Can a fast signature scheme without secret key be secure
Un Schema de Signature Courte et Rapide N'Utilisant pas de CLE Secrete Peut-IL Etre Fiable?
Another title could have been "A probabilistic factorization algorithm in GL(2,p)". However, the problem is to calculate a fast and short signature associated with a plaintext inscribed on an erasable support. The signature should be written down in a book accompanying the record in order that it could be check ed anytime that the latter has not been changed. J. BOSSET  suggest such a scheme together with an algorithm for computing a signature. The 64 characters needed for the plaintext are identified with a subset of GL(2,p), p=997. The signature is the product of the matrices corresponding to the plaintext characters taken in the order where they appear. Such a scheme could be broken if it is possible to factorize an element of GL(2,p) into t=16 r factors, each one in a subset Ui of GL(2,p) of size 64 , i=1,...,t. We here assume one hypothesis only on uniform probability distributions of random variables defined on product sets Vj=Ujr+1×...×U(j+1)r, j=0,...,15. In consideration on which, a probabilistic factorization algorithm in GL(2,p) is introduced.
It is shown that for p=10,007, drawing according to a uniform probability distribution a sequence of 11,952 elements in each Vj provides the whole needed material to factorizing with a probability of success of at least 97%. The most expensive operation in the algorithm is sorting each of the sequences.
KeywordsGeometric Series Stirling Number Short Signature Bernoulli Trial Uniform Probability Distribution
Unable to display preview. Download preview PDF.
- J. BOSSET: "Contre les risques d'altération, un système de certification des informations", 01 Informatique no 107, Février 1977.Google Scholar
- W. FELLER: "An introduction to probability theory and its applications", Wiley, 1968.Google Scholar
- L. COMTET: "Advanced combinatoris", D. Reidel, 1974.Google Scholar