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基于Chebyshev多项式和离散对数问题设计了一种新的安全有效的公钥加密系统方案。该方案回避了现有大多数基于混沌的加密系统的实数域问题,即在实数域不存在难解的数学问题,而利用Chebyshev多项式的本群属性,在有限域上实现加密、解密和数字签名操作,而且本方案选择的变量是超过1的正整数,这就避免了不同Chebyshev多项式在|x|≤1区间通过同一点问题。通过深入的性能分析,可以证明本方案在安全性和效率方面都优于ElGamal加密方案。
Based on Chebyshev polynomial and discrete logarithm problem, a new scheme of public key encryption system is designed. The scheme avoids the real number domain problem of most existing chaos-based cryptosystems, that is, there is no math problem in the real number domain, and the properties of Chebyshev polynomials are used to realize the encryption, decryption and digital signature on the finite field Operation, and the variables selected by the program are positive integers over 1, which avoids the problem of different Chebyshev polynomials passing through the same point in the | x | ≤1 interval. Through in-depth performance analysis, we can prove that this scheme is superior to ElGamal encryption scheme in terms of security and efficiency.