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RSA Factoring Challenge - Wikipedia, the free encyclopedia The RSA Factoring Challenge is a challenge put forward by RSA Laboratories on March 18, 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers. As RSA Laboratories is a provider of RSA-based products, the challenge is used by them as an incentive for the academic community to attack the core of their solutions — in order to prove its strength. The first RSA numbers generated, from RSA-100 to RSA-500, were labeled according to their number of decimal digits; later, however, beginning with RSA-576, binary digits are counted instead. en.wikipedia.org /wiki/RSA_number   (384 words)

Institut für Numerische Simulation 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. 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). www.ins.uni-bonn.de /news/RSA576a.html   (764 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. There is one RSA number of length 100, one of length 110, and so on, up to one of length 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)

LinuxElectrons - RSA Security Encryption Software Receives FIPS Validation RSA BSAFE Micro Edition software is designed to offer developers the ability to rapidly add cryptographic security to wireless or embedded solutions and maximize an organization's security investment by ensuring interoperability with the existing wired infrastructure. RSA BSAFE Crypto-C Micro Edition software is designed to provide all organizations and government agencies with unmatched levels of quality and performance for their business applications," said Rick Welch, vice president of developer solutions and professional services at RSA Security. RSA BSAFE Crypto-C ME 1.7.2 software is available immediately on Microsoft(R) Windows(R) 32-bit operating system platforms, and will be available on a wide range of platforms in the future, including Solaris, Linux and PocketPC in 2004. www.linuxelectrons.com /article.php?story=20040211113951895   (624 words)

RSA Laboratories Bulletin #13: A Cost-Based Security Analysis of Symmetric and Asymmetric Key Lengths   (Site not responding. Last check: 2007-10-19) While the TWINKLE device of Shamir seems to be a very effective way of doing the sieving for RSA keys in the (say) 512 to 700 bit range, even Shamir admits that the device is unlikely to scale to where it is effective in attacking 1024 bit keys. The large difference in RSA key size (760 bits vs. 1024) comes solely from the fact that for fixed FINANCIAL resources, the cost of memory is by far the largest cost associated with breaking an RSA key and computational equivalence ignores memory. Two-prime 1024 bit RSA is equivalent to an 80 bit symmetric key in terms of time, but much stronger in terms of cost. www.nullify.org /docs/bulletin13/bulletin13.html   (9701 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.php?sid=6826   (2661 words)

RSA Security Announces First Quarter Results Business Outlook RSA Security's financial guidance for the second quarter of 2003 assumes that there will be no improvement or further deterioration in the global IT spending environment. RSA Security's strong reputation is built on its history of ingenuity and leadership, proven technologies and long-standing relationships with more than 1,000 technology partners. RSA, ACE/Server, BSAFE, ClearTrust, Keon, SecurID and The Most Trusted Name in e-Security are either registered trademarks or trademarks of RSA Security Inc. in the United States and/or other countries. www.prnewswire.com /cgi-bin/stories.pl?ACCT=104&STORY=/www/story/04-10-2003/0001924199&EDATE=   (1155 words)

Factsheet RSA is an encryption method invented some twenty years ago by Rivest, Shamir, and Adleman at MIT in the USA, which is widely used nowadays in hardware and software to secure electronic data transport. The inventors of the RSA cryptosystem in 1978: Factoring numbers on this list measures how secure the RSA method actually is. For special numbers, for example of the form ab ±1, factoring has proceeded to well over two hundred digits. www.cwi.nl /research/2001/TeRiele_Eng   (890 words)

An Overview of Cryptography RSA today is used in hundreds of software products and can be used for key exchange, digital signatures, or encryption of small blocks of data. RSA is used during negotiation to exchange keys and identify the actual cryptographic algorithm (DES, IDEA, RC2, RC4, or 3DES) to use for the session. RSA keylengths of 512 and 768 bits are considered to be pretty weak. www.garykessler.net /library/crypto.html   (17397 words)

