Showing papers on "GF(2) published in 1987"
Patent•
9 Oct 1987TL;DR: In this paper, a circuit effects regular multiplication of two field elements in a Galois field GF(2 m ) is described, where each of the field elements is expressed by an m-bit binary member.
Abstract: A circuit effects regular multiplication of two
field elements in a Galois field GF(2 m ). Each of the field
elements is expressed by an m-bit binary member. The two
field elements are applied to a binary multiplier array
which generates (2m - 1)-bit partial prodcuts. The partial
products are divided by a generator polynomial of the Galois field to
produce final m-bit binary products.
36 citations
1 Jan 1987
TL;DR: Different data structures in GF(2n) and their correspondence to silicon architectures are investigated to examine possible hardware implementations of the Diffie-Hellman key exchange system.
Abstract: We investigate different data structures in GF(2n) and their correspondence to silicon architectures to examine possible hardware implementations of the Diffie-Hellman key exchange system.
27 citations
Patent•
26 Jun 1987TL;DR: In this article, the multiplicative inverse of the original divisor, A, is found by computing a conversion factor, D, and then multiplying A by D to convert it to an element C, where C is also an element of a smaller Galois Field, GF(2 M ), which is a subfield of GF( 2 2M ).
Abstract: The invention is an apparatus and/or method which enables one to divide two elements, A and B, of GF(2 2M ), that is, perform the operation B/A, by finding the multiplicative inverse of the divisor A, and then multiplying the inverse by the numerator, B. The multiplicative inverse, A -1 , of A is found by computing a conversion factor, D, and then multiplying A by D to convert it to an element C, where C is also an element of a smaller Galois Field, GF(2 M ), which is a subfield of GF(2 2M ). Specifically, C is equal to A 2 .spsp.M.sbsp.+1), or A 2 .spsp.M *A, in the field GF(2 2M ). Next, the multiplicative inverse, C -1 , of C in GF(2 M ) is found by appropriately entering a stored look-up table containing the 2 M elements of GF(2 M ). The multiplicative inverse, C -1 , of C is thereafter converted, by multiplying it by the conversion factor D calculated above, to the element of GF(2 2M ) which is the multiplicative inverse, A -1 , of the original divisor, A. The multiplicative inverse, A -1 , of A is then multiplied by B to calculate the quotient, B/A.
26 citations