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The security of RSA relies on the practical difficulty of factoring the product of two large prime numbers, the "factoring problem". Breaking RSA encryption is known as the RSA problem. Whether it is as difficult as the factoring problem is an open question. [3] There are no published methods to defeat the system if a large enough key is used.
In cryptography, the RSA problem summarizes the task of performing an RSA private-key operation given only the public key. The RSA algorithm raises a message to an exponent, modulo a composite number N whose factors are not known. Thus, the task can be neatly described as finding the e th roots of an arbitrary number, modulo N.
Cryptography, or cryptology (from Ancient Greek: ... often from number theory. For example, the hardness of RSA is related to the integer factorization problem, ...
For example, RSA relies on the assertion that factoring large numbers is hard. A weaker notion of security, defined by Aaron D. Wyner, established a now-flourishing area of research that is known as physical layer encryption. [4] It exploits the physical wireless channel for its security by communications, signal processing, and coding techniques.
The RSA Factoring Challenge was a challenge put forward by RSA Laboratories on March 18, 1991 [1] to encourage research into computational number theory and the practical difficulty of factoring large integers and cracking RSA keys used in cryptography.
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation in Galois fields , such as the RSA cryptosystem and ElGamal cryptosystem .
A deterministic encryption scheme (as opposed to a probabilistic encryption scheme) is a cryptosystem which always produces the same ciphertext for a given plaintext and key, even over separate executions of the encryption algorithm.
Asymmetric key cryptography, Diffie–Hellman key exchange, and the best known of the public key / private key algorithms (i.e., what is usually called the RSA algorithm), all seem to have been independently developed at a UK intelligence agency before the public announcement by Diffie and Hellman in 1976.