# RSA encryption

**RSA encryption** A method of public key encryption (see cryptography) devised by Rivest, Shamir, and Adleman. A message is encrypted by mapping it onto an integer, *M* say, raising *M* to a (publicly known) power *e* and forming the remainder on division by a (publicly known) divisor, *n*, to give the encrypted message *S*. Decryption is achieved by similarly raising *S* to a (secret) power *d*, and again forming the remainder on division by *n*; the result will be the value of *M*. The method relies on the choice of *n* as the product of two large secret prime numbers, *p* and *q*. The values of *e* and *d* are chosen such that *e *∗ *d* ≡ 1 mod ((*p*–1) ∗ (*q*–1))

Security is achieved largely by the difficulty of finding the prime factors of *n*.

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**RSA encryption**