Patent ID: 7778414

Claim:
A method for encrypting data according to an asymmetrical method using a processor, based on a factorization problem, comprising: providing a public key to the processor; and providing a private key to the processor; wherein the public key includes composite number n; the private key is made up of the factorization of n; a message m=(m 1 , m 2 ) to be encrypted is made up of at least components m 1 and m 2 ; an encryption function f(x) is iterated a total of L times, with c=(c 1 , c 2 )=f L (m), c 1 , and c 2 being integral numbers; f(m)=(f 1 (m),f 2 (m)) being applicable, and f 1 =(m 1 op 1 m 2 ) mod n as well as f 2 =(m 1 , op 2 m 2 ) mod n; the encryption function f(x) being selected in such a way that the encryption iteration can be reversed by the L-fold solution of a quadratic equation modulo n, it thus being possible to retrieve the original message from the encrypted information c=(c 1 , c 2 ), wherein a multivaluedness of the quadratic equation is eliminated by additional bits of a i and b i to obtain a set of roots and by calculating a parity and a Jacobi symbol which, in the case of prime numbers of form 3 mod 4, can be communicated by 2bits per iteration step.