一种基于有限域乘法单群的公钥密码算法及实现

A Public-key Cryptographic Algorithm Based on Galois Field Multiplication Single Group

公钥密码是一种非对称加密密码算法,典型的公钥密码算法有RSA、ElGamal和椭圆曲线密码(Elliptic Curves Cryptography,ECC)算法,这些算法都有各自的优缺点,适应不同场合。基于阶为梅森素数的有限域乘法单群,提出了一种新的Diffie-Hellman公钥密码算法。该算法本身基于模2运算,便于软硬件实现,若用硬件实现,只需移位寄存器和异或门。理论分析和计算仿真均证明了该算法的有效性,性能优于经典的RSA和ElGamal公钥算法。

Public key cryptography is an asymmetric encryption algorithm. Typical public key cryptography algorithms include RSA, ElGamal and ECC(Elliptic Curves Cryptography). These algorithms have their own advantages and disadvantages and are suitable for different occasions. In this paper, a new DiffieHellman public key cryptography algorithm based on the finite field multiplicative single group whose order is Mersenne prime is proposed. The algorithm itself is based on modulo-2 operation, which is convenient for software and hardware implementation. If it is implemented by hardware, only a shift register and an XOR gate are needed. Theoretical analysis and computational simulation both prove its effectiveness and performance are better than the classical RSA and ElGamal public key cryptography.