Multipartite Modular Multiplication
نویسندگان
چکیده
Current processors typically embeds many cores running at high speed. We may then ask ourselves whether software parallelism is practical for low level arithmetic operations. In this paper we generalize the bipartite modular multiplication method of Kaihara and Takagi. We present a multipartite multiplication. We carefully analyze its asymptotic complexity and measure its practical efficiency and scalability for nowadays multi-core architectures. We present several experimental results which illustrate the efficiency of our method and which bring a positive answer to the above question for a wide range of operand’s sizes.
منابع مشابه
An Efficient Parallel CMM-CSD Modular Exponentiation Algorithm by Using a New Modified Modular Multiplication Algorithm
This paper presents a new modified Montgomery modular multiplication algorithm based on canonical signed-digit (CSD) representation, and sliding window method. In this modified Montgomery modular multiplication algorithm, signed-digit recoding technique is used in order to increase probability of the zero bits. Also sliding window method is used in order to reduce the multiplication steps consi...
متن کاملHigh-speed Algorithms for Public-key Cryptosystems in an e-Commerce Environment
Modular exponentiation is one of the most important operations in public-key cryptosystems. A modular exponentiation is composed of repetition of modular multiplications. Again, the modular multiplication consists of a multi-precision multiplication and a modular reduction. Therefore, we can reduce the execution time of the modular exponentiation by two methods. One is to reduce the number of m...
متن کاملDesign and Implementation of Fast Multiplication Algorithms in Public Key Cryptosystems for Smart Cards
Most practical public-key cryptosystems are based on modular exponentiation. A modular exponentiation is composed of repeated modular multiplications. Several methods have been proposed to reduce the execution time of a modular exponentiation, essentially aiming to reduce the execution time of each modular multiplication. The goal of this paper is to investigate three different integer multipli...
متن کاملA New Modified CMM Modular Exponentiation Algorithm
Modular exponentiation is fundamental operation in the many cryptosystem such as RSA. This operation is implemented by repeating modular multiplication which is time consuming for large operands. This paper presents a new modified Montgomery modular multiplication algorithm based on multiple bit scan-multiple bit shift technique, sliding window method and signed-digit representation. This new a...
متن کاملA New Method of Serial Modular Multiplication
A novel serial algorithm is described for modular multiplication of large integers and a proof is given of its correct behaviour. Comparisons are made with published designs by Brickell [1] and Montgomery [2]. The new algorithm is advantageous where modular multiplications need to be performed individually and not chained for exponentiation.
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 2011