E - exponentiation 中文

exponentiation n.【數學】取冪。

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This article provides a brief description of rsa public key cryptography , an analysis and compare of all kinds of present existed modular exponentiation in rsa public key cryptography , a colligation of the fastest accelerating software algorithm - vlnw sliding window methods and hardware mapping fast montgomery modular multiplication algorithm that can improve the implementary efficiency of rsa public key cryptography for achieving the novel algorithm - mnexp algorithm 本文簡單介紹了rsa公鑰密碼體制,分析比較rsa公鑰密碼中已有的模冪運算方法,將得到的最快軟件加速算法vlnw滑動窗口法和硬件映射最快的montgomery模乘算法綜合,得到改進后的mnexp算法能有效提高rsa公鑰密碼的實現效率。橢圓曲線密碼系統被認為可以替代rsa算法的一種公鑰密碼體制。
One special feature of this paper is that it provides fast implementation means for the all kinds of modular exponentiation algorithms , which facilitate the implementation of the rsa public key algorithms . the paper improved the sliding window algorithm by largely reducing the space complexity . meanwhile this paper represents an efficient combined algorithm to improve the processing of encryption and decryption 大數模冪乘運算是實現rsa等公鑰密碼的基本運算,其運行效率決定了rsa公鑰密碼的性能,文章主要研究了各種模冪算法的快速實現方法,提出運用組合算法的思想來減少算法運行時間;并對滑動窗口取冪算法進行了部分改進,用線性表來存儲預計算數據,從而減少了算法的復雜度,進一步提高了rsa加/解密的效率,并在試驗測試中得到較為滿意的結果。
Round these two respects , how to structure security elliptic curve cryptography and the implementations of ecc is first discussed in this paper . then we have analysed especially the scalar multiplication on the elliptic curves , and present a new algorithm to quickly implement the fixed point scalar multiplication according to the idea of interleaving exponentiation algorithm and power division . this algorithm is much faster than fixed - base windowing method ; and a little faster than fixed - base comb method 圍繞這兩個方面的問題，本文首先討論了如何構造安全的橢圓曲線密碼體制和橢圓曲線密碼體制的應用；然后重點分析了橢圓曲線上數乘運算的快速實現，并結合interleavingexponentiation算法和冪分割的思想，提出一種計算固定點數乘的快速算法，該算法的計算速度明顯快于fixed - basewindowing算法，稍快于fixed - basecomb算法。
Most overheads of an ot protocol are modular exponentiations that are computationally intensive tasks . by expanding from one - out - of - two ot protocol to one - out - n ot protocol and combining n one - out - of - two ot protocol to one one - out - n ot protocol , define a new simultaneous one - out - n ot protocol , and the number of modular exponentiation is consequently reduced to small constant 由于ot協議的計算開銷主要集中在計算密集的取冪運算，通過擴展二選一ot協議為n選一ot協議，把n個二選一ot調用合并成單個n選一ot調用，并在此基礎上定義新的并發ot協議，使取冪運算次數減少為常數次。
The main place of innovation of this paper is to grasp the advantage of different algorithms , from different angles and levels improve modular exponentiation algorithm and scalar multiplication algorithm , and achieve new algorithm which can provide reference to the implementation of rsa and ecc , meantime the new algorithm have greater practical value 本文的創新點在于綜合各種算法在不同方面的優勢,從不同角度和不同層次去改進模冪算法和標量乘算法,得到的新算法可供在實現rsa和橢圓曲線密碼體制時參考,具有較大的實用價值。
The latter pay special attention to the software implementation environments , including the technical details such as programming interface , data structures and 32 - bits visual c + + inline assembler . a sorftware packet is designed and implemented at last , which can perform the modular multiplication with equal 2048 - bits long of modulu and operands within approximately 5 . 239ms and the modular exponentiation with equal 2048 - bits long of modulu , exponent and base within approximately 4290 . 559ms 經測試，在intelceleron400mhz ， ram64mb的pc機上，進行一次乘數與被乘數的最大位數均為2048位長的模乘運算所需平均時間約為5 . 239ms ，在進行一次底數和指數的最大位數均為2048位長的模指數運算所需的平均時間約為4290 . 559ms 。
Asymmetric - key cryptography , which we will discuss in chapter 10 , is based on some topics in number theory , including theories related to primes , factorization of composites into primes , modular exponentiation and logarithm , quadratic residues , and the chinese remainder theorem 我們將在第十章中討論非對稱密鑰密碼學，非對稱密鑰密碼學基于一些數論的論題，這些論題與素數、把復合數分解為素數的因數分解、模指數與模對數、二次剩余和中國剩余定理有關。
