CCA Secure Extended ElGamal Encryption Scheme Over CF(pⁿ)

This subject investigates the discrete logarithm problem over finite field CF(pⁿ), 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 implemented 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.