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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.
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.
Cryptography, or cryptology (from Ancient Greek: ... often from number theory. For example, the hardness of RSA is related to the integer factorization problem, ...
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 .
RSA (Rivest–Shamir–Adleman) is another notable public-key cryptosystem. Created in 1978, it is still used today for applications involving digital signatures. [17] Using number theory, the RSA algorithm selects two prime numbers, which help generate both the encryption and decryption keys. [18]
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.