In 1979, Michael O. Rabin published a related cryptosystem that is provably secure, at least as long as the factorization of the public key remains difficult-it remains an assumption that RSA also enjoys this security.

In addition to RSA, Shamir's other numerous inventions and contributions to cryptography include the Shamir secret sharing scheme, the breaking of the Merkle-Hellman knapsack cryptosystem, visual cryptography, and the TWIRL and TWINKLE factoring devices.

He is known for being a co-inventor of the RSA ( Rivest – Shamir – Adleman ) cryptosystem in 1977, and of DNA computing.

For his contribution to the invention of the RSA cryptosystem, Adleman, along with Ron Rivest and Adi Shamir, has been a recipient of the 1996 Paris Kanellakis Theory and Practice Award and the 2002 ACM Turing Award, often called the Nobel Prize of Computer Science.

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

The Rabin cryptosystem is an asymmetric cryptographic technique, whose security, like that of RSA, is related to the difficulty of factorization.

However the Rabin cryptosystem has the advantage that the problem on which it relies has been proved to be as hard as integer factorization, which is not currently known to be true of the RSA problem.

It has been proven that decoding the Rabin cryptosystem is equivalent to the integer factorization problem, which is rather different than for RSA.

The NTRUEncrypt public key cryptosystem, also known as the NTRU encryption algorithm, is a lattice-based alternative to RSA and ECC and is based on the shortest vector problem in a lattice ( i. e. is not known to be breakable using quantum computers ).

Rabin's oblivious transfer scheme is based on the RSA cryptosystem.

He implemented the RSA cryptosystem in an export-friendly

These names were used by Ron Rivest in the 1978 Communications of the ACM article presenting the RSA cryptosystem, and in A Method for Obtaining Digital Signatures and Public-Key Cryptosystems published April 4, 1977, revised September 1, 1977 as technical Memo LCS / TM82.

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

The McEliece cryptosystem has some advantages over, for example, RSA.

It has been largely superseded by the Miller – Rabin primality test, but has great historical importance in showing the practical feasibility of the RSA cryptosystem.

To achieve the full strength of the RSA problem, an RSA-based cryptosystem must also use a padding scheme like OAEP, to protect against such structural problems in RSA.

Examples of deterministic encryption algorithms include the RSA cryptosystem ( without encryption padding ), and many block ciphers when used in ECB mode or with a constant initialization vector.

The modulus used in GM encryption is generated in the same manner as in the RSA cryptosystem.

The difficulty of breaking the RSA cipher — recovering a plaintext message given a ciphertext and the public key — is connected to the difficulty of factoring large numbers.

For her Intel Science Fair project Flannery prepared a demonstration where the same plaintext was enciphered using both RSA and her new Cayley – Purser algorithm and it did indeed show a significant time improvement.

Then, to encrypt a message, each message block is encoded as a number ( as in RSA ) and they are placed four at a time as elements of a plaintext matrix.

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.

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 ).

The computation is roughly equivalent to breaking a 700 bit RSA key.

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.

An RSA key length of 3072 bits should be used if security is required beyond 2030.

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.

The primary benefit promised by ECC is a smaller key size, reducing storage and transmission requirements — i. e., that an elliptic curve group could provide the same level of security afforded by an RSA-based system with a large modulus and correspondingly larger key — e. g., a 256bit ECC public key should provide comparable security to a 3072bit RSA public key ( see # Key sizes ).

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

The presumed difficulty of this problem is at the heart of widely used algorithms in cryptography such as RSA.

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.

RSA relies on the assumption that it is much easier ( i. e., more efficient ) to perform the multiplication of two ( large ) numbers x and y than to calculate x and y ( assumed coprime ) if only the product xy is known.

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

Whether breaking RSA encryption is as hard as factoring is an open question known as the RSA problem.

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.

Because of this, it has not been distributed by some of the more " inventive " methods used to distribute the RSA algorithm during the days of ITAR — it is not suitable for tattoos, email signatures, etc.

" Huneker encrypted the alien message with a 512-digit number using RSA, knowing that it would be decades before computer technology could decode it.

RSA Security, which has a patent on the algorithm, offered a series of US $ 10, 000 prizes for breaking ciphertexts encrypted with RC5, but these contests have been discontinued as of May 2007.

The Bleichenbacher attacks, also known as the million message attack, took advantage of flaws within the PKCS # 1 function to gradually reveal the content of an RSA encrypted message.

In Windows 2000, the user's RSA private key is not only stored in a truly encrypted form, but there is also a backup of the user's RSA private key that is more weakly protected.

This is because the backup of the user's RSA private key is encrypted with an LSA secret, which is accessible to any attacker who can elevate their login to LocalSystem ( again, trivial given numerous tools on the Internet ).

In Windows 2000, XP or later, the user's RSA private key is encrypted using a hash of the user's NTLM password hash plus the user name – use of a salted hash makes it extremely difficult to reverse the process and recover the private key without knowing the user's passphrase.

Files encrypted with EFS can only be decrypted by using the RSA private key ( s ) matching the previously used public key ( s ).

Gpcode. AG, which was detected in June 2006, was encrypted with a 660-bit RSA public key.