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Bits Time Memory used 128 0.4886 seconds 0.1 MiB 192 3.9979 seconds 0.5 MiB 256 103.1746 seconds 3 MiB 300 1175.7826 seconds 10.9 MiB In 2009, Benjamin Moody factored an RSA-512 bit key in 73 days using only public software (GGNFS) and his desktop computer (a dual-core Athlon64 with a 1,900 MHz cpu.). Just less than five gigabytes of disk storage was required and about 2.5 gigabytes of RAM for the sieving process.

RSA General Designers,, and First published 1977 Certification,, Cipher detail 1,024 to 4,096 bit typical Rounds 1 Best public for classical computers for quantum computers A has been broken RSA ( RivestShamirAdleman) is one of the first and is widely used for secure data transmission.

In such a, the is public and it is different from the which is kept secret (private).

In RSA, this asymmetry is based on the practical difficulty of the of the product of two large, the.

The RSA is made of the initial letters of the surnames of,, and, who first publicly described the algorithm in 1978., an English mathematician working for the British intelligence agency (GCHQ), had developed an equivalent system in 1973, but this was not until 1997.

A user of RSA creates and then publishes a public key based on two large, along with an auxiliary value.

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E Prime 2 0 S Code The Message

Anyone can use the public key to encrypt a message, but with currently published methods, and if the public key is large enough, only someone with knowledge of the prime numbers can decode the message feasibly.

Whether it is as difficult as the factoring problem remains an open question.

More often, RSA passes encrypted shared keys for cryptography which in turn can perform bulk encryption-decryption operations at much higher speed.

See also:,, and The security of the RSA cryptosystem is based on two mathematical problems: the problem of and the.

Full decryption of an RSA ciphertext is thought to be infeasible on the assumption that both of these problems are hard, i.e., no efficient algorithm exists for solving them.

Providing security against partial decryption may require the addition of a secure.

Currently the most promising approach to solving the RSA problem is to factor the modulus n.

With the ability to recover prime factors, an attacker can compute the secret exponent d from a public key ( n, e), then decrypt c using the standard procedure.

To accomplish this, an attacker factors n into p and q, and computes lcm( p 1, q 1) which allows the determination of d from e.

No polynomial-time method for factoring large integers on a classical computer has yet been found, but it has not been proven that none exists.

Multiple polynomial quadratic sieve (MPQS) can be used to factor the public modulus n.

Bits Time 128 Less than 2 seconds 192 16 seconds 256 35 minutes 260 1 hour A tool called YAFU can be used to optimize this process.

Just less than five gigabytes of disk storage was required and about 2.5 gigabytes of RAM for the sieving process.

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