Geometry.Net - Theorems_And_Conjectures: Chinese Remainder Theorem


Home - Theorems_And_Conjectures - Chinese Remainder Theorem

e99.com Bookstore

Images

Newsgroups

61-80 of 90 Back | 1 | 2 | 3 | 4 | 5 | Next 20

Chinese Remainder Theorem: more detail

Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography by C. Ding, D. Pei, et all 1999-06
Secret Sharing Using the Chinese Remainder Theorem: Secret Sharing, Chinese Remainder Theorem, Threshold Cryptosystem, Cardinality, Access Structure, Shamir's ... Polynomial Interpolation, George Blakley
Remainder: Natural Number, Real Number Modulo Operation, Chinese Remainder Theorem, Division Algorithm, Euclidean Algorithm
A hierarchical single-key-lock access control using the Chinese remainder theorem (OSU-CS-TR) by Kim Sin Lee, 1994
Fundamental Number Theory with Applications (Discrete Mathematics and Its Applications) by Richard A. Mollin, 1998-01-31
Fundamental Number Theory with Applications, Second Edition (Discrete Mathematics and Its Applications) by Richard A. Mollin, 2008-02-21

lists with details

Chinese Remainder Theorem And The Chinese Problem
Mathematics Simultaneous Congruence Equations Number Theory Chinese Remainder Theorem and the Chinese Problem Number Theory Contents
http://www.trans4mind.com/personal_development/mathematics/numberTheory/chineseR

Extractions: Number Theory Contents Chinese Problem Chinese Remainder Theorem Solving the Problem Using Successive Substitution Rationale The Chinese Problem was first introduced by Sun Tsu (460 AD), and problems of that kind are often referrred to as the Chinese Problem:Oystein Ore mentions the following problem due to Brahmagupta (598) Apparently such problems amused both the high and the low at that time. The divisors are not relatively prime, and relative primality is not a condition for solvability. The Chinese Remainder Theorem is a statement of the conditions under which a set of simultaneous congrent equations is solvable. We will answer this question later. We have already used a method to solve think kind of problem. The following "low-tech" method is more efficient, however.
The Chinese Remainder Theorem
Aug 7, 1995 The Chinese Remainder Theorem (CRT) gives the answer to the problem Find the number x, that satisfies all the n equations simultaneously
http://www.apfloat.org/crt.html

Extractions: Last updated: August 7th, 1995 The Chinese Remainder Theorem (CRT) gives the answer to the problem: Find the number x, that satisfies all the n equations simultaneously: We will assume here (for practical purposes) that the moduli pk are primes. Then there exists a unique solution x modulo p1*p2*...*pn. The solution can be found with the following algorithm: Let P=p1*p2*...*pn Let the numbers T1...Tn be defined so that for each Tk (k=1...n) (P/pk)*Tk=1 (mod pk) that is, Tk is the inverse of P/pk (mod pk). The inverse of a (mod p) can be found for example by calculating a^(p-2) (mod p). Note that a*a^(p-2)=a^(p-1)=1 (mod p). Then the solution is x = (P/p1)*r1*T1 + (P/p2)*r2*T2 + ... + (P/pn)*rn*Tn (mod P) The good thing is, that you can calculate the factors (P/pk)*Tk beforehand, and then to get x for different rk, you only need to do simple multiplications and additions (supposing that the primes pk remain the same). When using the CRT in a number theoretic transform, the algorithm can be implemented very efficiently using only single-precision arithmetic when rk
Chinese Remainder Theorem
Definition of Chinese remainder theorem, possibly with links to more information and implementations.
http://xw2k.nist.gov/dads/HTML/chineseRmndr.html

Extractions: (algorithm) Definition: An integer n can be solved uniquely mod LCM(A(i)) Note: For example, knowing the remainder of n when it's divided by 3 and the remainder when it's divided by 5 allows you to determine the remainder of n when it's divided by LCM(3,5) = 15. After LK. Author: PEB Go to the Dictionary of Algorithms and Data Structures home page. If you have suggestions, corrections, or comments, please get in touch with Paul E. Black Entry modified 17 December 2004.
RSA Speedup With Chinese Remainder Theorem Immune Against Hardware
File Format PDF/Adobe Acrobat Quick View
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.122.9916&rep=rep1&a
Modular Arithmetic
File Format PDF/Adobe Acrobat Quick View
http://www.cs.cmu.edu/~adamchik/21-127/lectures/congruences_print.pdf
Chinese Remainder Theorem | Facebook
Welcome to the Facebook Community Page about Chinese remainder theorem, a collection of shared knowledge concerning Chinese remainder theorem.
http://www.facebook.com/pages/Chinese-remainder-theorem/106339806071525

Extractions: Wall Info Fan Photos Chinese remainder theorem + Others Chinese remainder theorem Just Others Chinese remainder theorem changed their Description Thursday at 4:32pm Chinese remainder theorem changed their Description September 27 at 11:52pm Chinese remainder theorem joined Facebook. April 4 at 6:01pm See More Posts English (US) Español More… Download a Facebook bookmark for your phone.
Section 7.1: Solving Two Congruences
7.1 Solving Two Congruences. The Chinese Remainder Theorem is one of the oldest theorems in number theory. Your first job is to discover the right statement of this theorem.
http://www.math.mtu.edu/mathlab/COURSES/holt/dnt/chinese1.html

