RSA cryptosystem

RSA is a public-key cryptographic system whose security relies on the difficulty of factoring products of large primes. It supports encryption and digital signatures through modular exponentiation.

RSA key generation: The procedure for creating RSA public and private keys from two prime numbers. Choosing the primes produces the modulus and exponents at the heart of an RSA key pair.
RSA encryption: An encryption method that uses an RSA public key to protect a message for its private-key holder. This is RSA’s confidentiality use, usually applied to a short secret or key rather than bulk data.
Elliptic-curve cryptography: Public-key cryptography based on algebraic operations on elliptic curves over finite fields. It offers comparable security with smaller keys and often less computation than RSA.
Public-key cryptography: Cryptography using related public and private keys for encryption, signatures, or key exchange. RSA became one of the earliest widely deployed systems in this broader family.
Integer factorization: The decomposition of an integer into prime factors. Factoring RSA’s public modulus can reveal the primes needed to recover its private key.
Modular exponentiation: Exponentiation in which results are reduced modulo a fixed integer. RSA transforms messages and signatures by raising values to powers modulo its public modulus.
RSA signature: A digital signature scheme that uses an RSA private key to authenticate a message or its digest. RSA signatures provide authenticity and integrity through a separate signing operation.
Diffie–Hellman key exchange: A protocol that lets parties establish a shared secret over a public channel. Unlike RSA encryption, Diffie–Hellman establishes shared keys rather than encrypting messages directly.
Rivest–Shamir–Adleman: The three cryptographers who introduced the RSA public-key cryptosystem in 1977. Their surnames form RSA, and their 1977 paper presented the system.
Shor's algorithm: A quantum algorithm that factors integers in polynomial time on a sufficiently capable quantum computer. It threatens RSA’s factoring-based security if large fault-tolerant quantum computers become practical.

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