# RSA Cipher in 8 Steps - Cryptography Tutorial

## Do the RSA Cipher Step by Step Cryptography >  Public Key Ciphers  > RSA Cipher (3/6) : RSA in 8 Steps (30 min.)   Objectives: 1) Understand  the 8 RSA Encryption steps.

RSA Cipher in 8 Steps

 On this page, perform the 8 steps involved when encoding using the RSA Cipher. Different from its practical usage, I am using primes p and q that are less than 30. As a consequence, the decoding key d could easily be broken and the cipher is far from being secure. This page serves solely demonstration purposes. Observe that the first 6 steps are the key generation steps that are performed quickly by a computer. Steps 7 and 8 display the actual coding process.
 Steps 1-6: Preparation Exercise 1: Why does the modulus m = p * q have to be greater than 26? Give a counterexample and explain it. For instance, if the modulus is 13 only 13 different letters can be encrypted. i.e. b=1 and 0=14 are encrypted to the same cipher letter since 1=14 mod 13. Exercise 2: When using p=17 and q=23 the modulus is m = 391. If e=3, how could you find the decoding key d? Try to find it yourself. d has to be the inverse of e=3 mod phi where phi=(p-1)*(q-1)=16*22=352. The Extended Euclidean Algorithm finds d=235.     Exercise 3: When m = 209, among how many possible encoding keys e can we choose from? Is there a faster way than trial and error to find the number?  e has to be relative prime to phi=(11-1)*(19-1)=180.  Euler's j-function shows that there are j(180) = 48  such integers. The Euclidean Algorithm finds such integers. 1) 2) 3) Having generated 2 distinct random primes less than 30, we have to assure that their product is greater than 26. 4) 5) The key e has to be relative prime to (p-1)*(q-1). It is selected by simply checking 3, 5, 7, etc.  Remember that the security of RSA does not rely on the choice of e. 6)

 Steps 7 and 8: CODING PROCESS Plain text (use lower case letters only) Cipher text Cipher text Plain text

 The RSA Cipher was invented in 1976 by the 3  Mathematicians Rivest, Shamir and Adleman. Read Textbook on the RSA Cipher and its History

Related web sources:

RSA.com

Pictures of the 3 RSA Inventors

Yahoo.com on the 3 RSA inventors

Encarta.com

Yahoo's Encryption & Security

Glossary

PBS Online

Introduction to Cryptography

Enigma and the Codebreakers

Enigma History

Enigma Emulator

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