RSA-ELGamal encryption and digital signature scheme over finite fields
A RSA-ELGamal encryption scheme for polynomials over finite fields was proposed based on enhanced RSA and ELGamal encryption algorithms.The new encryption scheme was based on the combination of large integer factorization problem(IFP)and difficult to solve discrete logarithm problem(DLP),making its security higher than that of a single RSA encryption algorithm and ELGamal encryption system using polynomial form over finite fields.The newly proposed encryption scheme can encrypt multiple plaintexts.When encrypting plaintexts,RSA's public key was introduced to hide them,resulting in high encryption efficiency and strong security.On the basis of the new encryption scheme,a one-way hash function was introduced,and a corresponding digital signature scheme was proposed.The signature scheme utilizes multiple receivers to verify and encrypt messages separately,further enhancing the probability of signature attacks.The security of encryption schemes and digital signatures were mainly based on the dual difficulty problem of factoring large integers and solving discrete logarithms,which were made signatures invincible and improved the security of such signature schemes.
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