Nowadays, alternative models of elliptic curves like Montgomery, Edwards, twisted Edwards, Hessian, twisted Hessian, Huff’s curves and many others are very popular and many people use them in cryptosystems which are based on elliptic curve cryptography. Most of these models allow to use fast and complete arithmetic which is especially convenient in fast implementations that are side-channel attacks resistant. Montgomery, Edwards and twisted Edwards curves have always order of group of rational points divisible by 4. Huff’s curves have always order of rational points divisible by 8. Moreover, sometimes to get fast and efficient implementations one can choose elliptic curve with even bigger cofactor, for example 16. Of course the bigger cofactor is, the smaller is the security of cryptosystem which uses such elliptic curve. In this article will be checked what influence on the security has form of cofactor of elliptic curve and will be showed that in some situations elliptic curves with cofactor divisible by 2m are vulnerable for combined small subgroups and side-channel attacks.
Among rapid development of wireless communication, technology cryptography plays a major role in securing the personal information of the user. As such, many authentication schemes have been proposed to ensure secrecy of wireless communication but they fail to meet all the required security goals. The proposed signcryption scheme uses multi-factor authentication techniques such as user biometrics, smart card and passwords to provide utmost security of personal information. In general, wireless devices are susceptible to various attacks and resource constraint by their very nature. To overcome these challenges a lightweight cryptographic scheme called signcryption has evolved. Signcryption is a logical combination of encryption and digital signature in a single step. Thereby it provides necessary security features in less computational and communication time. The proposed research work outlines the weaknesses of the already existing Cao et al.’s authentication scheme, which is prone to biometric recognition error, offline password guessing attack, impersonation attack and replay attack. Furthermore, the proposed study provides an enhanced multi-factor authentication scheme using signcryption based on hyper elliptic curve cryptography and bio-hash function. Security of the proposed scheme is analyzed using Burrows-Abadi-Needham logic. This analysis reveals that the proposed scheme is computational and communication-efficient and satisfies all the needed security goals. Finally, an analysis of the study results has revealed that the proposed scheme protects against biometric recognition error, password guessing attack, impersonation attack, DoS attack and dictionary attack.