Abstract
We extend and improve biclique attacks, which were recently introduced for the cryptanalysis of block ciphers and hash functions. While previous attacks required a primitive to have a key or a message schedule, we show how to mount attacks on the primitives with these parameters fixed, i.e. on permutations. We introduce the concept of sliced bicliques, which is a translation of regular bicliques to the framework with permutations.
The new framework allows to convert preimage attacks into collision attacks and derive the first collision attacks on the reduced SHA-3 finalist Skein in the hash function setting up to 11 rounds. We also demonstrate new preimage attacks on the reduced Skein and the output transformation of the reduced Grøstl. Finally, the sophisticated technique of message compensation gets a simple explanation with bicliques.
Chapter PDF
Similar content being viewed by others
References
Aoki, K., Guo, J., Matusiewicz, K., Sasaki, Y., Wang, L.: Preimages for Step-Reduced SHA-2. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 578–597. Springer, Heidelberg (2009)
Aoki, K., Sasaki, Y.: Preimage Attacks on One-Block MD4, 63-Step MD5 and More. In: Avanzi, R.M., Keliher, L., Sica, F. (eds.) SAC 2008. LNCS, vol. 5381, pp. 103–119. Springer, Heidelberg (2009)
Aoki, K., Sasaki, Y.: Meet-in-the-Middle Preimage Attacks Against Reduced SHA-0 and SHA-1. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 70–89. Springer, Heidelberg (2009)
Aumasson, J.-P., Çalık, Ç., Meier, W., Özen, O., Phan, R.C.-W., Varıcı, K.: Improved Cryptanalysis of Skein. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 542–559. Springer, Heidelberg (2009)
Biham, E., Chen, R.: Near-Collisions of SHA-0. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 290–305. Springer, Heidelberg (2004)
Biryukov, A., Khovratovich, D.: Related-Key Cryptanalysis of the Full AES-192 and AES-256. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 1–18. Springer, Heidelberg (2009)
Black, J., Rogaway, P., Shrimpton, T.: Black-Box Analysis of the Block-Cipher-Based Hash-Function Constructions from PGV. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 320–335. Springer, Heidelberg (2002)
Bogdanov, A., Khovratovich, D., Rechberger, C.: Biclique Cryptanalysis of the Full AES. In: Lee, D.H. (ed.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 344–371. Springer, Heidelberg (2011)
Diffie, W., Hellman, M.: Special feature exhaustive cryptanalysis of the NBS Data Encryption Standard. Computer 10, 74–84 (1977)
Ferguson, N., Lucks, S., Schneier, B., Whiting, D., Bellare, M., Kohno, T., Callas, J., Walker, J.: The Skein hash function family. Submission to NIST, Round 3 (2010), http://www.skein-hash.info/sites/default/files/skein1.3.pdf
Gauravaram, P., Knudsen, L.R., Matusiewicz, K., Mendel, F., Rechberger, C., Schläffer, M., Thomsen, S.S.: Grøstl – a SHA-3 candidate. Submission to NIST (2008), http://www.groestl.info/Groestl.pdf
Gilbert, H., Peyrin, T.: Super-Sbox Cryptanalysis: Improved Attacks for AES-Like Permutations. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 365–383. Springer, Heidelberg (2010)
Jia, K., Yu, H., Wang, X.: A meet-in-the-middle attack on the full KASUMI. Cryptology ePrint Archive, Report 2011/466 (2011)
Khovratovich, D.: Bicliques for permutations: collision and preimage attacks in stronger settings. Cryptology ePrint Archive, Report 2012/141 (2012), http://eprint.iacr.org/2012/141
Khovratovich, D., Leurent, G., Rechberger, C.: Narrow-Bicliques: Cryptanalysis of Full IDEA. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 392–410. Springer, Heidelberg (2012)
Khovratovich, D., Rechberger, C., Savelieva, A.: Bicliques for Preimages: Attacks on Skein-512 and the SHA-2 Family. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 244–263. Springer, Heidelberg (2012), http://eprint.iacr.org/2011/286.pdf
Li, J., Isobe, T., Shibutani, K.: Converting Meet-In-The-Middle Preimage Attack into Pseudo Collision Attack: Application to SHA-2. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 264–286. Springer, Heidelberg (2012)
Mala, H.: Biclique cryptanalysis of the block cipher Square. Cryptology ePrint Archive, Report 2011/500 (2011), http://eprint.iacr.org/
Mendel, F., Rechberger, C., Schläffer, M., Thomsen, S.S.: The Rebound Attack: Cryptanalysis of Reduced Whirlpool and Grøstl. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 260–276. Springer, Heidelberg (2009)
Mendel, F., Rechberger, C., Schläffer, M., Thomsen, S.S.: Rebound Attacks on the Reduced Grøstl Hash Function. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 350–365. Springer, Heidelberg (2010)
Peyrin, T.: Improved Differential Attacks for ECHO and Grøstl. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 370–392. Springer, Heidelberg (2010)
Sasaki, Y.: Meet-in-the-Middle Preimage Attacks on AES Hashing Modes and an Application to Whirlpool. In: Joux, A. (ed.) FSE 2011. LNCS, vol. 6733, pp. 378–396. Springer, Heidelberg (2011)
Sasaki, Y., Aoki, K.: Preimage Attacks on Step-Reduced MD5. In: Mu, Y., Susilo, W., Seberry, J. (eds.) ACISP 2008. LNCS, vol. 5107, pp. 282–296. Springer, Heidelberg (2008)
Sasaki, Y., Aoki, K.: Finding Preimages in Full MD5 Faster Than Exhaustive Search. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 134–152. Springer, Heidelberg (2009)
Sasaki, Y., Li, Y., Wang, L., Sakiyama, K., Ohta, K.: Non-full-active Super-Sbox Analysis: Applications to ECHO and Grøstl. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 38–55. Springer, Heidelberg (2010)
Su, B., Wu, W., Wu, S., Dong, L.: Near-Collisions on the Reduced-Round Compression Functions of Skein and BLAKE. In: Heng, S.-H., Wright, R.N., Goi, B.-M. (eds.) CANS 2010. LNCS, vol. 6467, pp. 124–139. Springer, Heidelberg (2010)
van Oorschot, P.C., Wiener, M.J.: Parallel collision search with cryptanalytic applications. J. Cryptology 12(1), 1–28 (1999)
Wagner, D.: The Boomerang Attack. In: Knudsen, L.R. (ed.) FSE 1999. LNCS, vol. 1636, pp. 156–170. Springer, Heidelberg (1999)
Wang, X., Yin, Y.L., Yu, H.: Finding Collisions in the Full SHA-1. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 17–36. Springer, Heidelberg (2005)
Wu, S., Feng, D., Wu, W., Guo, J., Dong, L., Zou, J.: (Pseudo) Preimage Attack on Reduced-Round Grøstl Hash Function and Others. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 127–145. Springer, Heidelberg (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 International Association for Cryptologic Research
About this paper
Cite this paper
Khovratovich, D. (2012). Bicliques for Permutations: Collision and Preimage Attacks in Stronger Settings. In: Wang, X., Sako, K. (eds) Advances in Cryptology – ASIACRYPT 2012. ASIACRYPT 2012. Lecture Notes in Computer Science, vol 7658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34961-4_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-34961-4_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34960-7
Online ISBN: 978-3-642-34961-4
eBook Packages: Computer ScienceComputer Science (R0)