A Design Principle for Hash Functions
- Ivan Bjerre Damgård
- … show all 1 hide
We show that if there exists a computationally collision free function f from m bits to t bits where m > t, then there exists a computationally collision free function h mapping messages of arbitrary polynomial lengths to t-bit strings.
Let n be the length of the message. h can be constructed either such that it can be evaluated in time linear in n using 1 processor, or such that it takes time O(log(n)) using O(n) processors, counting evaluations of f as one step. Finally, for any constant k and large n, a speedup by a factor of k over the first construction is available using k processors.
Apart from suggesting a generally sound design principle for hash functions, our results give a unified view of several apparently unrelated constructions of hash functions proposed earlier. It also suggests changes to other proposed constructions to make a proof of security potentially easier.
We give three concrete examples of constructions, based on modular squaring, on Wolfram’s pseudoranddom bit generator [Wo], and on the knapsack problem.
- Damgård: “Collision Free Hash Functions and Public Key Signature Schemes”, Proceedings of EuroCrypt 87, Springer.
- D. Denning: “Digital Signatures with RSA and other Public Key Cryptosystems”, CACM, vol.27, 1984, pp.441–448.
- Davis and Price: “The Application of Digital Signatures Based on Public Key Crypto-Systems”, Proc. of CompCon 1980, pp.525–530.
- Godlewski and Camion: “Manipulation and Errors, Localization and Detection”, Proceedings of EuroCrypt 88, Springer.
- Gibson: “A Collision Free Hash Function and the Discrete Logarithm Problem for a Composite Modulus”, Manuscript, 1/10/88, London, England.
- Girault: “Hash Functions Using Modulo-n Operations”, Proceedings of EuroCrypt 87, Springer.
- Girault, Toffin and Vallée: “Computation of Approximate L-th Roots Modulon and Application to Cryptography”, Proceedings of Crypto 88, Springer.
- Impagliazzo and Naor: “Efficient Cryptographic Schemes Provably as Secure as Subset Sum”, Proc. of FOCS 89.
- Merkle: “One Way Hash Functions and DES”, these proceedings.
- Naor and Yung: “Universal One-Way Hash Functions”, Proc. of STOC 89.
- Winternitz: “Producing a one-way Hash Function from DES”, Proceedings of Crypto 83, Springer.
- Wolfram: “Random Sequence Generation by Cellular Automata”, Adv. Appl. Math., vol 7, 123–169, 1986. CrossRef
- A Design Principle for Hash Functions
- Book Title
- Advances in Cryptology — CRYPTO’ 89 Proceedings
- Book Part
- Session 10:
- pp 416-427
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer New York
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Industry Sectors
- eBook Packages
To view the rest of this content please follow the download PDF link above.