Patent
Method for arithmetic operation and recording medium of method of operation
TLDR
In this article, 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
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Patent
Division of binary numbers
TL;DR: In this paper, an abridged value k determined, satisfies k = 2*(bl(b)-1) - bl(a) -bl(a), and a division with remainder is executed in which the dividend a is shortened by its k smallest bits, and the divisor b is divided by its smallest bits to obtain a quotient q and a shortened remainder t. This satisfies the relationship r = a - q*b and -b = r = b.
Patent
Polynomial quotient estimating method for e.g. cryptographic processor, involves dividing polynomial by right shifting bits, if polynomial`s degree is less than or equal to maximum degree, for obtaining polynomial quotient
TL;DR: In this paper, a polynomial is divided by performing a shift of bits towards the right of the set of bits, if a degree of the polylogarithm is less than or equal to the maximum degree.
References
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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.
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.
Patent
Method and apparatus for computing residue with respect to arbitrary modulus
TL;DR: In this paper, a method and apparatus for computing a residue of a modulo-"a" number with respect to an arbitrary modulus was presented. But it requires only a small memory capacity for the residue tables.
Patent
Early detection of overflow and exceptional quotient/remainder pairs for nonrestoring twos complement division
TL;DR: In this paper, a system for early detection of overflow or exceptional quotient/remainder pairs is used in conjunction with performing nonrestoring division using two's complement 2n bit dividends N and two n bit divisors D. The detection system uses only the divisor, dividend, and first partial remainder.
Proceedings ArticleDOI
Fast convolution using generalized Fermat/Mersenne number transforms
TL;DR: By using the generalized modulus numbers in computing fast convolution, the transform sequence lengths can be much greater than those obtained by either Fermat numbers or Mersenne numbers.