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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

Citation
symposium on Computer architecture toc 1993 , San Diego, California, United StatesThe chinese remainder theorem and the prime memory system Also published
http://portal.acm.org/citation.cfm?id=165172&dl=ACM&coll=portal&CFID=11111111&CF
The Chinese Remainder Theorem
Factorization The chinese remainder theorem. This is an application of Euclid'stheorem (although the ancient Chinese proved it differently).
http://vorpal.mcs.drexel.edu/course/founds/numbertheory/node8.html
Chinese Remainder Theorem
chinese remainder theorem. Dustin Davis CS 2310 SLCC 9/15/02 Pleasefill the necessary values in the form,then click OK button.
http://school.davisvillage.com/cs2310/assignments/3.html
[pac] Chinese Remainder Theorem
pac chinese remainder theorem. Previous message pac ANNOUNCECryptRSA 1.33; Next message pac chinese remainder theorem;
http://lists.vipul.net/pipermail/pac/2001-April/000034.html

Extractions: Fri, 06 Apr 2001 21:17:21 -0700 Vipul In another message (in the "A few bugs/wishes") thread you said: > They are not used yet. These parameters can be used instead of decryption exponent `d' for faster decryption using the Chinese Remainder Theorum. This is also on TODO. Previous message: [pac] [ANNOUNCE] Crypt::RSA 1.33 Next message: [pac] Chinese Remainder Theorem Messages sorted by: [ date ] [ thread ] [ subject ] [ author ]
[pac] Chinese Remainder Theorem
pac chinese remainder theorem. Previous message pac chinese remainder theorem;Next message pac Re Using keys not generated by your module
http://lists.vipul.net/pipermail/pac/2001-April/000037.html

Extractions: Fri, 6 Apr 2001 15:00:39 -0700 Vipul In another message (in the "A few bugs/wishes") thread you said: I have some code that implements the CRT (from Net::SSH::Perl::Util). It lying around, as well. 'u', I believe, is just: where mod_inverse is my($a, $n) = @_; my $m = Mod(1, $n); lift($m / $a); Here's the code: my %params = @_; my $p2 = mod_exp($I % $p, $d % ($p-1), $p); my $q2 = mod_exp($I % $q, $d % ($q-1), $q); my $r = (($q2 - $p2) * $u) % $q; return $p2 + ($p * $r); my($a, $exp, $n) = @_; my $m = Mod($a, $n); lift($m ** $exp); Hope this is useful. Excellent! Unless you want to send me a patch, I'll integrate this with :: http://www.vipul.net/ PGP Fingerprint d5f78d9fc694a45a00ae086062498922 Previous message: [pac] Chinese Remainder Theorem Next message: [pac] Re: Using keys not generated by your module ...
EECS 658 Problem Set #2 Fall 1999
30, 1999. THIS WEEK chinese remainder theorem, Euclidian algorithm. Apply thechinese remainder theorem to derive the Lagrange interpolation formula.
http://www.eecs.umich.edu/~aey/eecs658/probset2.html

Extractions: Use as moduli: 2,3,5,7,11,13,17,19; their product is about 10 million (large enough). Compute the residues of 3458 and 2992 for each modulus (total of 16 numbers). Compute the residues of the product for each modulus (total of 8 numbers). Use the Chinese remainder theorem to compute (3458)(2992). Confirm this is right.
Math Resources From Grau-Hall Scientific
Arapahulian Rope Computer Big Math Attack The chinese remainder theorem The ChineseRemainder Theorem from University of Colorado - Denver Fields Medal
http://www.grauhall.com/math.htm
CHALLENGING PROOFS BY MATHEMATICAL INDUCTION
006 Two definition of Even are equivalent. 007 - All numbersare odd or even. 008 - chinese remainder theorem
http://cs-www.cs.yale.edu/homes/carsten/challenges/challenges.html

Extractions: Home This collection of challenging examples has been assembled for researchers who are working on inductive theorem provers for the purpose of provoding a body of test examples. The description of the example problems is purposely kept informal, in order not to intervene with the representation of a problem in a particular theorem prover. Major contributions to this corpus have come from If you want to contribute to the corpus, please send mail to Carsten Schuermann . New additions will be annouced on the challenges mailing list. You may subscribe to the mailing list by sending email to majordomo@twelf.org with "subscribe challenge" in the body (the header might stay empty). Everybody is invited to submit challenges. 001 - Arithmetic Geometric Mean First Order Version of the Arithmetic/Geometric Mean Higher Order Version of the Arithmetic/Geometric Mean (Version 1) Higher Order Version of the Arithmetic/Geometric Mean (Version 2) 002 - Length of the joined list of two lists of even length is even ... 003 - A member of a list is a member of that list joined to another 004 - Rotate Length
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Lenore Blum, B6511, mablum@cityu.edu.hk. ALGEBRA, ALGORITHMS and APPLICATIONSPrototype example The chinese remainder theorem (CRT).
http://moscow.cityu.edu.hk/~maweb/history/discrete_mathematics/outline.html

