Related papers: Efficient Parallel Verification of Galois Field Mu…
Galois field (GF) arithmetic circuits find numerous applications in communications, signal processing, and security engineering. Formal verification techniques of GF circuits are scarce and limited to circuits with known bit positions of…
Current techniques for formally verifying circuits implemented in Galois field (GF) arithmetic are limited to those with a known irreducible polynomial P(x). This paper presents a computer algebra based technique that extracts the…
The finite field multiplier is mainly used in many of today's state of the art digital systems and its hardware implementation for bit parallel operation may require millions of logic gates. Natural causes or soft errors in digital design…
The utilization of finite field multipliers is pervasive in contemporary digital systems, with hardware implementation for bit parallel operation often necessitating millions of logic gates. However, various digital design issues, whether…
Galois Field arithmetic blocks are the key components in many security applications, such as Elliptic Curve Cryptography (ECC) and the S-Boxes of the Advanced Encryption Standard (AES) cipher. This paper introduces a novel hardware…
Finite field multiplier is mainly used in error-correcting codes and signal processing. Finite field multiplier is regarded as the bottleneck arithmetic unit for such applications and it is the most complicated operation over finite field…
This paper presents a fast and effective computer algebraic method for analyzing and verifying non-linear integer arithmetic circuits using a novel algebraic spectral model. It introduces a concept of algebraic spectrum, a numerical form of…
Word-level verification of arithmetic circuits with large operands typically relies on arbitrary-precision arithmetic, which can lead to significant computational overhead as word sizes grow. In this paper, we present a hybrid algebraic…
Galois field arithmetic circuits find application in a range of domains including error correction codes, communications, signal processing, and security engineering. This paper aims to elucidate the importance of error detection and…
Linear network coding requires arithmetic operations over Galois fields, more specifically over finite extension fields. While coding over GF(2) reduces to simple XOR operations, this field is less preferred for practical applications of…
We present optimized quantum circuits for GF$(2^m)$ multiplication and division operations, which are essential computing primitives in various quantum algorithms. Our ancilla-free GF multiplication circuit has the gate count complexity of…
We show how the output of the algorithm to compute modular Galois representations described in our previous article can be certified. We have used this process to compute certified tables of such Galois representations obtained thanks to an…
This work presents an algorithm to generate depth, quantum gate and qubit optimized circuits for $GF(2^m)$ squaring in the polynomial basis. Further, to the best of our knowledge the proposed quantum squaring circuit algorithm is the only…
Multiplication over binary fields is a crucial operation in quantum algorithms designed to solve the discrete logarithm problem for elliptic curve defined over $GF(2^n)$. In this paper, we present an algorithm for constructing quantum…
We describe an efficient implementation of a hierarchy of algorithms for multiplication of dense matrices over the field with two elements (GF(2)). In particular we present our implementation -- in the M4RI library -- of Strassen-Winograd…
Masking is a widely-used effective countermeasure against power side-channel attacks for implementing cryptographic algorithms. Surprisingly, few formal verification techniques have addressed a fundamental question, i.e., whether the masked…
This paper generalizes the method proposed by Poulliat et al. for the determination of the optimal Galois Field coefficients of a Non-Binary LDPC parity check constraint based on the binary image of the code. Optimal, or almost-optimal,…
The problem of verifying multi-threaded execution against the memory consistency model of a processor is known to be an NP hard problem. However polynomial time algorithms exist that detect almost all failures in such execution. These are…
Automatic and efficient verification of multiplier designs, especially through a provably correct method, is a difficult problem. We show how to utilize a theorem prover, ACL2, to implement an efficient rewriting algorithm for multiplier…
Phase-field models are widely employed to simulate microstructure evolution during processes such as solidification or heat treatment. The resulting partial differential equations, often strongly coupled together, may be solved by a broad…