The invention relates to a public key
encryption method based on a finite field (shown in the formula in the specification) multiplication group, in particular to a public key
encryption method basedon the finite field ( shown in the formula in the specification) multiplication group. wherein p is a prime number, and the formula (1) is shown in the specification, and p is a prime number and is made to be a Mesene number. Finite field isomorphism and polynomial field (
img field RE-482803DEST _ PATH _ IMAGE001. TIF) isomorphism and polynomial field (
img field RE-637709DEST _ PATH _ IM wherein the
structural formula of the polynomial is as shown in the specification, the
structural formula of the polynomial is as shown in the specification, and the
structural formula of the polynomial is asshown in the specification, wherein the structural formula of the polynomial is as shown in the specification, and the structural formula of the polynomial is as shown in the specification. In the Finite field multiplication group wherein the order of the formula (I) is shown in the specification, the order of the formula (I) is shown in the specification, and the order of the formula (I) is shownin the specification. The order of the formula (II) is shown in the specification. Therefore, the order of the element a of any non-unit element is shown in the specification, wherein the order of the element a of any non-unit element is shown in the specification; the order of the element b of any non-unit element is shown in the specification; The invention discloses a
public key cryptosystem.the
receiver B discloses a random element a; the primitive polynomial q is used as a
system parameter; the k1 is seen as a private key by the random number; A public key g (shown in the specification)is disclosed. An
encryption party A generates a random number k2, and the random number k2 is smaller than or equal to 1 and smaller than or equal to 1. carrying out a
modular exponentiation operation (shown in the formula in the specification), carrying out a
modular exponentiation operation (shown in the formula in the specification), and carrying out a
modular exponentiation operation (shown in the formula in the specification), carrying out modular multiplication on the encrypted
plaintext m (shown in the formula in the specification), and carrying out modular multiplication on the encrypted
plaintext m, The method comprises the following steps that: a decryption party receives a
ciphertext, generates a
ciphertext according to the
ciphertext, and generates the ciphertext according tothe ciphertext. The decryption party receives the ciphertext and generates the ciphertext according to the ciphertext. and decrypting by using the private key k1 to obtain a
plaintext m. The method disclosed by the invention can be applied to the aspects of symmetric passwords, public key passwords, digital signatures and the like. The method disclosed by the invention can be applied to the fieldsof the symmetric passwords, the public key passwords, the digital signatures and the like.