Abstract
Tweakable block ciphers are important primitives for designing cryptographic schemes with high security. In the absence of a standardized tweakable block cipher, constructions built from classical block ciphers remain an interesting research topic in both theory and practice. Motivated by Mennink’s \(\widetilde{F}[2]\) publication from 2015, Wang et al. proposed 32 optimally secure constructions at ASIACRYPT’16, all of which employ two calls to a classical block cipher each. Yet, those constructions were still limited to n-bit keys and n-bit tweaks. Thus, applications with more general key or tweak lengths still lack support. This work proposes the XHX family of tweakable block ciphers from a classical block cipher and a family of universal hash functions, which generalizes the constructions by Wang et al. First, we detail the generic XHX construction with three independently keyed calls to the hash function. Second, we show that we can derive the hash keys in efficient manner from the block cipher, where we generalize the constructions by Wang et al.; finally, we propose efficient instantiations for the used hash functions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Beierle, C., et al.: The SKINNY family of block ciphers and its low-latency variant MANTIS. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 123–153. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53008-5_5
Bellare, M., Rogaway, P.: The security of triple encryption and a framework for code-based game-playing proofs. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 409–426. Springer, Heidelberg (2006). https://doi.org/10.1007/11761679_25
Black, J.: The ideal-cipher model, revisited: an uninstantiable blockcipher-based hash function. In: Robshaw, M. (ed.) FSE 2006. LNCS, vol. 4047, pp. 328–340. Springer, Heidelberg (2006). https://doi.org/10.1007/11799313_21
Chen, S., Steinberger, J.: Tight security bounds for key-alternating ciphers. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 327–350. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_19
Gaži, P., Maurer, U.: Cascade encryption revisited. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 37–51. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_3
Jean, J., Nikolić, I., Peyrin, T.: Tweaks and keys for block ciphers: the TWEAKEY framework. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 274–288. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45608-8_15
Jha, A., List, E., Minematsu, K., Mishra, S., Nandi, M.: XHX - a framework for optimally secure tweakable block ciphers from classical block ciphers and universal hashing. IACR Cryptology ePrint Archive 2017:1075 (2017)
Lampe, R., Seurin, Y.: Tweakable blockciphers with asymptotically optimal security. In: Moriai, S. (ed.) FSE 2013. LNCS, vol. 8424, pp. 133–151. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-43933-3_8
Landecker, W., Shrimpton, T., Terashima, R.S.: Tweakable blockciphers with beyond birthday-bound security. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 14–30. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_2
Lee, J.: Towards key-length extension with optimal security: cascade encryption and Xor-cascade encryption. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 405–425. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_25
Liskov, M., Rivest, R.L., Wagner, D.: Tweakable block ciphers. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 31–46. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45708-9_3
Mennink, B.: Optimally secure tweakable blockciphers. In: Leander, G. (ed.) FSE 2015. LNCS, vol. 9054, pp. 428–448. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48116-5_21
Minematsu, K.: Beyond-birthday-bound security based on tweakable block cipher. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 308–326. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03317-9_19
Minematsu, K., Iwata, T.: Tweak-length extension for tweakable blockciphers. In: Groth, J. (ed.) IMACC 2015. LNCS, vol. 9496, pp. 77–93. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-27239-9_5
Naito, Y.: Tweakable blockciphers for efficient authenticated encryptions with beyond the birthday-bound security. IACR Trans. Symmetric Cryptol. 2017(2), 1–26 (2017)
Patarin, J.: The “Coefficients H” technique. In: Avanzi, R.M., Keliher, L., Sica, F. (eds.) SAC 2008. LNCS, vol. 5381, pp. 328–345. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04159-4_21
Rogaway, P.: Efficient instantiations of tweakable blockciphers and refinements to modes OCB and PMAC. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 16–31. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30539-2_2
Schroeppel, R., Orman, H.: The Hasty Pudding Cipher. AES candidate submitted to NIST (1998)
Shrimpton, T., Terashima, R.S.: A modular framework for building variable-input-length tweakable ciphers. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8269, pp. 405–423. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-42033-7_21
Wang, L., Guo, J., Zhang, G., Zhao, J., Gu, D.: How to build fully secure tweakable blockciphers from classical blockciphers. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 455–483. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_17
Acknowledgments
This work was initiated during the group sessions of the 6th Asian Workshop on Symmetric Cryptography (ASK 2016) held in Nagoya. We thank the anonymous reviewers of the ToSC 2017 and Latincrypt 2017 for their fruitful comments.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Jha, A., List, E., Minematsu, K., Mishra, S., Nandi, M. (2019). XHX – A Framework for Optimally Secure Tweakable Block Ciphers from Classical Block Ciphers and Universal Hashing. In: Lange, T., Dunkelman, O. (eds) Progress in Cryptology – LATINCRYPT 2017. LATINCRYPT 2017. Lecture Notes in Computer Science(), vol 11368. Springer, Cham. https://doi.org/10.1007/978-3-030-25283-0_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-25283-0_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-25282-3
Online ISBN: 978-3-030-25283-0
eBook Packages: Computer ScienceComputer Science (R0)