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Topic: RSA Factoring Challenge

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		RSA Laboratories sponsors the RSA Factoring Challenge to encourage research into computational number theory and the practical difficulty of factoring large integers, and because it can be helpful for users of the RSA encryption
		RSA numbers were originally spaced at intervals of 10 decimal digits between 100 and 500 digits, and prizes were awarded according to a complicated formula.
		RSA numbers received widespread attention when a 129-digit number known as RSA-129 was used by R. Rivest, A. Shamir, and L. Adleman to publish one of the first public-key messages together with a $100 reward for the message's decryption (Gardner 1977).
	users.skynet.be /fa956617/math/topics/RSANumber.html (733 words)

	The RSA Secret-Key Challenge
		RSA Laboratories is pleased to announce the establishment of a series of new cryptographic contests.
		The successful factorizations achieved as part of the RSA Factoring Challenge (launched by RSA Data Security, Inc. in 1991) show that for some types of problems, it is possible to recruit spare cycles on a large number of machines distributed around the Internet.
		RSA Data Security requests that participants not submit solutions to the practice contests, except possibly to test out the formatting of output produced by their software.
	www.fortify.net /related/97challenge.html (576 words)

	RSA Challenge (Site not responding. Last check: 2007-10-19)
		"The RSA Factoring challenge is an effort, sponsored by RSA Laboratories, to learn about the actual difficulty of factoring large numbers of the type used in RSA keys.
		Factoring 100-digit numbers is easy with today's hardware and algorithms Factoring numbers of more than 200 digits, however, is not currently feasible.
		It was factored in 1999 as part of the previous RSA Factoring Challenge, which this challenge replaces.
	www.turksa.net /rsa/default.asp?ch=1 (686 words)

	Institut für Numerische Simulation - News
		RSA numbers are composite numbers having exactly two prime factors (i.e., so-called semiprimes) that have been listed in the Factoring Challenge of RSA Security(R).
		RSA numbers are special types of composite numbers particularly chosen to be difficult to factor, and are identified by the number of digits they contain.
		RSA Laboratories sponsors the RSA Factoring Challenge to encourage research into computational number theory and the practical difficulty of factoring large integers and because it can be helpful for users of the RSA encryption public-key cryptography algorithm for choosing suitable key lengths for an appropriate level of security.
	www.ins.uni-bonn.de /news/RSA576a.html (801 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		RSA Challenge List ------------------ 5/19/94 Here is the RSA List for the RSA Factoring Challenge, with some description of how this list was generated.
		The RSA challenge numbers are thus tagged RSA-100, RSA-110, RSA-120,..., RSA-500.
		It is expected that the RSA challenge numbers will be at least as hard, if not harder, to factor than the partition numbers of the same length.
	home.imf.au.dk /niels/Alg1/RSAChallenge.txt (231 words)

	RSA Challenge
		The challenge proper will be launched during the RSA Data Security Conference to be held in San Francisco, Jan. 28-31, with the target ciphertexts for the different contests being simultaneously posted on the web-site.
		The successes of the RSA Factoring Challenge show that for some types of problems, it is possible to recruit spare "cycles" on a large number of machines distributed around the Internet.
		RSA Data Security Inc., a wholly owned subsidiary of Security Dynamics Technologies Inc., is the world's brand name for cryptography, with more than 75 million copies of RSA encryption and authentication technologies installed and in use worldwide.
	www.ncns.com /news/cryptocracker.html (765 words)

	A Discussion of RSA-129 Activity
		This document consists of excerpts from electronic posts by the originators of the RSA 129 Factoring Challenge Project and a short expository paper on the theory and history of the RSA-129 challenge which was given as a lecture here at OSU.
		Factoring it, a 425-bit number, would be a major milestone in cryptography, as it would show that current technology is able to break commonly-used RSA-cryptosystem keys within a reasonable time.
		The "RSA challenge" published in the August 1977 issue of Scientific American (in Martin Gardner's column) is still open, and the $100 prize offer still stands.
	www.math.okstate.edu /~wrightd/numthry/rsa129.html (1702 words)

