From Unpredictability to Indistinguishability: A Simple Construction of Pseudo-Random Functions from MACs (Extended Abstract)

This paper studies the relationship between unpredictable functions (which formalize the concept of a MAC) and pseudo-random functions. We show an efficient transformation of the former to the latter using a unique application of the Goldreich-Levin hard-core bit (taking the inner-product with a random vector r): While in most applications of the GL-bit the random vector r may be public, in our setting this is not the case. The transformation is only secure when r is secret and treated as part of the key. In addition, we consider weaker notions of unpredictability and their relationship to the corresponding notions of pseudo-randomness. Using these weaker notions we formulate the exact requirements of standard protocols for private-key encryption, authentication and identification. In particular, this implies a simple construction of a private-key encryption scheme from the standard challenge-response identification scheme.

[1]  Manuel Blum,et al.  How to generate cryptographically strong sequences of pseudo random bits , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[2]  Bart Preneel,et al.  On the Security of Two MAC Algorithms , 1996, EUROCRYPT.

[3]  Russell Impagliazzo,et al.  One-way functions are essential for complexity based cryptography , 1989, 30th Annual Symposium on Foundations of Computer Science.

[4]  Moni Naor,et al.  On the construction of pseudo-random permutations: Luby-Rackoff revisited (extended abstract) , 1997, STOC '97.

[5]  Leonid A. Levin,et al.  A Pseudorandom Generator from any One-way Function , 1999, SIAM J. Comput..

[6]  Richard J. Lipton,et al.  Cryptographic Primitives Based on Hard Learning Problems , 1993, CRYPTO.

[7]  Hugo Krawczyk,et al.  MMH: Software Message Authentication in the Gbit/Second Rates , 1997, FSE.

[8]  Amos Fiat,et al.  Tracing traitors , 2000, IEEE Trans. Inf. Theory.

[9]  Phillip Rogaway,et al.  Bucket Hashing and Its Application to Fast Message Authentication , 1995, Journal of Cryptology.

[10]  Manuel Blum,et al.  How to Generate Cryptographically Strong Sequences of Pseudo Random Bits , 1982, FOCS.

[11]  Adi Shamir,et al.  On the generation of cryptographically strong pseudorandom sequences , 1981, TOCS.

[12]  Mihir Bellare,et al.  A concrete security treatment of symmetric encryption , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[13]  Silvio Micali,et al.  On the Cryptographic Applications of Random Functions , 1984, CRYPTO.

[14]  Moni Naor,et al.  Number-theoretic constructions of efficient pseudo-random functions , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[15]  Andrew Chi-Chih Yao,et al.  Theory and Applications of Trapdoor Functions (Extended Abstract) , 1982, FOCS.

[16]  Leonid A. Levin,et al.  A hard-core predicate for all one-way functions , 1989, STOC '89.

[17]  Mihir Bellare,et al.  New Paradigms for Digital Signatures and Message Authentication Based on Non-Interative Zero Knowledge Proofs , 1989, CRYPTO.

[18]  Michael Luby,et al.  How to Construct Pseudo-Random Permutations from Pseudo-Random Functions (Abstract) , 1986, CRYPTO.

[19]  Larry Carter,et al.  New Hash Functions and Their Use in Authentication and Set Equality , 1981, J. Comput. Syst. Sci..

[20]  Moni Naor,et al.  Non-malleable cryptography , 1991, STOC '91.

[21]  Johan Hstad,et al.  Construction of a pseudo-random generator from any one-way function , 1989 .

[22]  Moni Naor,et al.  Multicast security: a taxonomy and some efficient constructions , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[23]  Oded Goldreich,et al.  Two Remarks Concerning the Goldwasser-Micali-Rivest Signature Scheme , 1986, CRYPTO.

[24]  Silvio Micali,et al.  How to construct random functions , 1986, JACM.

[25]  Phillip Rogaway Bucket Hashing and its Application to Fast Message Authentication , 1995, CRYPTO.

[26]  Hugo Krawczyk,et al.  Keying Hash Functions for Message Authentication , 1996, CRYPTO.

[27]  Oded Goldreich,et al.  Foundations of Cryptography (Fragments of a Book) , 1995 .

[28]  Gilles Brassard,et al.  Modern cryptology , 2006 .

[29]  Oded Goldreich,et al.  Towards a Theory of Software Protection , 1986, CRYPTO.

[30]  Moni Naor,et al.  Synthesizers and their application to the parallel construction of pseudo-random functions , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[31]  Mihir Bellare,et al.  The Security of Cipher Block Chaining , 1994, CRYPTO.