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This paper presents a new authenticated encryption scheme (AES) based on elliptic curve discrete logarithm problem (ECDLP) and discrete logarithm problem (DLP). Assume that we have one signer, and a set of U = (u1,u2,...,ul), which represents the verifiers group of L members. A single signer can encrypt and sign the message only if k (1 ≤ k ≤ l) or more verifiers agree to recover the message m on behalf of the whole verifier group U. In addition, we need a system authority with the task of generating the parameter, while a trusted clerk selected by the signer is needed to verify the signature’s validity. This scheme aims to overcome the modular exponentiation problem utilizing elliptic curve cryptography (ECC). To attain the desired benefit of enhanced performance and improved security, the presented technique is established based on the elliptic curve cryptosystem and discrete logarithm problems. Moreover, it resists strong attacks and operates efficiently. Compared to similar functional techniques, it requires a lower number of exponential and module operations.

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