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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 [1] 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.

Can a fast signature scheme without secret key be secure