In an asymmetric key algorithm ( e. g., RSA ), there are two separate keys: a public key is published and enables any sender to perform encryption, while a private key is kept secret by the receiver and enables only him to perform correct decryption.

Common families include symmetric systems ( e. g. AES ) and asymmetric systems ( e. g. RSA ); they may alternatively be grouped according to the central algorithm used ( e. g. elliptic curve cryptography ).

For example, the security available with a 1024-bit key using asymmetric RSA is considered approximately equal in security to an 80-bit key in a symmetric algorithm ( Source: RSA Security ).

As of 2002, an asymmetric key length of 1024 bits was generally considered the minimum necessary for the RSA encryption algorithm.

The Finite Field Diffie-Hellman algorithm has roughly the same key strength as RSA for the same key sizes.

Derivatives of Shor's algorithm are widely conjectured to be effective against all mainstream public-key algorithms including RSA, Diffie-Hellman and elliptic curve cryptography.

It is a key element of the RSA algorithm, a public-key encryption method widely used in electronic commerce.

The ease of primality testing is a crucial part of the RSA algorithm, as it is necessary to find large prime numbers to start with.

For instance, in the original version, the RSA algorithm was used to encrypt session keys ; RSA's security depends upon the one-way function nature of mathematical integer factoring.

After a report from RSA Data Security, Inc., who were in a licensing dispute with regard to use of the RSA algorithm in PGP, the Customs Service started a criminal investigation of Zimmermann, for allegedly violating the Arms Export Control Act.

The latter authors published their work in 1978, and the algorithm appropriately came to be known as RSA.

* RSA encryption algorithm ( PKCS # 1 )

In particular, most of the popular public key ciphers are based on the difficulty of factoring integers ( or the related discrete logarithm problem, which can also be solved by Shor's algorithm ), including forms of RSA.

RSA is an algorithm for public-key cryptography that is based on the presumed difficulty of factoring large integers, the factoring problem.

The RSA algorithm was publicly described in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman at MIT ; the letters RSA are the initials of their surnames, listed in the same order as on the paper.

The patent would have expired on September 21, 2000 ( the term of patent was 17 years at the time ), but the algorithm was released to the public domain by RSA Security on 6 September 2000, two weeks earlier.

The RSA algorithm involves three steps: key generation, encryption and decryption.

The keys for the RSA algorithm are generated the following way:

RSA Security has never officially released the algorithm ; Rivest has, however, linked to the English Wikipedia article on RC4 in his own course notes.

* Details of the RSADSI ( RSA Data Security, Inc .) cryptographic algorithm software were revealed, probably deliberately, through publication of alleged RC4 source on Usenet.

In 1995 Adam Back wrote a version of the RSA algorithm for public-key cryptography in three lines of Perl and suggested people use it as an email signature file:

However, the CSS algorithm seems to require more characters to describe in a computer programming language than the RSA algorithm ; one of the shortest implementations of DeCSS ( called " efdtt ") is 434 bytes.

Cryptography professor Arjen Lenstra observed that " Last time, it took nine years for us to generalize from a special to a nonspecial, hard-to-factor number " and when asked whether 1024-bit RSA keys are dead, said: " The answer to that question is an unqualified yes.

According to Professor Gilles Brassard, an expert in quantum computing: " The time needed to factor an RSA integer is the same order as the time needed to use that same integer as modulus for a single RSA encryption.

At the RSA Conference 2005, the National Security Agency ( NSA ) announced Suite B which exclusively uses ECC for digital signature generation and key exchange.

* RSA BSAFE ( R ) Share for Java Platform and Share for C / C ++: Free binary toolkits

The sender uses PGP to create a digital signature for the message with either the RSA or DSA signature algorithms.

Several public-key cryptography algorithms, such as RSA and the Diffie – Hellman key exchange, are based on large prime numbers ( for example 512 bit primes are frequently used for RSA and 1024 bit primes are typical for Diffie – Hellman .).

Thus, Jevons anticipated a key feature of the RSA Algorithm for public key cryptography, although he certainly did not invent the concept of public key cryptography.

RSA stands for Ron Rivest, Adi Shamir and Leonard Adleman, who first publicly described it in 1977.

Five members of the Scott family are directors, and all have worked for RSA.

* RFC 4432, RSA Key Exchange for the Secure Shell ( SSH ) Transport Layer Protocol ( March 2006 )

** publickey: a method for public key-based authentication, usually supporting at least DSA or RSA keypairs, with other implementations also supporting X. 509 certificates.

* ECDSA: support for elliptic curve DSA rather than DSA or RSA for signing.

If a quantum computer with a sufficient number of qubits were to be constructed, Shor's algorithm could be used to break public-key cryptography schemes such as the widely used RSA scheme.

While modes of operation are commonly associated with symmetric encryption, they may also be applied to public-key encryption primitives such as RSA in principle ( though in practice public-key encryption of longer messages is generally realized using hybrid encryption ).

DNSCurve uses techniques from elliptic curve cryptography to give a vast decrease in computational time over the RSA public-key algorithm used by DNSSEC, and uses the existing DNS hierarchy to propagate trust by embedding public keys into specially formatted ( but backward-compatible ) DNS records.

* Ronald L. Rivest, Adi Shamir, and Leonard M. Adleman's first public-key cryptosystem ( RSA ).

* Branch prediction analysis attacks ( relating to RSA public-key cryptography )

RSA Laboratories stated: " Now that the industry has a considerably more advanced understanding of the cryptanalytic strength of common symmetric-key and public-key algorithms, these challenges are no longer active.

A primary application is for choosing the key length of the RSA public-key encryption scheme.

According to RSA Laboratories, " Now that the industry has a considerably more advanced understanding of the cryptanalytic strength of common symmetric-key and public-key algorithms, these challenges are no longer active.

In cryptography, PKCS is a group of public-key cryptography standards devised and published by RSA Security Inc, starting in the early 1990s.

* RSA ( algorithm ), an algorithm for public-key encryption

* LUC is a public-key cryptosystem based on Lucas sequences that implements the analogs of ElGamal ( LUCELG ), Diffie-Hellman ( LUCDIF ), and RSA ( LUCRSA ).

Modern cryptographic systems include symmetric-key algorithms ( such as DES and AES ) and public-key algorithms ( such as RSA ).

As such, the task can be neatly described as finding the e < sup > th </ sup > roots of an arbitrary number, modulo N. For large RSA key sizes ( in excess of 1024 bits ), no efficient method for solving this problem is known ; if an efficient method is ever developed, it would threaten the current or eventual security of RSA-based cryptosystems — both for public-key encryption and digital signatures.