相关论文: Secure Montgomery Multiplication and Repeated Squa…

We present a method to increase the dynamical range of a Residue Number System (RNS) by adding virtual RNS layers on top of the original RNS, where the required modular arithmetic for a modulus on any non-bottom layer is implemented by…

We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…

We present Modular Polynomial (MP) Codes for Secure Distributed Matrix Multiplication (SDMM). The construction is based on the observation that one can decode certain proper subsets of the coefficients of a polynomial with fewer evaluations…

As society becomes more reliant on computers, cryptographic security becomes increasingly important. Current encryption schemes include the ElGamal signature scheme, which depends on the complexity of the discrete logarithm problem. It is…

Residue number systems (RNS) represent numbers by their remainders modulo a set of relatively prime numbers. This paper pro- poses an efficient hardware implementation of modular multiplication and of the modulo function (X(mod P)), based…

Montgomery modular multiplication is widely-used in public key cryptosystems (PKC) and affects the efficiency of upper systems directly. However, modulus is getting larger due to the increasing demand of security, which results in a heavy…

This paper presents a new refutation procedure for multimodular systems of integer constraints that commonly arise when verifying cryptographic protocols. These systems, involving polynomial equalities and disequalities modulo different…

In this paper, we derive a new computational algorithm for Barrett technique for modular polynomial multiplication, termed BA-P. BA-P is then applied to a new residue arithmetic based Barrett algorithm for modular polynomial multiplication…

In classic settings of garbled circuits, each gate type is leaked to improve both space and speed optimization. Zahur et al. have shown in EUROCRYPT 2015 that a typical linear garbling scheme requires at least two $\lambda$-bit elements per…

Parallel supercomputer-based Monte Carlo applications depend on pseudorandom number generators that produce independent pseudorandom streams across many separate processes. We propose a new scalable class of parallel pseudorandom number…

In this paper, new schemes for a squarer, multiplier and divider of complex numbers are proposed. Traditional structural solutions for each of these operations require the presence some number of general-purpose binary multipliers. The…

With the surge of the powerful quantum computer, lattice-based cryptography proliferated the latest cryptography hardware implementation due to its resistance against quantum computers. Among the computational blocks of lattice-based…

We study the problem of differentially private (DP) secure multiplication in distributed computing systems, focusing on regimes where perfect privacy and perfect accuracy cannot be simultaneously achieved. Specifically, N nodes…

Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular,…

We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly…

In this paper, we present secure distributed matrix multiplication (SDMM) schemes over the complex numbers with good numerical stability and small mutual information leakage by utilizing polynomial interpolation with roots of unity.…

Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus…

Multiplication of quantum states is a frequently used function or subroutine in quantum algorithms and applications, making quantum multipliers an essential component of quantum arithmetic. However, quantum multiplier circuits suffer from…

We consider the problems of Private and Secure Matrix Multiplication (PSMM) and Fully Private Matrix Multiplication (FPMM), for which matrices privately selected by a master node are multiplied at distributed worker nodes without revealing…

Garbling schemes are vital primitives for privacy-preserving protocols and secure two-party computation. This paper presents a projective garbling scheme that assigns $2^n$ values to wires in a circuit comprising XOR and unary projection…