Related papers: A Non-commutative Cryptosystem Based on Quaternion…
The most known of public key cryptosystem was introduced in 1978 by Rivest, Shamir and Adleman [19] and now called the RSA public key cryptosystem in their honor. Later, a few authors gave a simply extension of RSA over algebraic numbers…
Quantum money is the cryptographic application of the quantum no-cloning theorem. It has recently been instantiated by Montgomery and Sharif (Asiacrypt '24) from class group actions on elliptic curves. In this work, we propose a concrete…
The best qubit one-way quantum key distribution (QKD) protocol can tolerate up to 14.1% in the error rate. It has been shown how this rate can be increased by using larger quantum systems. The polarization state of a biphoton can encode a…
Post-Quantum Cryptographic (PQC) algorithms are mathematically secure and resistant to quantum attacks but can still leak sensitive information in hardware implementations due to natural faults or intentional fault injections. The intent…
Although blockchain, the supporting technology of Bitcoin and various cryptocurrencies, has offered a potentially effective framework for numerous applications, it still suffers from the adverse affects of the impossibility triangle.…
The Burrows-Wheeler-Transform (BWT), a reversible string transformation, is one of the fundamental components of many current data structures in string processing. It is central in data compression, as well as in efficient query algorithms…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
Rotary Positional Embeddings (RoPE) have demonstrated exceptional performance as a positional encoding method, consistently outperforming their baselines. While recent work has sought to extend RoPE to higher-dimensional inputs, many such…
Blockchain is a decentralized system that allows transaction transmission and storage according to the roles of the Consensus algorithm and Smart contracts. Non-fungible tokens (NFTs) consolidate the best characteristics of blockchain…
Quantum cryptography -- the application of quantum computing techniques to cryptography has been extensively investigated. Two major directions of quantum cryptography are quantum key distribution (QKD) and quantum encryption, with the…
Commutative hypercomplex algebras offer significant advantages over traditional quaternions due to their compatibility with linear algebra techniques and efficient computational implementation, which is crucial for broad applicability. This…
Qutrit (or ternary) structures arise naturally in many quantum systems, particularly in certain non-abelian anyon systems. We present efficient circuits for ternary reversible and quantum arithmetics. Our main result is the derivation of…
In this paper we propose a method to construct logarithmic signatures which are not amalgamated transversal and further do not even have a periodic block. The latter property was crucial for the successful attack on the system MST3 by…
The Number Theoretic Transform (NTT) is a critical computational bottleneck in many lattice-based postquantum cryptographic (PQC) algorithms. By leveraging the Fast Fourier Transform (FFT) algorithm, the NTT of a polynomial of degree N - 1…
The study of quantum cryptography and quantum non-locality have traditionnally been based on two-level quantum systems (qubits). In this paper we consider a generalisation of Ekert's cryptographic protocol [Ekert] where qubits are replaced…
This work presents some novel techniques to enhance an encryption scheme motivated by classical McEliece cryptosystem. Contributions include: (1) using masking matrices to hide sensitive data, (2) allowing both legitimate parties to…
We propose a framework for constructing efficient code-based encryption schemes from codes that do not hide any structure in their public matrix. The framework is in the spirit of the schemes first proposed by Alekhnovich in 2003 and based…
Lattice-based cryptography is a foundation for post-quantum security, with the Learning with Errors (LWE) problem as a core component in key exchange, encryption, and homomorphic computation. Structured variants like Ring-LWE (RLWE) and…
We bring in here a novel algebraic approach for attacking the McEliece cryptosystem. It consists in introducing a subspace of matrices representing quadratic forms. Those are associated with quadratic relationships for the component-wise…
The Bivariate Function Hard Problem (BFHP) has been in existence implicitly in almost all number theoretic based cryptosystems. This work defines the BFHP in a more general setting and produces an efficient asymmetric cryptosystem. The…