	RSA Factoring Challenge - Wikipedia, the free encyclopedia
		They published a list of semiprimes (numbers with exactly two prime factors) known as the RSA numbers, with a cash prize for the successful factorization of some of them.
		A primary application is for choosing the key length of the RSA public-key encryption scheme.
		The challenge numbers in pink lines are numbers expressed in base 10, while the challenge numbers in yellow lines are numbers expressed in base 2, and for which a cash prize is still assigned.
	en.wikipedia.org /wiki/RSA_Factoring_Challenge (402 words)

	CS267 Assignment 0
		RSA Laboratories researches and develops cryptographic techniques for use by the public and (particularly) standardization groups.
		As long as the amount of processing time it takes to guess the encryption key is longer than the amount of time the information is useful (or if the cost of the resources required to break the code is higher than the total value of the information), the data is logically considered secure.
		In order to quantify the safety of data protected by a given encryption technique, RSA tries to determine the amount of time in which the encryption key could be guessed by state-of-the-art computers using best known algorithms.
	bwrc.eecs.berkeley.edu /People/kcamera/CS267/assign0.htm (971 words)

	RSA poses $200,000 crypto challenge \| The Register
		RSA Security is running a factoring challenge that offers would-be code breakers a prize of up to $200,000 for finding the two numbers of the kind used to create ultra-secure 2048-bit encryption key.
		The idea of the RSA Factoring Challenge, which has been set before with lower-strength ciphers, is to encourage research into computational number theory and the practical difficulty of factoring large integers.
		Previous RSA Factoring Challenges have revealed that the US-government backed Data Encryption Standard (DES) was vulnerable to a brute force attack that yielded the result of a 56-bit key in a little over 22 hours.
	www.theregister.co.uk /2001/07/25/rsa_poses_200_000_crypto (445 words)

	Factoring Resources at FindInside.com (Site not responding. Last check: 2007-10-19)
		Factoring is selling invoices to receive your money today, instead of waiting 30, 60, or 90 days to be paid.
		Factoring is an important finance management tool for a small company that does not create debt, nor does it require you to give up any ownership in your company.
		Unlike a loan, collateral is not required in the factoring process, there is no interest, and no debt shows up on your balance sheet.
	factoringpowerhouse.com (118 words)

	Prime Numbers and Factoring
		This FAQ from RSA Labs surveys a modern topic which may be applied to factoring very large numbers using techniques reminiscent of quantum mechanics.
		The New RSA Factoring Challenge RSA is offering prizes for factoring large numbers suitable for encryption keys.
		The RSA Data Security Secret-Key Challenge RSA is offering large prizes for breaking their RC5 codes.
	www.ontko.com /~rayo/primes (561 words)

	Factoring Papers
		Factoring Integers with Large Prime Variations of the Quadratic Sieve by H. Boender and H.J.J. te Riele (compressed postscript, 109K) from CWI (http://www.cwi.nl/ftp/CWIreports/NW/NM-R9513.ps.Z).
		Factoring estimates for a 1024-bit RSA modulus by Arjen K. Lenstra, Eran Tromer, Adi Shamir, Wil Kortsmit, Bruce Dodson, James Hughes, Paul Leyland.
		Factorization of the Eighth Fermat Number by Richard Brent and John Pollard, from Richard Brent's homepage (http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub061.html).
	www.crypto-world.com /FactorPapers.html (629 words)

	RSA-129 article
		The group was led by Arjen Lenstra, a computer scientist and factoring specialist at Bellcore in New Jersey, and included Paul Leyland from Oxford (England) and graduate students from MIT and Iowa State.
		RSA stands for Ronald Rivest of MIT, Adi Shamir of the Weizmann Institute of Science, Israel, and Leonard Adleman of USC, who in 1977 announced a new cryptographic scheme that became know as the RSA public-key system.
		To support their claim that such factorization was hard, RSA published several numbers in Scientific American, each of which were the products of two large primes, and offered token prizes for their factorization.
	www.willamette.edu /~mjaneba/rsa129.html (1068 words)

	Q48: What are the Best Factoring Methods in Use Today?
		Factoring is a very active field of research among mathematicians and computer scientists; the best factoring algorithms are mentioned below with some references and their big-O asymptotic efficiency.
		Factoring algorithms come in two flavors, special purpose and general purpose; the efficiency of the former depends on the unknown factors, whereas the efficiency of the latter depends on the number to be factored.
		Clearly, the number field sieve will overtake the mpqs as the most widely used factoring algorithm, as the size of the numbers being factored increases from about 130 digits, which is the current threshold of general numbers which can be factored, to 140 or 150 digits.
	www.x5.net /faqs/crypto/q48.html (501 words)

	Prime Factorizations - Factoring Large Integers into Primes - Numericana
		This is the right idea but it won't do theoretically "as is", because the "least special" prime factors of numbers of bounded size may be used to establish a generous overall upper bound on the running time of any dubiously defined "special-purpose" algorithm (provided it's "general" enough to discover any factor, albeit slowly).
		Long before the notion became relevant to the factorization algorithms discussed here, number theorists had defined a primitive factor of a term in a sequence as a prime divisor of that term which does not divide earlier terms in the sequence.
		This method is intended for the factorization of a fairly large number n, preferably once smaller factors have been removed, using preliminary methods which are more efficient at weeding out small or medium-sized divisors...
	home.att.net /~numericana/answer/factoring.htm (2746 words)

	[No title]
		RSA is a public-key cryptosystem for both encryption and authentication; it was invented in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman [74].
		An RSA digital signature is superior to a handwritten signature in that it attests to the contents of a message as well as to the identity of the signer.
		RSA is patented under U.S. Patent 4,405,829, issued 9/20/83 and held by Public Key Partners (PKP), of Sunnyvale, California; the patent expires 17 years after issue, in 2000.
	www.ussrback.com /crypto/bruce_schneier/applied-crypto/rsa-faq.txt (21032 words)

	Cryptography Tutorial - RSA-160 CHALLENGE
		The security of the RSA cipher is based on the fact that the modulus m can not be factored into the two primes p and q.
		Instead of factoring in a clever manner we simply create random prime numbers consisting of about 80 decimals to test if they are factors of RSA-160.
		The RSA Cipher was invented in 1976 by the 3 Mathematicians Rivest, Shamir and Adleman.
	www.antilles.k12.vi.us /math/cryptotut/rsa6.htm (375 words)

	Xref: info.physics.utoronto.ca alt.answers:4737 alt.security.ripem:1126 news.answers:30103
		Factoring is the act of splitting an integer into a set of smaller integers (factors) which, when multiplied together, form the original integer.
		One paper [45] cites experimental evidence that the discrete log problem is slightly harder than factoring: the authors suggest that the effort necessary to factor a 110-digit integer is the same as the effort to solve discrete logarithms modulo a 100-digit prime.
		Use of RSA or some other public-key technique for key management solves both these issues: a different DES key is generated for each session, and secure key management is provided by encrypting the DES key with the receiver's RSA public key.
	www.skepticfiles.org /faq/rsa2faq.htm (8718 words)

	Q50: What is the RSA Factoring Challenge? (Site not responding. Last check: 2007-10-19)
		The RSA Factoring Challenge was started in March 1991 by RSA Data Security, Inc. to keep abreast of the state of the art in factoring.
		The Factoring Challenge provides one of the largest test-beds for factoring implementations and provides one of the largest collections of factoring results from many different experts worldwide.
		Since the Security of the RSA public-key cryptosystem relies on the inability to factor large numbers of a special type, the cryptographic significance of these results is self-evident.
	www.x5.net /faqs/crypto/q50.html (134 words)

