Systems and computer-implemented methods for generating pseudo random numbers

A non-transitory machine-readable medium storing instructions which, when executed by one or more processors, cause an electronic apparatus to perform operations including:

• a) receiving, by a pseudo random number generator module, an instruction to generate pseudo random numbers from a security application;
• b) 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 electronic apparatus, wherein the transcendental equation comprises a transcendental function that is capable of generating transcendental number outputs from algebraic number inputs;
• c) calculating, by the pseudo random number generator module, a solution to the transcendental equation based on the at least one algebraic input parameter value;
• d) determining, by the pseudo random number generator module, one or more pseudo random numbers based on the solution;
• and
• e) storing, by the pseudo random number generator module, the one or more pseudo random numbers 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.

A device comprising:

• one or more processors;
• and
• memory comprising non-transitory machine-readable instructions which, when executed by the one or more processors, causes the device to perform:
• a) receiving, by a pseudo random number generator module of the device, an instruction to generate pseudo random numbers from a security application;
• b) determine, 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;
• c) calculate, by the pseudo random number generator module, a solution to the transcendental equation based on the at least one algebraic input parameter value;
• d) determine, by the pseudo random number generator module, one or more pseudo random numbers based on the solution;
• and
• e) store, by the pseudo random number generator module, the one or more pseudo random numbers 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.

A host computer comprising:

• one or more processors;
• memory comprising a non-transitory machine-readable instructions;
• and
• one or more virtual machines, each virtual machine being configured to perform:
• a) receiving, by a pseudo random number generator module of the host computer, an instruction to generate pseudo random numbers from a security application;
• b) determine, 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 host computer, wherein the transcendental equation comprises a transcendental function that is capable of generating transcendental number outputs from algebraic number inputs;
• c) calculate, by the pseudo random number generator module, a solution to the transcendental equation based on the at least one algebraic input parameter value;
• d) determine, by the pseudo random number generator module, one or more pseudo random numbers based on the solution;
• and
• e) store, by the pseudo random number generator module, the one or more pseudo random numbers 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.

A computer implemented method comprising:

• determining data to be encrypted, wherein the data comprises plaintext converted into a first bit stream;
• determining an encryption key, wherein the encryption key comprises at least one algebraic input value;
• generating a set of pseudo random numbers by:
• using the encryption key as an at least one algebraic input parameter value for a transcendental equation, wherein the transcendental equation comprises a transcendental function capable of generating transcendental number outputs from algebraic number inputs;
• calculating a solution to the transcendental equation based on the at least one algebraic input parameter value;
• and
• generating a pseudo random value based on the solution;
• determining a second bit stream based on the generated set of pseudo random numbers;
• performing a stream cipher operation based on the first bit stream and the second bit stream to produce an encrypted bit stream;
• and
• outputting the encrypted bit stream.

A computer implemented method comprising:

• determining an encrypted bit stream data to be decrypted;
• determining a decryption key for decrypting the encrypted bit stream, wherein the decryption key comprises at least one algebraic input value used to generate a bit stream for decrypting the encrypted bit stream data;
• generating a set of pseudo random numbers by:
• determining at least one algebraic input parameter value for a transcendental equation, wherein the transcendental equation comprises a transcendental function capable of generating transcendental number outputs from algebraic number inputs, and wherein the at least one algebraic input parameter value comprises the decryption key;
• calculating a solution to the transcendental equation based on the at least one algebraic input parameter value;
• and
• generating a pseudo random number value based on the solution;
• determining a second bit stream based on the generated set of pseudo random numbers;
• performing a stream cipher operation based on the encrypted bit stream and the second bit stream to produce a first bit stream;
• and
• outputting the first bit stream as the decrypted bit stream.

A non-transitory machine-readable medium storing instructions which, when executed by one or more processors, cause an electronic apparatus to perform operations including:

• determining data to be encrypted, wherein the data comprises plaintext converted into a first bit stream;
• determining an encryption key, wherein the encryption key comprises at least one algebraic input value;
• generating a set of pseudo random numbers by:
• using the encryption key as an at least one algebraic input parameter value for a transcendental equation, wherein the transcendental equation comprises a transcendental function capable of generating transcendental number outputs from algebraic number inputs;
• calculating a solution to the transcendental equation based on the at least one algebraic input parameter value;
• and
• generating a pseudo random value based on the solution;
• determining a second bit stream based on the generated set of pseudo random numbers;
• performing a stream cipher operation based on the first bit stream and the second bit stream to produce an encrypted bit stream;
• and
• outputting the encrypted bit stream.

An encryption/decryption system comprising:

• one or more processors;
• and
• memory comprising a non-transitory machine-readable instructions which, when executed by the one or more processors, causes the system to:
• determine data to be encrypted, wherein the data comprises plaintext converted into a first bit stream;
• determine an encryption key, wherein the encryption key comprises at least one algebraic input value;
• generate a set of pseudo random numbers by:
• using the encryption key as an at least one algebraic input parameter value for a transcendental equation, wherein the transcendental equation comprises a transcendental function capable of generating transcendental number outputs from algebraic number inputs;
• calculating a solution to the transcendental equation based on the at least one algebraic input parameter value;
• and
• generating a pseudo random value based on the solution;
• determine a second bit stream based on the generated set of pseudo random numbers;
• perform a stream cipher operation based on the first bit stream and the second bit stream to produce an encrypted bit stream;
• and
• output the encrypted bit stream.

A non-transitory machine-readable medium storing instructions which, when executed by one or more processors, cause an electronic apparatus to perform operations including:

• determining an encrypted bit stream data to be decrypted;
• determining a decryption key for decrypting the encrypted bit stream, wherein the decryption key comprises at least one algebraic input value used to generate a bit stream for encrypting the encrypted bit stream data;
• generating a set of pseudo random numbers by:
• determining at least one algebraic input parameter value for a transcendental equation, wherein the transcendental equation comprises a transcendental function capable of generating transcendental number outputs from algebraic number inputs, and wherein the at least one algebraic input parameter value comprises the decryption key;
• calculating a solution to the transcendental equation based on the at least one algebraic input parameter value;
• and
• generating a pseudo random number value based on the solution;
• determining a second bit stream based on the generated set of pseudo random numbers;
• performing a stream cipher operation based on the encrypted bit stream and the second bit stream to produce a first bit stream;
• and
• outputting the first bit stream as the decrypted bit stream.

An encryption/decryption system comprising:

• one or more processors;
• and
• memory comprising non-transitory machine-readable instructions which, when executed by the one or more processors, causes the system to:
• determine an encrypted bit stream data to be decrypted;
• determine a decryption key for decrypting the encrypted bit stream, wherein the decryption key comprises at least one algebraic input value used to generate a bit stream for encrypting the encrypted bit stream data;
• generate a set of pseudo random numbers by:
• determining at least one algebraic input parameter value for a transcendental equation, wherein the transcendental equation comprises a transcendental function capable of generating transcendental number outputs from algebraic number inputs, and wherein the at least one algebraic input parameter value comprises the decryption key;
• calculating a solution to the transcendental equation based on the at least one algebraic input parameter value;
• and
• generating a pseudo random number value based on the solution;
• determine a second bit stream based on the generated set of pseudo random numbers;
• perform a stream cipher operation based on the encrypted bit stream and the second bit stream to produce a first bit stream;
• and
• output the first bit stream as the decrypted bit stream.