Extractions: 7.1 Solving Two Congruences The Chinese Remainder Theorem is one of the oldest theorems in number theory. Your first job is to discover the right statement of this theorem. Most of the statement of the theorem is provided in the next section - you just need to fill in the missing part. Below is an incomplete statement of the Chinese Remainder Theorem for two congruences. Chinese Remainder Theorem : If m and m are positive integers such that , then for any integers a and a , the pair of congruences x a (mod m ) and x a (mod m has a unique solution x modulo m m To complete Research Question 1, you need to figure out what condition is required in place of the above to make the statement true. Notice that the placement occurs after the introduction of m and m but before a and a . This means that the missing condition should involve m and m but not a or a . So to complete the statement of the theorem, you need to determine what condition on m and m allows one to find a unique solution to the congruences for all choices of a and a Complete the statement of the Chinese Remainder Theorem for two congruences.
Math Forum - Ask Dr. Math
Jul 25, 2001 Professor Carroll tries to divide his class into three groups, but two students are left
http://mathforum.org/dr.math/problems/donald.07.21.01.html

Extractions: Associated Topics Dr. Math Home Search Dr. Math Date: 07/25/2001 at 13:34:55 From: Donald Subject: Chinese Remainder Theorem I was wondering if there is any way to solve this using the Chinese Remainder Theorem rather than just trial and error. Professor Carroll tries to divide his class into three equal groups, but two students do not have a group. When he tries to divide them into five groups, three people are left. Finally, a configuration of seven equal groups leaves two people hanging. What is the smallest possible number of students in Professor Caroll's class? Thank you for your help. http://mathforum.org/dr.math/problems/prufrock.4.25.00.html http://mathforum.org/dr.math/ Associated Topics
Summer High School 2009 Aaron Bertram 5. The Chinese Remainder
File Format PDF/Adobe Acrobat Quick View
http://www.math.utah.edu/~bertram/HighSchool/5Chinese.pdf
Chinese Remainder Theorem
A Mechanical Proof of the Chinese Remainder Theorem David M. Russinoff. This paper (ps, pdf), which was presented at ACL2 Workshop 2000 (see slides ps, pdf), describes an ACL2
http://www.russinoff.com/papers/crt.html

Extractions: A Mechanical Proof of the Chinese Remainder Theorem David M. Russinoff This paper ( ps pdf ), which was presented at ACL2 Workshop 2000 (see slides: ps pdf ), describes an ACL2 proof of the Chinese Remainder Theorem: If m m k are pairwise relatively prime moduli and a a k are natural numbers, then there exists a natural number x that simultaneously satisfies x a i (mod m i i k The entire proof is contained in the single event file crt.lisp , except that it depends on some lemmas from the author's library of floating-point arithmetic . In order to certify this file (after obtaining and certifying the library), first replace each of the two occurrences of " /u/druss/ " with the path to the directory under which your copy of the library resides. A second event file, summary.lisp , which contains the definitions and main lemmas involved in the proof, may then be certified.
MODULAR EXPONENTIATION VIA THE EXPLICIT CHINESE REMAINDER THEOREM
File Format PDF/Adobe Acrobat Quick View
http://cr.yp.to/antiforgery/meecrt-20060914-ams.pdf
Chinese Remainder Theorem
Pascal Paillier, Publickey cryptosystems based on composite degree residuosity classes, Proceedings of the 17th international conference on Theory and application of cryptographic
http://portal.acm.org/citation.cfm?id=260951
Math 126 Number Theory
File Format PDF/Adobe Acrobat Quick View
http://aleph0.clarku.edu/~djoyce/ma126/meeting17.pdf
Chinese Remainder Theorem HTML Page
Millersville University/Department of Mathematics Chinese Remainder Theorem Applet. The Chinese Remainder Theorem is an ancient result taking its name from the work entitled
http://banach.millersville.edu/~bob/math478/ChineseRemainder.html

Extractions: The Chinese Remainder Theorem is an ancient result taking its name from the work entitled Suangching by Sun Tsu. It is used to solve a system of linear congruences. In the left-hand column of textfields below fill in the remainders obtained when mod-ing by the relatively prime positive integers in the textfields in the right-hand column. Press the Solve button to find the solution. If you find a case in which the applet fails to function or gives erroneous results, please send me the values of the remainders and divisors which you entered and the contents of your Java console. My modest goal is to have this applet run reliably and accurately. You need a Java-enabled browser running JDK 1.1.x or greater to run this applet. Page maintained by: Bob Buchanan
S.O.S. Mathematics CyberBoard :: View Topic - Chinese Remainder Theorem
3 posts 3 authors - Last post May 3Since , the Chinese Remainder Theorem is not applicable. Mathematicians are like lovers. Grant a mathematician the least principle,
http://www.sosmath.com/CBB/viewtopic.php?p=204036&sid=b9a59bfc7faccadbade821
The Chinese Remainder Theorem (the CRT)
The Chinese Remainder Theorem (the CRT) Brain Teasers discussion
http://www.physicsforums.com/showthread.php?t=243035
COMPUTING IGUSA CLASS POLYNOMIALS VIA THE CHINESE REMAINDER
File Format PDF/Adobe Acrobat Quick View
http://research.microsoft.com/en-us/um/people/klauter/ELMay10.pdf
Chinese Remainder Theorem Due To Gauss
Mathematics This formula is what is normally called the Chinese Remainder Theorem.
http://www.trans4mind.com/personal_development/mathematics/numberTheory/chineseR
A Mechanical Proof Of The Chinese Remainder Theorem David M. Russino
File Format Adobe PostScript View as HTML
http://www.cs.utexas.edu/users/moore/acl2/v4-1/distrib/acl2-sources/books/worksh
THEORY OF NUMBERS Computations (1) Use The Chinese Remainder
File Format PDF/Adobe Acrobat Quick View
http://www.cims.nyu.edu/~burr/Classes/Homework3Solutions.pdf

61-80 of 90 Back | 1 | 2 | 3 | 4 | 5 | Next 20