GCD
For Greatest Common Divisor, Enter integers like this 9,21,33
Prime Factorization
For Prime Factorization, Enter an integer you want to factor
Multiplicative Inverse
For Multiplcative Inverses, Enter integer N and modulus M to return the inverse of N mod M.
Modular Arithmetic
For Modular Arithmetic, Enter integer N and modulus M to return the answer
Prime Number Theorem
Prime Number Theorem returns the number of Primes less than the Integer entered
Discrete Logarithms
Discrete Logarihms, enter integer n, the base of the logarithm b, and a prime p. L (the logarithm) is returned.
From Dr. Desoky
Here is a zip copy of the Cryptology Laboratory
It's written in java, just unzip it to any directory and on the CMD line, type "make".
Here is a zip copy of the Applets.
ElGamal Cipher
Hill Cipher
Railsplitter Cipher
RSA Cipher
Shift Cipher
Vigenere Cipher
One Time Pad Cipher
DES Cipher
Affine Analysis
Frequency Analysis
Code for each applet is included on each page.
Probability
Insert integers for n and r (r must be geater than n). This returns nCr = the number of combinations where
order isnt important and nPr = the number of permutations where the ordering of results is important.
Primitive Roots
Primitive roots input integers n and m and this will tell you if n is a primitive root mod m
Fast Exponentiation
Fast Exponentiation returns the solution to x^e mod m.
Roots mod P
Roots mod P returns the root.
Eulers Totient Function
Returns the number of integers less than n that are relatively prime to n. Obviously if n is prime,
the answer will be n-1.
Charmichael Lambda Function
Returns Lambda(n)
Euler Criterion
Answers the question is n a rth power mod m?
As in "Is 14 a square modulo 101?"
Fermat Pseudoprimes
A Fermat Pseudoprime tests for primality. An integer n is a Fermat Pseudoprime if 2^(n-1)=1 mod n.
Euclidean Algorithm
The Euclidean Algorithm finds the GCD of two numbers by using the modulo function.
As an example try Integer 1 = 983, and Integer 2 = 888.
As these two numbers are relatively prime, the GCD will be 1.
By changing Integer 1 to 984, the GCD is shown to be 24.
Miller-Rabin Test
This is a test for compositeness of an integer. It will determine
if the integer is composite with certainty, and is probabilistic in
its determination of primality.
Pollard Rho Test
This is a method to find a small factor of a large integer.
Pollard P-1 Test
Also a method to factor an integer. Please choose n to be larger than b.