[Chapter 6] 6.4 Common Cryptographic Algorithms   (Site not responding. Last check: 2007-10-19) RSA can be used both for encrypting information and as the basis of a digital signature system. Instead of using RSA to encrypt the entire message, RSA is used to encrypt a session key, which itself is used to encrypt the message using a high-speed, private key algorithm such as DES or IDEA. When the folks at RSA are contacted by somebody who claims a factoring breakthrough (and usually promises to keep the breakthrough a secret in exchange for some cash), they give the person a copy of the RSA challenge numbers. ninja.kinsuth-mar.com /security/puis/ch06_04.htm   (5318 words)

RSA Labs - An Analysis of Shamir’s Factoring Device RSA Labs - An Analysis of Shamir’s Factoring Device The table below gives, for different RSA key sizes, the amount of time required by the Number Field Sieve to break the key (expressed in total number of arithmetic operations), the size of the required factor base, the amount of memory, per machine, to do the sieving, and the final matrix memory. The idea presented by Dr. Shamir is a nice theoretical advance, but until it can be implemented and the matrix difficulties resolved it will not be a threat to even 768-bit RSA keys, let alone 1024. www.ussrback.com /crypto/rsa/TWINKLE/twinkle.html   (1782 words)

State v. Herbert Barnett To argue that the legislature intended to prohibit the sexual assault of a child clothed during her waking hours, but did not intend to extend those protections to that same child when she later rests under a blanket, denies fair import to the terms of the statute, fails to promote justice and defies logic. Neither are we persuaded that a post-offense amendment to RSA 632-A:1, IV is dispositive. Since the interpretation of statutory language is a question of law, it is not for the jury to decide whether "clothing," as used in RSA 632-A:1, IV, may also include blankets. www.state.nh.us /judiciary/supreme/opinions/2001/barne212.htm   (1758 words)

Open Source Software Institute FIPS 140 is a hardware standard that preceded FIPS 140-1. RSA can be used for signatures only in FIPS mode. Actually, the RSA signature code is a valid implementation; it just didn't yet have a FIPS test as of the time we began this effort, so it is "self-validated". oss-institute.org /fips-faq.html   (3527 words)

Math 5410 Factoring In the RSA application, one must ensure that the primes p and q have the property that p-1 and q-1 have at least one large prime factor to avoid an attack by this method. In 2001, RSA Labs renamed and reissued the "challenge" numbers and assigned specific monetary rewards for their factoring. The new list (available at RSA Labs) uses the number of digits in the binary representation in the name, starting at RSA-576 (worth $10K) and going up to RSA-2048 ($200K). www-math.cudenver.edu /~wcherowi/courses/m5410/ctcfactor.html   (1736 words)

IP: CRYPTO An Analysis of Shamir's Factoring Device (fwd)   (Site not responding. Last check: 2007-10-19) Larger RSA > key sizes are still out of reach, one of the obstacles being the amount > of work and storage involved in the rest of the process of factoring a > large number. Very few of the RSA numbers > have been factored so far, however, the largest one being about 450 bits > long, still short of the 512-bit mark targeted by the new device. Several > years ago, recognizing that 512-bit keys might be at risk in the near > future, RSA Laboratories recommended that developers choose a minimum > key size of 768 bits for user keys and 1024 bits for enterprise keys. www.interesting-people.org /archives/interesting-people/199905/msg00019.html   (2670 words)

RSA140 Factored   (Site not responding. Last check: 2007-10-19) Cc: jya@pipeline.com [Forward] Date: Thu, 4 Feb 1999 11:09:47 -0500 (EST) From: Christof Paar To: "WPI.Crypto.Seminar":; Subject: RSA140 broken The next RSA challenge, RSA140, has just been factored. RSA140 is a 140 decimal digit number (or about 465 bit). The number RSA-140 is taken from the RSA Challenge list (http://www.rsa.com/rsalabs/html/factoring.html). cryptome.quintessenz.at /mirror/rsa140.htm   (942 words)

How to Restrict the Use of Certain Cryptographic Algorithms and Protocols in Schannel.dll RSA appears only once in the corresponding cipher suite definitions. This registry key refers to the RSA as the key exchange and authentication algorithms. To allow RSA, change the DWORD value data of the Enabled value to the default value 0xffffffff, otherwise change the DWORD data to 0x0. support.microsoft.com /?kbid=245030   (1896 words)

An Overview of Cryptography   (Site not responding. Last check: 2007-10-19) RSA today is used in hundreds of software products and can be used for key exchange or encryption of small blocks of data. Unlike Diffie-Hellman, RSA can be used for key exchange as well as the encryption of small blocks of data. While RSA can be successfully attacked, the mathematics of the algorithm have not been comprised, per se; instead, computational brute-force has broken the keys. solution.ecn.purdue.edu /~simmons/crypto.html   (15994 words)

Abstract of: Factorization of a 512--bit RSA modulus   (Site not responding. Last check: 2007-10-19) This is a new record for factoring general numbers. Moreover, 512--bit RSA keys are frequently used for the protection of electronic commerce---at least outside the USA---so this factorization represents a breakthrough in research on RSA--based systems. The previous record, factoring the 140--digit number RSA--140, was established on February 2, 1999, also with the help of NFS, by a subset of the team which factored RSA--155. db.cwi.nl /rapporten/abstract.php?abstractnr=690   (171 words)

Xbox100.com - Neo Project update Factoring of the RSA challenges to date has shown that theoretical security margins for large keys are dramatically different than real-world security margins. The RSA team estimated that the RSA-155 factoring should be 7.2 times harder in terms of time. In fact, the RSA-155 factoring was accomplished in 3.7 months at a cost of 35.7 CPU years. www.xbox100.com /forums/showthread.php?t=1831   (704 words)

Choosing an Encryption Key Length Earlier this year, RSA Laboratories issued a challenge to crack a 140- bit RSA encryption key. RSA said it issued these challenges to back up its suggestion that people use a stronger 768-bit key as a baseline for minimum key length. Needless to say, the RSA challenges point out how risky this mentality can be if you use a key less than 768 bits in length. www.windowsitpro.com /Articles/Index.cfm?ArticleID=7164   (539 words)

Brent_k58_98 An important ingredient in maintaining this security is the use of cryptographic techniques such as "public key" cryptography. The most popular public key cryptosystem, the RSA system, depends on the difficulty of factoring a composite number which is the product of two or three large prime numbers. Murphy (PhD student, ANU) in collaboration with Montgomery (CWI, Amsterdam) has improved the polynomial selection phase of the number field sieve algorithm and used this to factor the 140-digit RSA challenge number. anusf.anu.edu.au /annual_reports/annual_report98/Appendix_A/I_Brent_k38_98.html   (503 words)

[No title] The first practical system and the one that gained most in popularity was the RSA cryptosystem introduced by Rivest, Shamir, and Adleman in 1977. Admittedly, cracking RSA-155 was computationally expensive (taking 8000 Mips-years), but the business community is already turning to 768-bit RSA or 1024-bit RSA for fear of future advances in attack algorithms. It took four months and was about 50 times that required to solve the 512-bit RSA cryptosystem. www.iccip.csl.uiuc.edu /research.html   (1274 words)

[No title] From: challenge-administrator@majordomo.rsasecurity.com (RSA Factoring Challenge Administrator) To: rayo@ontko.com X-IMAPbase: 1128097135 1 Status: RO X-Status: X-Keywords: X-UID: 1 RSA Honor Roll -------------- As of March 5, 1999 RSA-100 Factors: 40094690950920881030683735292761468389214899724061 * 37975227936943673922808872755445627854565536638199 Date: April 1, 1991 Method: ppmpqs Time: Approx. The $100 prize was won by factoring the RSA modulus published there, which is: RSA-129 = 114381625757888867669235779976146612010218296721242362562561842935706935245733897830597123563958705058989075147599290026879543541 (129 digits, checksum = 105443) Please note that this number is NOT part of the current RSA Factoring Challenge and is included here for informational purposes only. Better use was made of these procedures for the RSA-155 factorisation than for the RSA-140 factorisation. www.ontko.com /~rayo/primes/hr_rsa.txt   (284 words)

An Overview of Cryptography   (Site not responding. Last check: 2007-10-19) This method could be also used to prove who sent a message; Alice, for example, could encrypt some plaintext with her private key; when Bob decrypts using Alice's public key, he knows that Alice sent the message and Alice cannot deny having sent the message (non-repudiation). An alternative to RSA is the Diffie-Hellman scheme which is used only for key exchange. I tried to be careful in the first paragraph of this section to state that Diffie and Hellman "first described publicly" a PKC scheme. mia.ece.uic.edu /~papers/WWW/cryptography/crypto.html   (17526 words)

B. Dodson's Home Page   (Site not responding. Last check: 2007-10-19) The matrix equation was solved on a Cray C90, using 62 hours of CPUtime, breaking a 430-bit RSA key (130 decimal digits) into two 65-digit primes. While the RSA cryptosytem, used to provide security for web browsers and computer operating systems, currently relies upon 768-bit or 1024-bit keys; our computation [gave] the largest key broken in public, and [was] described at AsiaCrypt'96, a cryptography conference. An update on the above may be found at the RSA Factoring Challege, for information on my part in breaking RSA-140 and RSA-155 (a 512-bit RSA-key) in 1999; or see the published paper Factorization of a 512-bit RSA Modulus. www.lehigh.edu /~bad0/bad0new.html   (282 words)

Factorization of a 512-bits RSA key   (Site not responding. Last check: 2007-10-19) Factorization of a 512-bits RSA key using the Number Field Sieve On August 22, 1999, we found that the 512-bits number The number RSA-155 is taken from the RSA Challenge list (see http://www.rsa.com/rsalabs/html/factoring.html). www.hamline.edu /~wnk/rsa/rsa.html   (1312 words)

Factorization of RSA-140 Using the Number Field Sieve - Cavallar, Kioen, Riele, Dodson, Lenstra, Leyland, Montgomery, ...   (Site not responding. Last check: 2007-10-19) The amount of computing time spent on RSA--140 was roughly twice that needed for RSA--130, about half of what could be expected from a straightforward extrapolation of... 6.7%: Factorization of a 512-bit RSA Modulus - Cavallar, Dodson, Lenstra, Lioen,.. 6 the factorization of RSA - Denny, Dodson et al. citeseer.ist.psu.edu /436337.html   (608 words)

Asymmetric Key sizes   (Site not responding. Last check: 2007-10-19) > From: Brian Morrison [mailto:bdm@fenrir.demon.co.uk] > There was a posting to sci.crypt (might have been > sci.crypt.research) a > few days ago stating that the RSA-140 factoring challenge had been > completed, this involves factoring a 140 digit number, a similar > process to that required to break an RSA key. > > I think that this development means that it is now possible to break > 512 bit RSA keys, and reduces the security of 768 bit RSA keys. I > certainly can't claim to be able to rigorously state this, > but that was the tone of the post. www.chiark.greenend.org.uk /pipermail/ukcrypto/1999-February/003478.html   (264 words)

Asymmetric Key sizes   (Site not responding. Last check: 2007-10-19) The RSA challenge RSA-140, a 140-digit modulus (about 465-bits long) was factored into two 70-digit prime numbers, using the Number Field Sieve(NFS), recently, see http://jya.com/rsa140.htm. 512-bit keys were considered on the small size for a quite while now, but they are definitely too close for comfort after this (although key length is really dependent on the application, I feel, the (absolute) minimum key length (for RSA) one should really use is 640-bits). Has anyone any information on the latest successful attack position on asymmetric keys, RSA in particular? www.chiark.greenend.org.uk /pipermail/ukcrypto/1999-February/003477.html   (152 words)

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