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 that 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. Motivations and Summary of Results Data Encryption Standard (DES) designed by IBM about fifteen years ago is the first modern (secrete-key) block cipher whose algorithm is publicly available [NBS]. It is a kind of product ciphers with Lucifer as its direct predecessor [FNS] [K]. A little more specifically, both DES and Lucifer consist of 16 rounds of Feistel-type transformations (FTT’s) which are invented by and named (by us) after Feistel.