In cryptography, encryption keys are fixed in length, repeating over and over to produce the cyphertext. Brute force guesses and cryptanalysis deduces to determine the key and extract plaintext from cyphertext. 

The ASBE algorithm allows for keys of variable length from 2008 bits to 2 gigabyte. A 2008-bit key is a billion times a billion times a billion (times a Billion 58 times) stronger than a 256-bit key length. Every additional bit in a key doubles the number of possibilities and doubles the time to break it by brute force.

Each additional byte in the key increases by a multiplier of 2⁸ = 256 times.

The ASBE algorithm further allows digital signatures, with the same exponential characteristics as the key. Using the largest digital signature of 64KB this multiplies the number of possibilities by 2^{8 X 65535}, which is 2⁵²⁴²⁸⁰ which is approximately 10¹⁵⁷²⁸⁴. 

The cryptosystem of the ASBE algorithm extracts keys and digital signatures from any existing file or from randomly generated data. Using a 2-GB data source, there are up to 4,000,000,000,000,000,000 possible keys or 1,200,000,000,000,000 possible signatures.