Cryptography: True Randomness and Pseudorandomness

Sunday 24 May 2026

A random number (binary string) is a number drawn (selected) from a set of numbers in an unpredictable, independent manner. So each member of the set has an equal chance of being selected. This means the outcome (selected number) has nothing to do with the past or future selection. In computing, this is true randomness. Pseudorandomness is a number selection from the set of numbers that looks random-like. The application areas include cryptography, computer simulation, gaming, and statistics, to name a few. 

Example: Random string selection from a set of 3-bit binary strings 

Set = {0, 1}^3 = {000, 001, 010, 011, 100, 101, 110, 111}

Probability [ each 3-bit binary string ] = 1/8 

Probability distribution = {1/8, 1/8, 1/8, 1/8, 1/8, 1/8, 1/8, 1/8}

Example: Pseudorandom string selection from a set of 3-bit binary strings according to a given selection process Pr [ string ].

Pr [ string ] = ¼, for strings 001, 011, 101, 111

                   = 0,  for strings 000, 010, 100, 110

Probability distribution = {0, 1/4, 0, 1/4, 0, 1/4, 0, 1/4}