Cryptography and Residue Arithmetic

Montgomery multiplication methods constitute the core of modular exponentiation, the most popular operation for encrypting and signing digital data in public-key cryptography. In this article, we study the operations involved in computing the Montgomery product, describe several high-speed, space-efficient algorithms…

• ÇETİN KAYA KOÇ

Özet henüz yok.

Özet henüz yok.

• ÇETİN KAYA KOÇ

We present a new low-complexity bit-parallel canonical basis multiplier for the field GF(2m) generated by an all-one-polynomial. The proposed canonical basis multiplier requires m/sup 2/-1 XOR gates and m/sup 2/ AND gates. We also extend this canonical basis multiplier to obtain a new bit-parallel normal basis multipl…

• ÇETİN KAYA KOÇ

An efficient algorithm for the multiplication in GF(2/sup m/) was introduced by Mastrovito. The space complexity of the Mastrovito multiplier for the irreducible trinomial x/sup m/+x+1 was given as m/sup 2/-1 XOR and m/sup 2/ AND gales. In this paper, we describe an architecture based on a new formulation of the multi…

• ÇETİN KAYA KOÇ

Özet henüz yok.

This paper presents a new parallel multiplier for the Galois field GF(2/sup m/) whose elements are represented using the optimal normal basis of type II. The proposed multiplier requires 1.5(m/sup 2/-m) XOR gates, as compared to 2(m/sup 2/-m) XOR gates required by the Massey-Omura multiplier. The time complexities of…

• ÇETİN KAYA KOÇ

Özet henüz yok.

Özet henüz yok.

• ERKAY SAVAŞ

Fully homomorphic encryption (FHE) is a technique that allows computations on encrypted data without the need for decryption and it provides privacy in various applications such as privacy-preserving cloud computing. In this article, we present two hardware architectures optimized for accelerating the encryption and d…

• ERKAY SAVAŞ

We present a new formulation of the Mastrovito multiplication matrix for the field GF(2/sup m/) generated by an arbitrary irreducible polynomial. We study in detail several specific types of irreducible polynomials, e.g., trinomials, all-one-polynomials, and equally-spaced-polynomials, and obtain the time and space co…

• ÇETİN KAYA KOÇ

Efficient lattice-based cryptosystems operate with polynomial rings with the Number Theoretic Transform (NTT) to reduce the computational complexity of polynomial multiplication. NTT has therefore become a major arithmetic component (thus computational bottleneck) in various cryptographic constructions like hash funct…