Extractions: Lecturer: Prof. Lenore Blum mablum@cityu.edu.hk ALGEBRA, ALGORITHMS and APPLICATIONS Review: Mathematical Reasoning Fundamentals: Algorithms, Number Theory Algorithms: Number Theory: The Integers and Division Applications of Number Theory: OTHER MATERIAL may include: Main Text: Elementary Number Theory and its Applications 3rd edition, by Kenneth H. Rosen, Addison Wesley Publishing Co., 1993.
URS
Symposium 2001 Abstract Winners On the chinese remainder theorem andIts Applications. David Tello and Carmelo Tapia. In a book similar
http://www.uic.edu/orgs/urs/abstracts/2001/10.html

Extractions: 2001 Abstract Winners On the Chinese Remainder Theorem and Its Applications David Tello and Carmelo Tapia In a book similar to that of the "Arithmetic in Nine Sections," (1257 AD) written by the Chinese mathematician, Sun-tzã, we encounter the first Chinese problem in indeterminate analysis. The problem says: "There are things of an unknown number which when divided by 3 leaves 2, by 5 leave 3, and by 7 leave 2. What is the (smallest) number?" This problem is considered to be the beginnings of the famous Chinese Remainder Theorem of Elementary Number Theory. In our process of extending the Chinese Remainder Theorem to polynomials, we found that in the particular case when the divisors are different prime polynomials of degree 1, the algorithm for finding the desired polynomial is the LaGrange Interpolation Formula found in Numerical Analysis. To return to the 2001 Abstract Winners, click here.
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The result is a problem called the chinese remainder theorem. It is because of SunTsusproposal, that this problem is called the chinese remainder theorem.
http://eiffel.ps.uci.edu/cyu/p231C/Projects/outlines00/shean.html
Chinese Remainder Theorem
23Oct-01 chinese remainder theorem
http://www.cs.appstate.edu/~blk/cs5110/ch31/ch31_part5.htm
Error Analysis Of Approximate Chinese-Remainder-Theorem Decoding
pp. 13441348 Error Analysis of Approximate chinese-remainder-theorem Decoding.
http://www.computer.org/tc/tc1995/t1344abs.htm

Extractions: p p. 1344-1348 Error Analysis of Approximate Chinese-Remainder-Theorem Decoding Behrooz Parhami, Ching Yu Hung Abstract Approximate Chinese-remainder-theorem decoding of residue numbers is a useful operation in residue arithmetic. The decoding yields an approximation to ( X ... Computation errors, computer arithmetic, residue numbers, RNS representation, scaled decoding. The full text of IEEE Transactions on Computers is available to members of the IEEE Computer Society who have an online subscription and an web account
The Chinese Remainder Problem
It has given rise to such terms as chinese remaindering and chineseremainder theorem. There even is a book entirely devoted to it.
http://members.tripod.com/~Probability/diophan/chinese.htm

Extractions: There is a number which divided by 3, the remainder is 2; by 5 the remainder is 3; and by 7 the remainder is 2. What is the number? Sun Tsu Suan Ching (4th century AD) The above is a classic problem that has had considerable impact. It has given rise to such terms as "Chinese remaindering" and "Chinese remainder theorem." There even is a book entirely devoted to it. The problem usually is formulated in modular number notation but here we shall use the equivalent arbitrary integer constant notation. N = 3t + 2 N = 5u + 3 N = 7v + 2 This is a system of three linear Diophantine equations in four unknowns. In solving the system algebraically the usual procedure is to substitute the first equation into the second, resulting in a single equation in two unknowns. This is solved for t or u in terms of a new arbitrary integer variable. This solution for N then is substituted into the third equation which is then solved for v. Once v is known, then N can be calculated from the last equation. Let's do it!
A Possible New Quantum Algorithm: Arithmetic With Large Integers Via The Chinese
computation is more likely to be of this type. Arithmetic by the Chineseremainder theorem is a highly parallel procedure The idea.
http://citeseer.nj.nec.com/337637.html

Extractions: Abstract: kind, in which the constructive interference that builds up the answer takes place at the level of classical waves or signals. Arguably, eventual general-purpose quantum computation is more likely to be of this type. Arithmetic by the Chinese remainder theorem is a highly parallel procedure [36]. The idea is that the fixed word size of a standard computer can be transcended by doing all addition, subtraction, and multiplication modulo each of a set of pairwise relatively prime integers... (Update)

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