| 摘要 |
The invention concerns a public key cryptographic method applicable to data recorded in the form of bits on a medium operable by one or more calculating entities adapted to processing input data x to supply output data x', comprising at least a data processing step, enabling, in accordance with the form of embodiment, to supply an encryption procedure, a Fiat-Shamir zero-knowledge identity proof procedure, an electronic signature procedure or a procedure performing a one-way function, while using square matrices. If a message to be encrypted is a vector x of a module with dimension 3, E, x is completed to form the base {x, y, z}, the resulting matrix g<-1> is then taken into consideration, and if F is a matrix 3x3 capable of diagonalization which constitutes the public key, the encrypted message is (g<-1>Fg, xi (y,z)<i>xi</i> + y + z). The zero-knowledge proof can be produced by using said method but in returning to the strike holder the decrypted message and by operating on a fraction ring of a non-commutative ring. The signature procedure is derived directly from Guillou and Quisquater application to transform a zero-knowledge proof into a signature schema. |
