Number RSA

The numbers RSA , listed by the company of safety RSA Security, are great particular numbers (Semi-first S) (c.a.d. of the numbers which have exactly two factors first); they formed the base of the Compétition of factorization RSA, where these numbers were required in these Factorization S. Of the silver Grands Prix were offered for successful factorizations of RSA-576 to RSA-2048. The competition was stopped in May 2007.

First generated numbers RSA, of RSA-100 to RSA-500, were labelled in reference to their numbers of decimal digits ; later, nevertheless, while starting with RSA-576, the binary digits were counted in the place. An exception to this is the number RSA-617, which was created before the change of the diagram of numeration.

Mathematics

That is to say N a number RSA. There exist Prime numbers p and Q such as

$n=pq\; \backslash ,\; \backslash !$.

The problem is to find these two prime numbers, knowing only N .

If $s=p+q\; \backslash ,\; \backslash !$; then the values of some basic functions arithmetic are

$d\; (N)\; =\; 2\; \backslash ,\; \backslash !$

$\backslash \; phi\; (N)\; =\; (p-1)\; (q-1)\; =\; N\; +\; 1\; -\; S\; \backslash ,\; \backslash !$

$\backslash \; sigma\; (N)\; =\; (p+1)\; (q+1)\; =\; N\; +\; 1\; +\; S\; \backslash ,\; \backslash !$

Prices and records

The following table gives an overall picture of all numbers RSA:

See too

• Algorithm RSA

External bonds

• RSA Security : Files on the competition of factorization RSA
• MathWorld: number RSA
• Mathematica Package for numbers RSA

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