基于CF(p^n)的CCA安全ElGamal加密体制

CCA Secure Extended ElGamal Encryption Scheme Over CF(p^n)

基于CF(pn)域上的离散对数困难性问题,提出一种基于CF(pn)域的ElGamal加密算法,并在标准模型下证明该加密算法满足IND-CCA安全性要求。该算法的安全参数k的大小由构成CF(pn)域的素数p和多项式的阶n共同决定,改变了传统ElGamal算法安全性对大素数p的唯一依赖的现状。利用C语言实现了基于CF(pn)的ElGamal算法,而且通过异或和移位这类简单操作即可编程实现。通过与RSA、ElGamal、ECC、AES算法的效率对比,发现基于CF(2n)的ElGamal算法在执行效率方面比传统的ElGamal加密算法快1 000倍,比RSA快3倍,比ECC快2 000倍。

This subject investigates the discrete logarithm problem over finite field CF （ p n ） , proposes a ElGamal encryption scheme over finite field CF（pn） , and proves that proposed the scheme satisfies IND - CCA security without oracle model. Futhermore, the size of algorithm,s security parameter k is contingent on prime p and polymonial degree n , which define the finite field CF（pn）. The method alters the status in which traditional ElGamal algorithm security only relies on size of big prime p. We not only utilize C laguage to implement ElGamal algorithm over finite field CF（2n） ,but also ElGamal algorithm over finite field CF（2n） could be imple-mented by simple operations such as xor and shifting in aspect of programing implement. By means of comparing efficiencies with other exist schemes, such as RSA, traditional ElGamal, ECC, and AES algorithm. Then, we found that ElGamal algorithm over finite field CF（2n） runs 1 000 times faster than traditional ElGamal algorithm, three times faster than RSA, and 2 000 times faster than ECC.