Related papers: Algorithmic Obfuscation over GF($2^m$)
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…
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…
Elliptic curves over finite fields GF(2^n) play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with affine or projective coordinates. In this…
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…
Galois field (GF) arithmetic is used to implement critical arithmetic components in communication and security-related hardware, and verification of such components is of prime importance. Current techniques for formally verifying such…
This paper presents a high-level circuit obfuscation technique to prevent the theft of intellectual property (IP) of integrated circuits. In particular, our technique protects a class of circuits that relies on constant multiplications,…
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…
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…
Irreducible polynomials play an important role till now, in construction of 8-bit S-Boxes in ciphers. The 8-bit S-Box of Advanced Encryption Standard is a list of decimal equivalents of Multiplicative Inverses (MI) of all the elemental…
Approximate circuits often achieve exceptional trade-offs between computational accuracy and hardware efficiency, making them attractive for deployment as reusable Intellectual Property (IP) cores. However, safeguarding such circuits…
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…
In this paper, we propose an elliptic curve key generation processor over GF(2m) and GF(P) with Network-on-Chip (NoC) design scheme based on binary scalar multiplication algorithm. Over the Two last decades, Elliptic Curve Cryptography…
Substitution Box or S-Box had been generated using 4-bit Boolean Functions (BFs) for Encryption and Decryption Algorithm of Lucifer and Data Encryption Standard (DES) in late sixties and late seventies respectively. The S-box of Advance…
Elliptic Curve Cryptography (ECC) is an encryption method that provides security comparable to traditional techniques like Rivest-Shamir-Adleman (RSA) but with lower computational complexity and smaller key sizes, making it a competitive…
Algebraic geometrical concepts are playing an increasing role in quantum applications such as coding, cryptography, tomography and computing. We point out here the prominent role played by Galois fields viewed as cyclotomic extensions of…
Elliptic curve cryptography (ECC) has emerged as the dominant public-key protocol, with NIST standardizing parameters for binary field GF(2^m) ECC systems. This work presents a hardware implementation of a Hybrid Multiplication technique…
Cryptography is the study of techniques for ensuring the secrecy and authentication of the information. Public-key encryption schemes are secure only if the authenticity of the public-key is assured. Elliptic curve arithmetic can be used to…
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…
Shor's quantum algorithm for discrete logarithms applied to elliptic curve groups forms the basis of a "quantum attack" of elliptic curve cryptosystems. To implement this algorithm on a quantum computer requires the efficient implementation…
Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum…