On factoring large numbers
نویسندگان
چکیده
منابع مشابه
Factoring Large Numbers with the TWIRL Device
The security of the RSA cryptosystem depends on the difficulty of factoring large integers. The best current factoring algorithm is the Number Field Sieve (NFS), and its most difficult part is the sieving step. In 1999 a large distributed computation involving hundreds of workstations working for many months managed to factor a 512-bit RSA key, but 1024-bit keys were believed to be safe for the...
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The quadratic sieve algorithm was used to factor a 47-digit number into primes. A comparison with Wagstaff's results using the continued fraction early abort algorithm suggests that QS should be faster than CFEA when the number being factored exceeds 60 digits (plus or minus ten or more digits, depending on details of the hardware and software).
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The current record in factoring large RSA keys is the factorization of a 465 bit (140 digit) number achieved in February 1999 by running the Number Field Sieve on hundreds of workstations for several months. This paper describes a novel factoring technique which is several orders of magnitude more e cient. It is based on a very simple handheld optoelectronic device which can analyse 100,000,000...
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This paper develops and evaluates an architecture for high-speed number factoring on a configurable computing system based on field programmable gate arrays (FPGA). Currently, the primary interest in factoring large integers is to test the integrity of a number of cryptosystems, particularly the RSA public key system developed by Rivest, Shamir, and Adleman [4, 5]. The RSA algorithm can be used...
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The ability to conduct secure electronic transactions is becoming more and more important everyday. One of the most popular cryptosystems for securing electronic data is RSA and it relies on the fact that it is computationally difficult to factor a large number into its prime factors. If an algorithm that can achieve this in a reasonable amount of time is discovered, the value of the RSA crypto...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1931
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1931-05271-x