Abstract: A methods comprises: receiving, by a pseudo random number generator module, an instruction to generate pseudo random numbers from a security application; determining, by the pseudo random number generator module, at least one algebraic input parameter value for a transcendental equation from a randomness library in memory of the device, wherein the transcendental equation comprises a transcendental function that is capable of generating transcendental number outputs from algebraic number inputs; calculating, by the pseudo random number generator module, a solution to the transcendental equation based on the at least one algebraic input parameter value; determining, by the pseudo random number generator module, pseudo random number(s) based on the solution; and storing, by the pseudo random number generator module, the pseudo random number(s) in a randomness library for use as seeds for keys by the security application and as subsequent input parameter values for the pseudo random number generator module.

Abstract: Described embodiments relate to systems and method for conditioning, de-biasing and/or whitening raw entropy data or for hashing data. The method comprises receiving data; determining at least a first algebraic number from the data; calculating at least one solution to one or more transcendental equations using the at least the first algebraic number as an input parameter value, wherein the one or more transcendental equations comprise a transcendental function that is capable of generating transcendental number outputs from algebraic number inputs; determining one or more sequences of pseudo random numbers based on the at least one solution; and determining an output based on the one or more sequences of pseudo random numbers. For example, the data may be received from a raw entropy source and comprise raw entropy to be transformed. Alternatively, the data may be data to be hashed and the output may comprise a hash of the data.