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This paper introduces the concept of public key cryptosystem, whose security is based on Double Discrete Logarithm Problem (DDLP) with distinct discrete exponents in the multiplicative group of finite fields. The adversary has to solve distinct discrete logarithm problems simultaneously in order to recover a corresponding plaintext from the received cipertext. Therefore, this scheme is expected to gain a higher level of security. The authors next show that, the newly developed scheme is efficient with respect to encryption and decryption and the validity of this algorithm is proven by applying to message that are text and returning the original message in various numerical examples.
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