The RSA Crypto System was released 1978 by Ronald Rivest, Adi Shamir and Leonard Adleman. It is the most known and used public-key-crypto system, so you better learn how it works.
Preparations 1) Choose two huge prime numbers: p and q; 2) Calculate: m= pq; 3) Calculate: w(m)=(p-1)(q-1);//Euler's Function 4) Choose a number e with: gcd(e,w(m)) = 1; 5) Calculate d with: ed = 1; //in Z/w(m)Z Fact: Any number x in Z will be: ed=xw(m)+1;//Fermat the public key pair is (m,e) the private keys are p,q and d the alphabet of RSA is Z/mZ
cipher plain text cipher a plain text "x" with: y=x^e in Z/mZ; The person with knowledge of the private keys can decrypt y.
decipher cipher text decipher y with: (x^e)^d => x^ed in Z/mZ; This works, because of the "Fact" above.