July 1981 - Vol. 24 No. 7

July 1981 issue cover image

Features

Research and Advances

Representing super-sparse matrices with perturbed values

This paper describes a form of purposeful data perturbation in a linear programming model which pertains to uncertainties in the magnitudes of the matrix coefficients. A problem in value pool construction is described first, then a resolution based on a new concept, “covering lattices.” Computer representations of real values, limited by finite precision, is an example of a covering lattice. After presenting the strategy and tactical variations, the effects of resident distortion are analyzed. Several theorems are presented that measure bias under a variety of assumptions. An appendix is included that contains mathematical proofs.
Research and Advances

On the security of multiple encryption

Double encryption has been suggested to strengthen the Federal Data Encryption Standard (DES). A recent proposal suggests that using two 56-bit keys but enciphering 3 times (encrypt with a first key, decrypt with a second key, then encrypt with the first key again) increases security over simple double encryption. This paper shows that although either technique significantly improves security over single encryption, the new technique does not significantly increase security over simple double encryption. Cryptanalysis of the 112-bit key requires about 256 operations and words of memory, using a chosen plaintext attack. While DES is used as an example, the technique is applicable to any similar cipher.

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