Abstract
We study the class of masking based domain extenders for UOWHFs. Our first contribution is to show that any correct masking based domain extender for UOWHF which invokes the compression UOWHF s times must use at least ⌈log2 s⌉ masks. As a consequence, we obtain the key expansion optimality of several known algorithms among the class of all masking based domain extending algorithms. Our second contribution is to present a new parallel domain extender for UOWHF. The new algorithm achieves asymptotically optimal speed-up over the sequential algorithm and the key expansion is almost everywhere optimal, i.e., it is optimal for almost all possible number of invocations of the compression UOWHF. Our algorithm compares favourably with all previously known masking based domain extending algorithms.
Chapter PDF
Similar content being viewed by others
References
Bellare, M., Rogaway, P.: Collision-resistant hashing: towards making UOWHFs practical. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 470–484. Springer, Heidelberg (1997)
Damgård, I.B.: A design principle for hash functions. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 416–427. Springer, Heidelberg (1990)
Lee, W., Chang, D., Lee, S., Sung, S., Nandi, M.: New Parallel Domain Extenders for UOWHF. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 208–227. Springer, Heidelberg (2003)
Impagliazzo, R., Naor, M.: Efficient Cryptographic Schemes provably as secure as subset sum. Journal of Cryptology 9(4) (1996)
Merkle, R.C.: One way hash functions and DES. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 428–446. Springer, Heidelberg (1990)
Mironov, I.: Hash functions: From merkle-damgård to shoup. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 166–181. Springer, Heidelberg (2001)
Nandi, M.: Optimal Domain Extension of UOWHF and a Sufficient Condition. In: Proceedings of SAC 2004. LNCS (2004) (to appear)
Nandi, M.: A New Tree based Domain Extension of UOWHF, Cryptology e-print archive, Report No. 2003/142, http://eprint.iacr.org
Naor, M., Yung, M.: Universal one-way hash functions and their cryptographic applications. In: Proceedings of the 21st Annual Symposium on Theory of Computing, pp. 33–43. ACM, New York (1989)
Rompel, J.: One-way functions are necessary and sufficient for digital signatures. In: Proceedings of the 22nd Annual Symposium on Theory of Computing. ACM, New York (1990)
Sarkar, P.: Masking Based Domain Extenders for UOWHFs: Bounds and Constructions, Cryptology e-print archive, Report No. 2003/225, http://eprint.iacr.org
Sarkar, P.: Domain Extenders for UOWHFs: A Finite Binary Tree Algorithm, Cryptology e-print archive, Report No. 2003/009, http://eprint.iacr.org
Sarkar, P.: Construction of UOWHF: Tree Hashing Revisited, Cryptology e-print archive, Report No. 2002/058, http://eprint.iacr.org
Shoup, V.: A composition theorem for universal one-way hash functions. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 445–452. Springer, Heidelberg (2000)
Simon, D.: Finding collisions on a one-way street: Can secure hash function be based on general assumptions? In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 334–345. Springer, Heidelberg (1998)
Stinson, D.R.: Some observations on the theory of cryptographic hash functions, http://www.cacr.math.uwaterloo.ca/~dstinson/papers/newhash.ps
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sarkar, P. (2004). Masking Based Domain Extenders for UOWHFs: Bounds and Constructions. In: Lee, P.J. (eds) Advances in Cryptology - ASIACRYPT 2004. ASIACRYPT 2004. Lecture Notes in Computer Science, vol 3329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30539-2_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-30539-2_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23975-8
Online ISBN: 978-3-540-30539-2
eBook Packages: Springer Book Archive