New Parallel Domain Extenders for UOWHF

  • Wonil Lee
  • Donghoon Chang
  • Sangjin Lee
  • Soohak Sung
  • Mridul Nandi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2894)


We present two new parallel algorithms for extending the domain of a UOWHF. The first algorithm is complete binary tree based construction and has less key length expansion than Sarkar’s construction which is the previously best known complete binary tree based construction. But only disadvantage is that here we need more key length expansion than that of Shoup’s sequential algorithm. But it is not too large as in all practical situations we need just two more masks than Shoup’s. Our second algorithm is based on non-complete l-ary tree and has the same optimal key length expansion as Shoup’s which has the most efficient key length expansion known so far. Using the recent result [9], we can also prove that the key length expansion of this algorithm and Shoup’s sequential algorithm are the minimum possible for any algorithms in a large class of “natural” domain extending algorithms. But its parallelizability performance is less efficient than complete tree based constructions. However if l is getting larger, then the parallelizability of the construction is also getting near to that of complete tree based constructions. We also give a sufficient condition for valid domain extension in sequential domain extension.


UOWHF hash function masking assignment sequential construciton parallel construction tree based construction 


  1. 1.
    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)Google Scholar
  2. 2.
    Damgard, I.B.: A design principle for hash functions. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 416–427. Springer, Heidelberg (1990)Google Scholar
  3. 3.
    Merkle, R.: One way hash functions and DES. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 428–446. Springer, Heidelberg (1990)Google Scholar
  4. 4.
    Mironov, I.: Hash functions: From merkle-damgård to shoup. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 166–181. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Nandi, M.: A New Tree based Domain Extension of UOWHF, Cryptology ePrint Archive,
  6. 6.
    Nandi, M.: Study of Domain Extension of UOWHF and its Optimality, Cryptology ePrint Archive,
  7. 7.
    Naor, M., Yung, M.: Universal one-way hash functions and their cryptographic applications. In: Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing, pp. 33–43. ACM Press, New York (1989)CrossRefGoogle Scholar
  8. 8.
    Sarkar, P.: Construction of UOWHF: Tree Hashing Revisited, Cryptology ePrint Archive,
  9. 9.
    Sarkar, P.: Domain Extenders for UOWHF: A Generic Lower Bound on Key Expansion and a Finite Binary Tree Algorithm, Cryptology ePrint Archive,
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Simon, D.: Findings Collisions on a One-Way Street: Can Secure Hash Functions Be Based on General Assumptions? In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 334–345. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Wonil Lee
    • 1
  • Donghoon Chang
    • 1
  • Sangjin Lee
    • 1
  • Soohak Sung
    • 2
  • Mridul Nandi
    • 3
  1. 1.Center for Information and Security TechnologiesKorea UniversitySeoulKorea
  2. 2.Applied Math. DepartmentPaichai UniversityDaejeonKorea
  3. 3.Applied Statistics UnitIndian Statistical InstituteKolkataIndia

Personalised recommendations