	RSA-640 Factored (Site not responding. Last check: 2007-10-19)
		The team responsible for this factorization is the same one that previously factored the 174-digit number known as RSA-576 (MathWorld headline news, December 5, 2003) and the 200-digit number known as RSA-200 (MathWorld headline news, May 10, 2005).
		RSA Laboratories sponsors the RSA Factoring Challenge to encourage research into computational number theory and the practical difficulty of factoring large integers and also because it can be helpful for users of the RSA encryption public-key cryptography algorithm for choosing suitable key lengths for an appropriate level of security.
		RSA numbers were originally spaced at intervals of 10 decimal digits between one and five hundred digits, and prizes were awarded according to a complicated formula.
	www.freerepublic.com /focus/f-news/1518642/posts (2182 words)

	Exploring RSA Encryption in OpenSSL \| Linux Journal
		The RSA encryption method often is used to hide your credit card number from would-be thiefs on the Internet, because it uses a public key to hide your information and a private key to reveal it.
		The security of RSA is based on the difficulty of factoring large numbers, which is next to impossible for 1,024-bit numbers today.
		Rather, RSA is used to exchange symmetric keys for algorithms such as DES or AES, since symmetric algorithms are significantly faster to compute.
	www.linuxjournal.com /article/6826 (2620 words)

	Open Directory - Science: Math: Number Theory: Factoring (Site not responding. Last check: 2007-10-19)
		Factorization of F10 - F10 = 2^(2^10) + 1 is the 10-th Fermat number.
		RSA Laboratories Factoring Challenge - Numbers representative of those used in the RSA cryptosystem are offered for factor attempts with prizes.
		Factorization of RSA-155 - Announcement of factorization of a 512-bit RSA key using the General Number Field Sieve (GNFS).
	dmoz.org /Science/Math/Number_Theory/Factoring (554 words)

	Cryptography FAQ (06/10: Public Key Cryptography)
		RSA is a public-key cryptosystem defined by Rivest, Shamir, and Adleman.
		The RSA system reduces communications overhead with the ability to have static, unchanging keys for each receiver that are `advertised' by a formal `trusted authority' (the hierarchical model) or distributed in an informal `web of trust'.
		Factorization is a fast-moving field---the state of the art just a few years ago was nowhere near as good as it is now.
	www.cs.uu.nl /wais/html/na-dir/cryptography-faq/part06.html (1808 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		Introduction Factoring is the act of splitting an integer into a set of smaller integers (factors) which, when multiplied together, form the original integer.
		RSA Factoring Challenge The RSA Factoring Challenge was started in March 1991 by RSA Data Security, Inc. to keep abreast of the state of the art in factoring.
		It was factored using the quadratic sieve factoring method and, according to Lenstra, will perhaps be the last large number to be factored using the quadratic sieve since the general number field sieve is now more efficient for numbers of this size and larger.
	math.cankaya.edu.tr /index/hedef/0102spring/fatih6.doc (2337 words)

	Boffins crack encryption challenge (Site not responding. Last check: 2007-10-19)
		Sharing a $10,000 cash prize from RSA Security are the Scientific Computing Institute, the Pure Mathematics Institute in Germany, the National Research Institute for Mathematics and Computer Science in The Netherlands, and several other organisations.
		Originally started by RSA Laboratories in 1991, the Factoring Challenge encryption 'puzzle' was established to encourage research into computational number theory and the practical difficulty of factoring large integers.
		To solve the factoring challenge, the consortium combined resources from around the world, including hardware from the Experimental Mathematics Institute in Essen, the Bundesamt fur Sicherheit in der Informationstechnologie, and experts from the Number Field Sieve network of mathematicians throughout Canada, the US and the UK.
	www.itweek.co.uk /articles/print/2124874 (277 words)

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