H., Sohn, Y., Song, J.H., Yeom, Y., Yoon, E.-J., Lee, S., Lee, J., Chee, S., Han, D., Hong, J.: New Block Cipher: ARIA. In: Lim, J.-I., Lee, D.-H. (eds.) ICISC 2003. LNCS, vol. 2971, pp. 432–445. Springer, Heidelberg (2004)
Kanda, M., Takashima, Y., Matsumoto, T., Aoki, K., Ohta, K.: A strategy for construction fast round functions with practical security against differential and linear cryptanalysis. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, pp. 264–279. Springer, Heidelberg (1999)
Biham, E., Shamir, A.: Differential Cryptoanalysis of DES-like Cryptosystems. Journal of Cryptology 4(1), 3–72 (1991); (The extended abstract appeared at CRYPTO 1990)
Matsui, M.: Linear Cryptanalysis Method for DES Cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)
Aoki, K., Kanda, M.: Search for impossible Differential of E2 (1999), Available at: http://csrc.nist.gov/CryptoToolkit/aes/round1/pubcmnts.htm
Knudsen, L.R.: Truncated and Higher Order Differentials. In: Preneel, B. (ed.) FSE 1994. LNCS, vol. 1008, pp. 196–211. Springer, Heidelberg (1995)
Kanda, M.: Practical Security Evaluation against Differential and Linear Cryptanalyses for Feistel Ciphers with SPN Round Function. In: Stinson, D.R., Tavares, S. (eds.) SAC 2000. LNCS, vol. 2012, pp. 324–338. Springer, Heidelberg (2001)
Litsyn, S., Rains, E.M., Sloane, N.J.A.: Available at: http://www.math.unl.edu/djaffe/codes/webcodes/codeform.html
Daemen, J., Rijmen, V.: AES proposal:Rijndael (Version 2) (1999), Available at NIST AES website, http://csrc.nist.gov/encryption/aes
NTT Laboratories. Security of E2 against Truncated Differential Cryptanalysis (in progress) (1999), Available at: http://csrc.nist.gov/CryptoToolkit/aes/round1/comments/990415-smoriai.pdf
Knudsen, L.R.: The Number of Rounds in Block Ciphers, NESSIE public reports, NES/DOC/UIB/WP3/003/a (2000), Available at: http://www.cosic.esat.kuleuven.ac.be/nessie/reports/
Park, J., Yun, Y., Kim, Y., You, Y.: ARIA Processor Design for Video Encryption. In: Proceedings of WISC 2004, pp. 83–90 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Koo, B.W., Jang, H.S., Song, J.H. (2006). On Constructing of a 32 ×32 Binary Matrix as a Diffusion Layer for a 256-Bit Block Cipher. In: Rhee, M.S., Lee, B. (eds) Information Security and Cryptology – ICISC 2006. ICISC 2006. Lecture Notes in Computer Science, vol 4296. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11927587_7
Download citation
DOI: https://doi.org/10.1007/11927587_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49112-5
Online ISBN: 978-3-540-49114-9
eBook Packages: Computer ScienceComputer Science (R0)