Higher Order Logic Theorem Proving and Its Applications: 7th by Sten Agerholm (auth.), Thomas F. Melham, Juanito Camilleri

By Sten Agerholm (auth.), Thomas F. Melham, Juanito Camilleri (eds.)

This quantity offers the court cases of the seventh foreign Workshop on greater Order good judgment Theorem Proving and Its functions held in Valetta, Malta in September 1994.
Besides three invited papers, the lawsuits comprises 27 refereed papers chosen from forty two submissions. In overall the ebook provides many new effects by way of top researchers engaged on the layout and purposes of theorem provers for greater order good judgment. specifically, this booklet supplies an intensive cutting-edge record on purposes of the HOL approach, some of the most ordinary theorem provers for better order logic.

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Additional resources for Higher Order Logic Theorem Proving and Its Applications: 7th International Workshop Valletta, Malta, September 19–22, 1994 Proceedings

Example text

The output of the S function is the concatenation of the outputs of the S-boxes. We refer to Shimoyama et al. [13] for the values in the S5 and S6 tables. The M function is a 32-bit input/output linear function. The output b for an input a is the product of a and a matrix M , b = a·M, where M is a square matrix of order 32 with entries that are elements of GF (2), the Galois field of order two, and a and b are row vectors with entries from GF (2). We refer to Shimoyama et al. [13] for the entries of the matrix M.

K10 , and we can obtain the pairs with about 212 chosen plaintexts. Repeating the analysis for k0 , . . , k4 breaks the whole cipher with 213 chosen plaintexts. This is surprisingly small considering the large key size. The work factor of breaking the cipher is quite low. Let (w1 , 2w1 ), . . , (w16 , 2w16 ) be right pairs that determine k6 . By definition of being right, bits 15 and 31 of k6 · wi are 0 for all i. Observe that bit 15 of k6 · wi is independent of bits 16 through 31 of k6 .

Thus the differential can be iterated. So we have found an iterative 1-round multiplicative differential that works for keys (i) (i) in which bit 1 of Z1 is 0 and bit 1 of Z2 is 0 in every round. This differential survives 8 rounds of IDEA-X with probability 2−32 , and works against 2−16 of the keys. The only thing left to consider is the output phase. This phase uses multiplications, which will not disturb the −1 differential, and xors. The differential will survive the xors even without weak key constraints on the subkeys used in the output phase.

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