Abstract
A key authentication scheme is a scheme that protects a user’s public key from modification and counterfeiting by an adversary. The new development and improvement of key authentication schemes should be made continuously so that the systems are safe and practical to be used. To the best of our knowledge, there is no key authentication using the elliptic curve so far. Thus, in this paper, we propose the first secure elliptic curve-based key authentication scheme with its security, relying on the difficulty of solving the elliptic curve discrete logarithm problem. We show that the proposed scheme is secure against various defined cryptographic attacks such as public keyword modification and keyword guessing attacks. Next, we analyze the computational time complexity of the algorithms by computing the number of modular operations needed in these algorithms together with asymptotical analysis of running time using O(g(n)) notation. It turns out that our scheme requires the least amount of time complexity of 203.36Tmul + Th for user registration phase, 58.12Tmul for key authentication phase, and offers less running time compared to some existing key authentication schemes.
Highlights
Diffie and Hellman (1976) solved a key distribution problem of secret key cryptography and proposed a novel idea of modern cryptography that is called the public-key cryptography. They proposed that any two communicating users need not be shared a common secret key, but instead, each user needs to generate two keys, namely public and private keys
There are many key authentication schemes developed based on factoring and discrete logarithm problems
We design a key authentication scheme based on the hardness of solving the elliptic curve discrete logarithm problem
Summary
Diffie and Hellman (1976) solved a key distribution problem of secret key cryptography and proposed a novel idea of modern cryptography that is called the public-key cryptography. They proposed that any two communicating users need not be shared a common secret key, but instead, each user needs to generate two keys, namely public and private keys. One of the main components in public-key cryptographic systems is a cryptosystem. One of the main issues in designing any public-key cryptographic systems is the security of its public key. The cryptographic solution to this problem is via Key Authentication Scheme (KAS). We make a comparison of the new and existing schemes in terms of attacks and time complexity
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