Abstract
Differential uniformity and nonlinearity are two basic properties of S-boxes, which measure the resistance of S-boxes to differential and linear attack respectively. Besides these two properties, the hardware cost of S-boxes is also an important property which should be considered primarily in a limited resource environment. By use of Feistel structure, we investigate the problem of constructing S-boxes with excellent cryptographic properties and low hardware implementation cost in the present paper. Feistel structure is a widely used structure in the design of block ciphers, and it can be implemented easily in hardware. Three-round Feistel structure has been used to construct S-boxes in symmetric algorithms, such as CS-Ciper, CRYPTON and ZUC. In the present paper, we investigate the bounds on differential uniformity and nonlinearity of S-boxes constructed with three-round Feistel structure. By choosing suitable round functions, we show that for odd k, differential 4-uniform S-boxes over \(\mathbb{F}_{2^{k}}^2\) with the best known nonlinearity can be constructed via three-round Feistel structure. Some experiment results are also given which show that optimal 4-bit S-boxes can be constructed with 4 or 5 round unbalanced Feistel structure.
Chapter PDF
Similar content being viewed by others
References
Aoki, K.: On maximum non-averaged differential probability. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, pp. 118–130. Springer, Heidelberg (1999)
Bogdanov, A., Knudsen, L.R., Leander, G., Paar, C., Poschmann, A., Robshaw, M.J.B., Seurin, Y., Vikkelsoe, C.: PRESENT: An ultra-lightweight block cipher. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 450–466. Springer, Heidelberg (2007)
Budaghyan, L., Carlet, C., Pott, A.: New classes of almost bent and almost perfect nonlinear polynomials. IEEE Trans. on Inform. Theory 52(3), 1141–1152 (2006)
Budaghyan, L., Pott, A.: On differential uniformity and nonlinearity of functions. Discrete Mathematics 309(2), 371–384 (2009)
Canright, D.: A Very Compact S-Box for AES. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 441–455. Springer, Heidelberg (2005)
Canteaut, A.: Differential cryptanalysis of Feistel ciphers and differentially δ-uniform mappings. In: Workshop on Selected Areas in Cryptography (SAC 1997), pp. 172–184 (1997)
Carlet, C., Charpin, P., Zinoviev, V.: Codes, bent functions and permutations sutiable for DES-like cryptosystems. Des. Codes Cryptogr. 15(2), 125–156 (1998)
Carlet, C.: Boolean Functions for Cryptography and Error Correcting Codes, Chapter of the monography. In: Crama, Y., Hammer, P.L. (eds.) Boolean Models and Methods in Mathematics, Computer Science, and Engineering, pp. 257–397. Cambridge University Press (2010)
Carlet, C.: Vectorial Boolean Functions for Cryptography, Chapter of the monography. In: Crama, Y., Hammer, P.L. (eds.) Boolean Models and Methods in Mathematics, Computer Science, and Engineering, pp. 398–469. Cambridge University Press (2010)
Chabaud, F., Vaudenay, S.: Links between differential and linear cryptanalysis. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 356–365. Springer, Heidelberg (1995)
Dobbertin, H.: One-to-one highly nonlinear power functions on GF(2n). Appl. Algebra Engrg. Comm. Comput. 9(2), 139–152 (1998)
Gold, R.: Maximal recursive sequences with 3-valued recursive crosscorrelation functions. IEEE Trans. Inform. Theory 14, 154–156 (1968)
Grosso, V., Leurent, G., Standaert, F.-X., Varici, K.: LS-Designs: Bitslice Encryption for Efficient Masked Software Implementations. In: FSE 2014 (2014)
Guo, J., Peyrin, T., Poschmann, A.: The PHOTON Family of Lightweight Hash Functions. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 222–239. Springer, Heidelberg (2011)
Guo, J., Peyrin, T., Poschmann, A., Robshaw, M.: The LED Block Cipher. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 326–341. Springer, Heidelberg (2011)
Hou, X.D.: Affinity of permutations of \(\mathbb{F}_{2}^{n}\). Discrete Appl. Math. 154(2), 313–325 (2006)
Leander, G., Poschmann, A.: On the Classification of 4 Bit S-Boxes. In: Carlet, C., Sunar, B. (eds.) WAIFI 2007. LNCS, vol. 4547, pp. 159–176. Springer, Heidelberg (2007)
Lim, C.H.: CRYPTON: A new 128-bit block cipher. In: The First AES Candidate Conference. National Institute for Standards and Technology (1998)
Matsui, M.: New Structure of Block Ciphers with Provable Security against Differential and Linear Cryptanalysis. In: Gollmann, D. (ed.) FSE 1996. LNCS, vol. 1039, pp. 205–218. Springer, Heidelberg (1996)
Matsui, M.: New block encryption algorithm MISTY. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 54–68. Springer, Heidelberg (1997)
Nyberg, K., Knudsen, L.R.: Provable security against differential cryptanalysis. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 566–574. Springer, Heidelberg (1993)
Nyberg, K.: Differentially uniform mappings for cryptography. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 55–64. Springer, Heidelberg (1994)
Shibutani, K., Isobe, T., Hiwatari, H., Mitsuda, A., Akishita, T., Shirai, T.: Piccolo: An Ultra-Lightweight Blockcipher. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 342–357. Springer, Heidelberg (2011)
Stern, J., Vaudenay, S.: CS-CIPHER. In: Vaudenay, S. (ed.) FSE 1998. LNCS, vol. 1372, pp. 189–204. Springer, Heidelberg (1998)
Specification of the 3GPP Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3. Document 4: Design and Evaluation Report, version 1.3 (2011)
Wu, S., Wang, M., Wu, W.: Recursive Diffusion Layers for (Lightweight) Block Ciphers and Hash Functions. In: Knudsen, L.R., Wu, H. (eds.) SAC 2012. LNCS, vol. 7707, pp. 355–371. Springer, Heidelberg (2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, Y., Wang, M. (2014). Constructing S-boxes for Lightweight Cryptography with Feistel Structure. In: Batina, L., Robshaw, M. (eds) Cryptographic Hardware and Embedded Systems – CHES 2014. CHES 2014. Lecture Notes in Computer Science, vol 8731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44709-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-662-44709-3_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44708-6
Online ISBN: 978-3-662-44709-3
eBook Packages: Computer ScienceComputer Science (R0)