Showing papers on "GF(2) published in 1982"
27 citations
TL;DR: In this article, the alternating group of degree 6 over the field of two elements is shown to be completely reducible to the case of 2 elements, and certain representations of the alternating groups of degree 2 over the two elements are shown to also be reducible.
Abstract: Certain representations of the alternating group of degree 6 over the field of 2 elements are shown to be completely reducible.
3 citations
1 Jan 1982
TL;DR: Attempts to evaluate the possible threat to the Pohlig-Hellman cryptosystem have centered on modeling the algorithm so that some predictions could be made analytically about the number of iterations required to find logarithms over GF(2/sup p/) for p > 31.
Abstract: At the 1981 IEEE Symposium on Information Theory, T. Herlestam and R. Johannesson presented a heurestic method for computing logarithms over GF(2/sup p/). They reported computing logarithms over GF(2/sup 31/) with surprisingly few iterations and claimed that the running time of their algorithm was polynomial in p. If this were true, the algorithm could be used to cryptanalyze the Pohlig-Hellman cryptosystem, currently in use by Mitre Corporation for key distribution. The Mitre system operates in GF(2/sup 127/). However, the algorithm was not implemented for GF(2/sup p/) for p > 31 because it would require multiple precision arithmetic. Consequently attempts to evaluate the possible threat to the Pohlig-Hellman cryptosystem have centered on modeling the algorithm so that some predictions could be made analytically about the number of iterations required to find logarithms over GF(2/sup p/) for p > 31.
1 citations