Homomorphic encryption and some black box attacks

This paper is a compressed summary of some principal definitions and concepts in the approach to the black box algebra being developed by the authors. We suggest that black box algebra could be useful in cryptanalysis of homomorphic encryption schemes, and that homomorphic encryption is an area of research where cryptography and black box algebra may benefit from exchange of ideas

On Decoding Schemes for the MDPC-McEliece Cryptosystem

Recently, it has been shown how McEliece public-key cryptosystems based on moderate-density parity-check (MDPC) codes allow for very compact keys compared to variants based on other code families. In this paper, classical (iterative) decoding schemes for MPDC codes are considered. The algorithms are analyzed with respect to their error-correction capability as well as their resilience against a recently proposed reaction-based key-recovery attack on a variant of the MDPC-McEliece cryptosystem by Guo, Johansson and Stankovski (GJS). New message-passing decoding algorithms are presented and analyzed. Two proposed decoding algorithms have an improved error-correction performance compared to existing hard-decision decoding schemes and are resilient against the GJS reaction-based attack for an appropriate choice of the algorithm's parameters. Finally, a modified belief propagation decoding algorithm that is resilient against the GJS reaction-based attack is presented

Variations of the McEliece Cryptosystem

Two variations of the McEliece cryptosystem are presented. The first one is based on a relaxation of the column permutation in the classical McEliece scrambling process. This is done in such a way that the Hamming weight of the error, added in the encryption process, can be controlled so that efficient decryption remains possible. The second variation is based on the use of spatially coupled moderate-density parity-check codes as secret codes. These codes are known for their excellent error-correction performance and allow for a relatively low key size in the cryptosystem. For both variants the security with respect to known attacks is discussed

Expanded Gabidulin Codes and Their Application to Cryptography

This paper presents a new family of linear codes, namely the expanded Gabidulin codes. Exploiting the existing fast decoder of Gabidulin codes, we propose an efficient algorithm to decode these new codes when the noise vector satisfies a certain condition. Furthermore, these new codes enjoy an excellent error-correcting capability because of the optimality of their parent Gabidulin codes. Based on different masking techniques, we give two encryption schemes by using expanded Gabidulin codes in the McEliece setting. According to our analysis, both of these two cryptosystems can resist the existing structural attacks. Our proposals have an obvious advantage in public-key representation without using the cyclic or quasi-cyclic structure compared to some other code-based cryptosystems

Developments in multivariate post quantum cryptography.

Ever since Shor\u27s algorithm was introduced in 1994, cryptographers have been working to develop cryptosystems that can resist known quantum computer attacks. This push for quantum attack resistant schemes is known as post quantum cryptography. Specifically, my contributions to post quantum cryptography has been to the family of schemes known as Multivariate Public Key Cryptography (MPKC), which is a very attractive candidate for digital signature standardization in the post quantum collective for a wide variety of applications. In this document I will be providing all necessary background to fully understand MPKC and post quantum cryptography as a whole. Then, I will walk through the contributions I provided in my publications relating to differential security proofs for HFEv and HFEv−, key recovery attack for all parameters of HFEm, and my newly proposed multivariate encryption scheme, HFERP

DAGS:Key encapsulation using dyadic GS codes

Code-based cryptography is one of the main areas of interest for NIST's Post-Quantum Cryptography Standardization call. In this paper, we introduce DAGS, a Key Encapsulation Mechanism (KEM) based on quasi-dyadic generalized Srivastava codes. The scheme is proved to be IND-CCA secure in both random oracle model and quantum random oracle model. We believe that DAGS will offer competitive performance, especially when compared with other existing code-based schemes, and represent a valid candidate for post-quantum standardization.</p

Envisioning the Future of Cyber Security in Post-Quantum Era: A Survey on PQ Standardization, Applications, Challenges and Opportunities

The rise of quantum computers exposes vulnerabilities in current public key cryptographic protocols, necessitating the development of secure post-quantum (PQ) schemes. Hence, we conduct a comprehensive study on various PQ approaches, covering the constructional design, structural vulnerabilities, and offer security assessments, implementation evaluations, and a particular focus on side-channel attacks. We analyze global standardization processes, evaluate their metrics in relation to real-world applications, and primarily focus on standardized PQ schemes, selected additional signature competition candidates, and PQ-secure cutting-edge schemes beyond standardization. Finally, we present visions and potential future directions for a seamless transition to the PQ era