On the Construction of Block Ciphers Provably Secure and Not Relying on Any Unproved Hypotheses

One of the ultimate goals of cryptography researchers is to construct a (secrete-key) block cipher which has the following ideal properties: (1) The cipher is provably secure, (2) Security of the cipher does not depend on any unproved hypotheses, (3) The cipher can be easily implemented with current technology, and (4) All design criteria for the cipher are made public. It is currently unclear whether or not there really exists such an ideal block cipher. So to meet the requirements of practical applications, the best thing we can do is to construct a block cipher such thai it approximates the ideal one as closely as possible. In this paper, we make a significant step in this direction. In particular, we construct several block ciphers each of which has the above mentioned properties (2), (3) and (4) as well as the following one: (1’) Security of the cipher is supported by convincing evidence. Our construction builds upon profound mathematical bases for information security recently established in a series of excellent papers.

[1]  J.L. Smith,et al.  Some cryptographic techniques for machine-to-machine data communications , 1975, Proceedings of the IEEE.

[2]  Rainer A. Rueppel,et al.  On the Security of Schnorr's Pseudo Random Generator , 1990, EUROCRYPT.

[3]  Ueli Maurer,et al.  Perfect Local Randomness in Pseudo-Random Sequences , 1989, CRYPTO.

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

[5]  Alan G. Konheim.  Cryptography, a primer , 1981 .

[6]  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).

[7]  Andrew Chi-Chih Yao,et al.  Theory and application of trapdoor functions , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[8]  Carl H. Meyer,et al.  Ciphertext/plaintext and ciphertext/key dependence vs. number of rounds for the data encryption standard , 1899, AFIPS National Computer Conference.

[9]  Leonid A. Levin,et al.  One-way functions and pseudorandom generators , 1985, STOC '85.

[10]  Hideki Imai,et al.  Impossibility and Optimality Results on Constructing Pseudorandom Permutations (Extended Abstract) , 1989, EUROCRYPT.

[11]  Claus-Peter Schnorr,et al.  On the Construction of Random Number Generators and Random Function Generators , 1988, EUROCRYPT.

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

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

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