A Public Key Encryption and Decryption Method for Finite Field Multiplicative Groups with Mersenne Prime Order
A technology of public key encryption and Mersenne prime number, which is applied to the public key of secure communication, digital transmission system, secure communication device, etc., and can solve the problem that the decryption private key cannot be obtained
Active Publication Date: 2022-04-15
江宝安
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Problems solved by technology
If only the encryption algorithm and the public key are known, the decryption private key cannot be obtained
Method used
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Embodiment Construction
[0015] Take p=5, primitive irreducible polynomial ,
[0016] array form .
[0017] random selection .
[0018] ;
[0019] in the same way
[0020]
[0021]
[0022]
[0023] Pick .
[0024] random private key .
[0025] but
[0026] .
[0027] Pick
[0028]
[0029] random pick .
[0030]
[0031]
[0032]
[0033]
[0034] Pick
[0035]
[0036] take plaintext
[0037] ,
[0038] encryption .
[0039] decrypt ,
[0040] ,
[0041]
[0042] That is, d=m.
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The invention is a public key encryption method based on finite field multiplication group, wherein p is a prime number and makes it a Mersenne prime number. Finite fields are isomorphic to polynomial fields, where is a primitive polynomial of degree p. The order of the finite field multiplication group is a Mersenne prime number, so the order of any non-identity element a is, in the public key cryptosystem, the receiver B discloses the random element a, and the primitive polynomial q is used as the system parameter. k1 is the private key, public key g (among them). Encryptor A generates random number k2, performs modular exponentiation operation, encrypts plaintext m and performs modular multiplication operation to generate ciphertext. Decryptor accepts the ciphertext and decrypts it using private key k1 Plaintext m The present invention can be applied to symmetric encryption, public key encryption, digital signature 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...
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IPC IPC(8): H04L9/30H04L9/40
Inventor 江宝安
Owner 江宝安