The discrete logarithm problem is to find the exponent in the expression Base^Exponent = Power (mod Modulus).

This applet works for both prime and composite moduli. The only restriction is that the base and the modulus, and the power and the modulus must be relatively prime.

In this version of the discrete logarithm calculator only the Pohlig-Hellman algorithm is implemented, so the execution time is proportional to the square root of the largest prime factor of the modulus minus 1. The applet works in a reasonable amount of time if this factor is less than 10¹⁷.

I will add the index-calculus algorithm soon. This algorithm has subexponential running time.

You can also enter expressions that use the following operators and parentheses:

• + for addition
• - for subtraction
• * for multiplication
• / for integer division
• ^ for exponentiation
• n!: factorial
• p#: primorial (product of all primes less or equal than p).
• B(n): Previous pseudoprime to n
• F(n): Fibonacci number F_n
• L(n): Lucas number L_n = F_n-1 + F_n+1
• N(n): Next pseudoprime to n
• P(n): Unrestricted Partition Number (number of decompositions of n into integer summands without regard to order).

The pseudoprime tests used in functions B and N includes trial division by the 100 first primes and then up to 20 Rabin-Miller strong pseudoprime tests. So it has a very high probability to find a prime number.

The final value must have 1000 or less digits, intermediate results must have 2000 or less digits and in the case of divisions, the dividend must be multiple of the divisor.

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