
[數] 孫子剩餘定理
This tinkering led them to apiece of ancient maths known as the Chinese remainder theorem.
這次改變使他們聯想到了古老的數學問題——中國剩餘定理。
The solution of system of linear congruence equations can be provided by the Chinese remainder theorem or recursive process.
一般可以用中國剩餘定理或者遞推算法等方法給出一次同餘方程組的解法。
A dynamic password authentication which is based on the Chinese remainder theorem and RSA public-key cryptography are represented. Finally analysis is made on the scheme security and feasibility.
最後提出一種基于公鑰密碼和中國剩餘定理的動态口令驗證方案,進行方案安全性及性能的分析。
Using the theorem of linear Diophantine equations and the Chinese remainder theorem, we have constructed a class of trap-door knapsack public-key cryptosystems, which have a better security.
利用不定方程理論及中國剩餘定理,我們設計了一類陷門背包公開鑰密碼系統,它們具有更好的安全性。
Finally, the paper explains the Chinese remainder theorem.
最後詳細介紹孫子剩餘定理。
On the basis of deeply delving into the coprime of polynome, several equivalent propositions are presented, including the reflection of number theorys Chinese remainder theorem in polynome theory.
給出十幾個關于多項式互素的等價命題,其中包括數論孫子定理在多項式理論中的反映。
In the fourth chapter, we introduce the lattice, the ideal and prove the Chinese remainder theorem in the distributive lattice on which we design a safe communication scheme.
第四章讨論了分配格上的中國剩餘定理及應用,介紹了格的預備知識、分配格上的理想和分配格上的中國剩餘定理,并由此結論設計了一套新的安全通信方案。
The scheme is based on the Chinese Remainder Theorem and the paper builds an enhanced proxy multiple signature scheme based on an overall analysis of attacking schemes.
本文的攻擊方案一基于中國剩餘定理,在全面分析攻擊方案的基礎上構造了一種增強的代理多重簽名方案。
Resolution of range and velocity ambiguities is the most important problem in medium PRF(MPRF) pulse doppler radar. The theory of the ambiguity resolution algorithms is Chinese Remainder Theorem.
解距離模糊和解速度模糊是中重複頻率脈沖多普勒雷達中需要解決的重要問題,其算法的依據都是中國餘數定理。
In this paper, a new authentication encryption scheme based on multi private key RSA and the Chinese Remainder Theorem (CRT) is proposed.
根據RSA加密系統和中國剩餘定理,提出了一種新的基于多密鑰的RSA認證加密方案。
But the Chinese Remainder Theorem cannot solve the error and the blind region made in range and doppler velocity measurements.
但是,單靠中國餘數定理仍無法解決距離測量和多普勒頻率測量中的誤差和遮擋問題。
In this article, some applications of the Chinese remainder theorem are given in the number theory, polynomial ring, commutative ring and valuation theory.
本文給出了孫子定理在數論、多項式環、一般可換環及賦值論中的若幹應用。
New PFA algorithm does not depend upon Chinese Remainder Theorem.
新算法不需要用餘數定理作為指标映射的工具。
As an application of Chinese remainder theorem in IS-algebras, an isomorphism theorem in IS-algebras is given.
作為IS-代數上的中國剩餘定理的應用 ,同時給出了一個IS-代數的同構定理。
Application of this network to Chinese Remainder Theorem is also considered.
它還被應用于中國餘數定理的實現。
In this paper, after introducing the Chinese remainder theorem of the number theory, the Chinese remainder theorem of polynomials is analyzed.
從數論中的中國剩餘定理出發,在分析基于多項式上的中國剩餘定理的基礎上,提出了一種新的通信編碼。
Meanwhile, in order to improve the computation speed of the server, the Chinese Remainder Theorem (CRT) is used in RSA decryption algorithm.
同時為進一步提高服務器的運算速度,在服務器端利用中國剩餘定理(CRT)對RSA解密算法中的模指數進行降幂處理。
The third part is the study and the educational functions of the Chinese Remainder Theorem.
第三部分是孫子定理數學原理的研究與其教育功能。
The temporary keys are protected by the Chinese Remainder Theorem (CRT) in the first protocol, which is provably secure under the CDH assumption.
第一個協議使用中國剩餘定理(CRT)隱蔽臨時密鑰,在CDH假設下可證安全;
This paper presents an extended Chinese Remainder Theorem (CRT) valid for moduli non-mutually prime in integer residue sub-rings.
本文描述了一種推廣的孫子定理,針對噪擾模糊數據發展了一種基于該定理的模糊分辨算法。
And on this basis, we completed the circuit design of the binary-to-residue converter and the residue-to-binary converter based on the Chinese Remainder Theorem (CRT).
以此為依據,完成了餘數系統和二進制系統之間的前向轉換電路設計,并基于中國剩餘定理完成了後向轉換電路設計。
The client balanced SSL handshake protocol, which is based on the Chinese Remainder Theorem, has effectively improved the performance of the server of the SSL VPN , the SSL VPN system.
基于中國剩餘定理的客戶端平衡的SSL握手協議有效地提高了SSLVPN服務器的處理能力,也就提高SSLVPN系統的性能。
This paper presents the application of the Chinese Remainder Theorem in the private key operations of RSA crypto chip, and analyzes the throughput of information based on such structure.
該文在介紹RSA算法實現數據加解密的基礎上,描述了用中國剩餘定理(CRT)實現RSA私鑰運算的實現方法,并且對CRT在硬件設計時的特性進行了分析。
The new signature algorithm is based on the Chinese Remainder Theorem which has a relative short private key.
該RSA簽名算法基于中國剩餘定理,采用較短的私人密鑰。
中國剩餘定理(Chinese Remainder Theorem,CRT)是數論中解決同餘方程組的重要定理,其核心思想是通過模數互質的條件,将多個同餘方程的解統一為一個唯一解(模所有模數的乘積)。以下是詳細解釋:
該定理最早見于中國南北朝時期的數學著作《孫子算經》中的“物不知數”問題:
問題:今有物不知其數,三三數之剩二,五五數之剩三,七七數之剩二,問物幾何?
解法:通過構造滿足條件的數,并利用模數(3、5、7)互質的特性,得到最小解為23。
條件:若模數 $m_1, m_2, dots, m_k$兩兩互質(即任意兩數的最大公約數為1),則同餘方程組
$$
begin{cases}
x equiv a_1(text{mod}m_1)
x equiv a_2(text{mod}m_2)
vdots
x equiv a_k(text{mod}m_k)
end{cases}
$$
在模 $M = m_1 times m_2 times dots times m_k$ 下有唯一解。
以《孫子算經》問題為例:
$$
begin{cases}
x equiv 2(text{mod}3)
x equiv 3(text{mod}5)
x equiv 2(text{mod}7)
end{cases}
$$
解:$M=105$, $M_1=35$, $M_2=21$, $M_3=15$,逆元 $y_1=2$, $y_2=1$, $y_3=1$,最終解 $x = (2 times 35 times 2) + (3 times 21 times 1) + (2 times 15 times 1) = 233 equiv 23(text{mod}105)$。
如需進一步學習,可參考數論教材或密碼學相關文獻。
Chinese 可以作為名詞,指代中國人或者中文語言。也可以作為形容詞,表示與中國有關的事物。
China-related,Chinese-speaking,Chinese-language
Non-Chinese,foreign,non-native
remainder 是一個名詞,指代剩餘部分或者餘數。
Residue,rest,balance
Quotient,total,whole
定理是指以一定條件和前提為基礎,通過論證而得出的結論。
Theorem,proposition,lemma
Hypothesis,conjecture,speculation
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