The modular exponentiation , are the core and the most time consuming steps in public key crytographic schemes such as ras and elgammal schemes , in those the security is guaranteed by the assumption that the integers is large enough , say 1024 or 2048 bits long 在rsa和elgammal等一類公鑰密碼體制中，計算形如的運算是最耗時的運算步驟，大整數模運算是其核心運算。提高這種運算的運算速度方法分為加快模乘法的運算速度和減少模乘法的次數兩個方面。
Fast implementation of the rsa public key algorithms is one of direction of current public key algorithm . the research of this paper has using value , improving the processing of encryption and decryption by fast implementation of modular exponentiation and modular multiplication algorithm Rsa算法的快速實現是現代密碼學研究的方向之一,本文研究表明通過改進公鑰密碼體制中的模冪乘算法,可以進一步提高rsa的效率,具有一定的實用價值。
This thesis , focused on the large integer modular computations , studies the two ways to reduce the time consumed by modular exponentiation - - - algorithms for fast modular multiplication and algorithms for computing powers with the least numbers of modular multiplication 本文對數據加密體制用到的大整數模運算進行研究。我們的工作分為兩個部分：一部分是對大整數快速模運算算法的分析、研究；另一部分是大整數快速模運算算法的實現。
Furthermore , the scheme is improved , and it is shown that the improved scheme is more secure than the original by analyzing the security of the improved scheme , and has only one exponentiation modulo p and two hash - function evaluations for verification 此外，對原方案進行了改進，通過對改進方案的安全性分析得出結論；改進方案此原方案更安全，并且消息恢復過程只需要計算一次大數模冪乘和兩次單向函數。
Modular exponentiation and modular multiplication are the basic algorithms for implementing the public key algorithms such as rsa , etc . however the time - consuming modulo exponentiation computation , which has always been the bottle - neck of rsa , restricts its wider application 大數模冪乘運算是實現rsa等公鑰密碼的基本運算,該算法存在的問題是在實現時耗時太多,這也是制約其廣泛應用的瓶頸。
Read and analysis for the advanced research papers : fast exponentiation computation , multisignature , proxy signature , threshold signature , group signature , identification authentications , visitor control , multisecret sharing 閱讀并討論專題論文：快速指數運算、多重簽名、代理簽名、門限簽名、群簽名、身份認證、訪問控制、（多）秘密共享。
The key of rsa is the modular exponentiation multiplication of large number , in this thesis , we modify the montgomery algorithm which be used to implement rsa Rsa算法的核心是大數模冪乘運算,本文選用montgomery模冪乘算法來實現ras算法,對montgomery模乘算法的fpga實現進行了改進。
At the same time , it is relatively colorfully that this paper makes use of some proverties of topological spaces to discuss the problems about countable ordinal exponentiation arithmetic 同時，本文用拓撲空間的一些性質來討論集合論中的可數序數指數運算問題也比較精彩。
Exponentiation , which normally has higher precedence than addition or multiplication , is evaluated last in this example because the other expressions are enclosed in parentheses 通常比加法或乘法具有更高優先級的求冪在此示例中最后計算，因為其他表達式都放在括號中。
Exponentiation fermat ' s little theorem sometimes is helpful for quickly finding a solution to some exponentiations . the following examples show the idea 雖然我們在本章后面只了解該定理的某些應用，但這該定理在解決一些問題時還是非常有用的。
However the time - consuming modulo exponentiation computation , which has always been the bottle - neck of rsa , restricts its wider application 但該算法所采用的冪剩余計算會耗費太多的時間，一直是制約其廣泛應用的瓶頸。
First , computers have circuits for performing arithmetic operations , such as : addition , subtraction , division , multiplication and exponentiation 第一，計算機具有進行加、減、乘、除及取冪等各種算術運算的電路。

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exponentiation

exponentiation n.【數學】取冪。

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Exponentiation fermat ' s little theorem sometimes is helpful for quickly finding a solution to some exponentiations . the following examples show the idea 雖然我們在本章后面只了解該定理的某些應用，但這該定理在解決一些問題時還是非常有用的。

However the time - consuming modulo exponentiation computation , which has always been the bottle - neck of rsa , restricts its wider application 但該算法所采用的冪剩余計算會耗費太多的時間，一直是制約其廣泛應用的瓶頸。

First , computers have circuits for performing arithmetic operations , such as : addition , subtraction , division , multiplication and exponentiation 第一，計算機具有進行加、減、乘、除及取冪等各種算術運算的電路。