arXiv subjects

M. Anwar Hasan

Publications and source records attributed to M. Anwar Hasan.

3 recordsLinked to original sources

arXiv2024

Sharing the Path: A Threshold Scheme from Isogenies and Error Correcting Codes

In 2022, a prominent supersingular isogeny-based cryptographic scheme, namely SIDH, was compromised by a key recovery attack. However, this attack does not undermine the isogeny path problem, which remains central to the security of isogeny-based cryptography. Following the attacks by Castryck and Decru, as well as Maino and Martindale, Robert gave a mature and polynomial-time algorithm that transforms the SIDH key recovery attack into a valuable cryptographic tool. In this paper, we combine this tool with advanced encoding techniques to construct a novel threshold scheme.

cs.CR↗

arXiv2024

On efficient normal bases over binary fields

Binary field extensions are fundamental to many applications, such as multivariate public key cryptography, code-based cryptography, and error-correcting codes. Their implementation requires a foundation in number theory and algebraic geometry and necessitates the utilization of efficient bases. The continuous increase in the power of computation, and the design of new (quantum) computers increase the threat to the security of systems and impose increasingly demanding encryption standards with huge polynomial or extension degrees. For cryptographic purposes or other common implementations of finite fields arithmetic, it is essential to explore a wide range of implementations with diverse bases. Unlike some bases, polynomial and Gaussian normal bases are well-documented and widely employed. In this paper, we explore other forms of bases of $\mathbb{F}_{2^n}$ over $\mathbb{F}_2$ to demonstrate efficient implementation of operations within different ranges. To achieve this, we leverage results on fast computations and elliptic periods introduced by Couveignes and Lercier, and subsequently expanded upon by Ezome and Sall. This leads to the establishment of new tables for efficient computation over binary fields.

cs.IT↗

arXiv2023

A code-based hybrid signcryption scheme

A key encapsulation mechanism (KEM) that takes as input an arbitrary string, i.e., a tag, is known as tag-KEM, while a scheme that combines signature and encryption is called signcryption. In this paper, we present a code-based signcryption tag-KEM scheme. We utilize a code-based signature and an IND-CCA2 (adaptive chosen ciphertext attack) secure version of McEliece's encryption scheme. The proposed scheme uses an equivalent subcode as a public code for the receiver, making the NPcompleteness of the subcode equivalence problem to be one of our main security assumptions. We then base the signcryption tag-KEM to design a code-based hybrid signcryption scheme. A hybrid scheme deploys asymmetric- as well as symmetric-key encryption. We give security analyses of both our schemes in the standard model and prove that they are secure against IND-CCA2 (indistinguishability under adaptive chosen ciphertext attack) and SUF-CMA (strong existential unforgeability under chosen message attack).

cs.CR↗