Patent
Method and apparatus for arithmetic operation and recording medium of method of operation
Reads0
Chats0
TLDR
In this paper, a polynominal comprising powers of the basic unit of computer operation is used to determine integer remainders, and no shift operation is required as opposed to the conventional method, which can be determined simply by addition and subtraction.Abstract:
An integer Z101 is divided by another integer I102 to determine the remainder R109 The integer I102 is expressed by a polynominal comprising powers of the basic unit of computer operation By limiting the divisor according to the basic unit of computer operation, no shift operation is required as opposed to the conventional method, and remainders can thus be determined simply by addition and subtraction This allows code size to be compact, resulting in high-speed determination of integer remaindersread more
Citations
More filters
Patent
Data processing system and data processing method
TL;DR: A technique for efficient encryption for use with devices such as smartcards restricted in memory resource was proposed in this article, including a calculation unit for reconstructing a large number of small primes, a sieving unit for checking the divisibility of an integer by small primimes, and a primality testing unit.
Patent
Computation method, computing device and computer program
Kouichi Itoh,Kenji Mukaida +1 more
TL;DR: In this paper, the computing device calculates an equivalence H0≡2m*k+1 (mod n) relating to a divisor n of 2m *k + 1 (step A), and performs a correction operation by H=REDC (H, G)n for g=2k*G(p, m, k) when 2p>m×k.
Patent
Parallel division algorithm and parallel division calculator
TL;DR: In this article, the remainder of dividing A by B in the K-th step is calculated, and a method of multiplying A by k-th of 10 mode B is utilized for parallelly working out the remainder.
Patent
Efficient remainder calculation for even divisors
TL;DR: In this article, the authors present a circuit, method, and computer-readable media for calculating xmody, wherein x and y are binary numbers, and y is an even number.
Patent
Method and apparatus for modulo operation with a class of divisors
TL;DR: In this paper, a low complexity implementation of remainder computation of any number when the divisor belongs to a type of numbers that can be represented as 2k+1 is presented.
References
More filters
Patent
Method and apparatus for public key exchange in a cryptographic system
TL;DR: In this article, the authors proposed an elliptic curve cryptosystem that uses elliptic curves defined over finite fields comprised of special classes of numbers to optimize the modulo arithmetic required in the enciphering and deciphering process.
Patent
Method and apparatus for performing finite field division
TL;DR: In this article, an apparatus and method for simplifying a finite field division, including inputs for the initial condition signals a, b, and p(x), and providing at an output node the signal c(x) without intermediate inverter circuitry for finding 1/b(x).
Journal ArticleDOI
Integer Convolutions over the Finite Field $GF( {3 \cdot 2^n + 1} )$
TL;DR: It is shown that the fast Fourier transform algorithm can be utilized to yield fast convolutions of integer numbers without round-off error.
Journal ArticleDOI
Generalized Fermat-Mersenne number theoretic transform
TL;DR: In this article, a generalization of the Fermat and Mersenne number transform is proposed, where transforms are defined over finite fields and rings, and conditions necessary for these numbers to be prime are established.