Multiplication by an Integer Constant
نویسنده
چکیده
We present and compare various algorithms, including a new one, allowing to perform multiplications by integer constants using elementary operations. Such algorithms are useful, as they occur in several problems, such as the Toom-Cook-like algorithms to multiply large multiple-precision integers, the approximate computation of consecutive values of a polynomial, and the generation of integer multiplications by compilers. Key-words: integer multiplication, addition chains Multiplication par une constante entière Résumé : Nous présentons et comparons divers algorithmes, dont un nouveau, permettant d’effectuer des multiplications par des constantes entières à l’aide d’opérations élémentaires. De tels algorithmes sont utiles, car ils interviennent dans plusieurs problèmes, comme les algorithmes du style Toom-Cook pour multiplier des entiers à grande précision, le calcul approché de valeurs consécutives d’un polynôme et la génération de multiplications entières par les compilateurs. Mots-clés : multiplication entière, châınes d’additions Multiplication by an Integer Constant 3
منابع مشابه
Applications of Fast Truncated Multiplication in Embedded Cryptography
Truncated Multiplications compute Truncated Products, contiguous subsequences of the digits of integer products. For an n-digit multiplication algorithm of time complexity O(n), with 1< α ≤ 2, there is a truncated multiplication algorithm, which is constant times faster when computing a short enough truncated product. Applying these fast truncated multiplications several cryptographic long inte...
متن کاملApplications of Fast Truncated Multiplication in Cryptography
Truncated multiplications compute truncated products, contiguous subsequences of the digits of integer products. For an n-digit multiplication algorithm of time complexity O(nα), with 1 < α ≤ 2, there is a truncated multiplication algorithm, which is constant times faster when computing a short enough truncated product. Applying these fast truncated multiplications, several cryptographic long i...
متن کاملOn a Lie group with constant negative sectional curvature
Let λ > 0 be a positive real number, and let n ≥ 1 be an integer. Let G = R×sR be a semi-direct product Lie group where the group multiplication in G is defined by (v1, x1) ∗ (v2, x2) = (v1 + ev2, x1 + x2) for all vi ∈ R, xi ∈ R, and i = 1, 2. We show G has constant sectional curvature −λ, and describe the irreducible unitary representations of G. 2010 Mathematic Subject Classification: 22D10, ...
متن کاملFpga Implementation of Fir Filter in Signal Processing
Multiple constant multiplication scheme is the most effective common sub expression sharing technique which is used for implementing the transposed FIR filters. Ripple carry operation allows adder tree to minimize hardware cost, unfortunately it detriment timing and gives low speed operation. To outperform this high speed adder is proposed and analyzed for real time speech signal applications. ...
متن کاملFast Truncated Multiplication and its Applications in Cryptography
Truncated Multiplication computes a truncated product, a contiguous subsequence of the digits of the product of 2 long integers. We review a few truncated multiplication algorithms and adapt them to integers. They are a constant times faster than n-digit full multiplications of time complexity O(n), with 1< α ≤ 2, important in cryptography. For example, the least significant half products with ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001