Abstract Since the proposal of NTRU cryptosystem, many variants were proposed by the researcher using different‐different algebraic structure. In this article, we try to explore the existing variants of NTRU cryptosystem with their comparative study. Copyright © 2016 John Wiley & Sons, Ltd.

ABSTRACT Proxy signature is a specific digital signature, which allows an original signer to delegate her signing capability to proxy signer and then, the later can perform message signing on behalf of the former. Authentication is a desired property in cryptographic protocols. The proxy signature provides this property. In this article, we cover the research progress made on proxy signature and investigate its relationships with other existing signature schemes having continuous progress until now. We also provide real‐world scenarios, to understand better the situations, where these schemes are applicable for security purposes. We analyze the security properties of existing schemes and make a comparison among them on the basis of different number theoretic problems. Some open problems are also discussed, to the best of our knowledge. In addition, we provide some future directions, which can be used as a hint to work further in the area of proxy signature. We hope that this article will provide a ready reference to work in the related area. Copyright © 2012 John Wiley & Sons, Ltd.