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RSA encryption

cryptography, algorithm A public-key cryptosystem for both

encryption and authentication, invented in 1977 by Ron

Rivest, Adi Shamir, and Leonard Adleman. Its name comes from

their initials.

The RSA algorithm works as follows: take two large primenumbers, p and q, and find their product n = pq; n is called

the modulus. Choose a number, e, less than n and relativelyprime to (p-1)(q-1), and find its inverse, d, mod (p-1)(q-1),

which means that ed = 1 mod (p-1)(q-1); e and d are called the

public and private exponents, respectively. The public key is

the pair (n,e); the private key is d. The factors p and q

must be kept secret, or destroyed. It is difficult

(presumably) to obtain the private key d from the public key

(n,e). If one could factor n into p and q, however, then one

could obtain the private key d. Thus the entire security of

RSA depends on the difficulty of factoring; an easy method for

factoring products of large prime numbers would break RSA.