public key encryption and decryption method of a finite field multiplication group with a Meisen prime number

Abstract

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.

Description

technical field [0001] The technology of the present invention about public key encryption and decryption is a public key encryption and decryption method using a finite field multiplicative group whose order is a Mersenne prime number. Background technique [0002] Throughout the history of cryptography, the key exchange or DH key exchange method invented by Whitfield Diffie and Martin Hellman in 1976 laid the foundation of the public key cryptosystem, and its proposal is considered a milestone in cryptography. The characteristic of public key cryptography is that two keys are used in its encryption and decryption algorithm, one is the private key for decryption; the other is the public key for encryption. Public and private keys are different but related. If only the encryption algorithm and the public key are known, the private key for decryption cannot be obtained. [0003] The basic steps of the public key encryption and decryption system are as follows. [0004] The...

AI Technical Summary

Problems solved by technology

If only the encryption algorithm and the public key are known, the decryption private key cannot be obtained

Images