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Title: Method for exponentiating in cryptographic systems

Abstract

An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a preapproved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g.sup.e ; transmitting the value g.sup.e to a remote facility by a communications network; receiving the value g.sup.e at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g.sup.xi ; computi The United States Government has rights in this invention pursuant to Contract No. DE-AC04-76DP00789 between the Department of Energy and AT&T Company.

Inventors:
 [1];  [2];  [1]
  1. Albuquerque, NM
  2. San Diego, CA
Issue Date:
Research Org.:
AT&T
OSTI Identifier:
869219
Patent Number(s):
5299262
Assignee:
United States of America as represented by United States (Washington, DC)
Patent Classifications (CPCs):
G - PHYSICS G06 - COMPUTING G06F - ELECTRIC DIGITAL DATA PROCESSING
H - ELECTRICITY H04 - ELECTRIC COMMUNICATION TECHNIQUE H04L - TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
DOE Contract Number:  
AC04-76DP00789
Resource Type:
Patent
Country of Publication:
United States
Language:
English
Subject:
method; exponentiating; cryptographic; systems; improved; utilizing; exponentiation; provided; advantage; reducing; multiplications; required; determine; legitimacy; message; user; basic; comprises; steps; selecting; key; preapproved; integer; keys; value; represents; digital; signature; generate; transmitting; remote; facility; communications; network; receiving; verifying; originating; legitimate; step; initializing; plurality; memory; locations; values; xi; computi; united; government; rights; pursuant; contract; de-ac04-76dp00789; department; energy; company; method comprises; method utilizing; method comprise; communications network; memory location; /380/713/

Citation Formats

Brickell, Ernest F, Gordon, Daniel M, and McCurley, Kevin S. Method for exponentiating in cryptographic systems. United States: N. p., 1994. Web.
Brickell, Ernest F, Gordon, Daniel M, & McCurley, Kevin S. Method for exponentiating in cryptographic systems. United States.
Brickell, Ernest F, Gordon, Daniel M, and McCurley, Kevin S. Sat . "Method for exponentiating in cryptographic systems". United States. https://www.osti.gov/servlets/purl/869219.
@article{osti_869219,
title = {Method for exponentiating in cryptographic systems},
author = {Brickell, Ernest F and Gordon, Daniel M and McCurley, Kevin S},
abstractNote = {An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a preapproved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g.sup.e ; transmitting the value g.sup.e to a remote facility by a communications network; receiving the value g.sup.e at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g.sup.xi ; computi The United States Government has rights in this invention pursuant to Contract No. DE-AC04-76DP00789 between the Department of Energy and AT&T Company.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1994},
month = {1}
}

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Works referenced in this record:

New directions in cryptography
journal, November 1976


A method for obtaining digital signatures and public-key cryptosystems
journal, February 1978


Some Observations on Parallel Algorithms for Fast Exponentiation in $\operatorname{GF}(2^n)$
journal, August 1990


Basic digit sets for radix representation
journal, October 1982


Efficient signature generation by smart cards
journal, January 1991


On the Evaluation of Powers
journal, March 1976


A public key cryptosystem and a signature scheme based on discrete logarithms
journal, July 1985