System and method to generate prime numbers in cryptographic applications
AssigneeCryptography Research, Inc.
InventorsQinglai Xiao, Michael Alexander Hamburg, Michael Tunstall
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Abstract
Aspects of the present disclosure involve a method, a system and a computer readable memory to generate and use prime numbers in cryptographic operations by determining one or more polynomial functions that have no roots modulo each of a predefined set of prime numbers, selecting one or more input numbers, generating a candidate number by applying one or more instances of the one or more polynomial functions to the one or more input numbers, determining that the candidate number is a prime number, and using the determined prime number to decrypt an input into the cryptographic operation.
Claims20
A method to perform a cryptographic operation, the method comprising:
- determining, by a processing device, one or more polynomial functions that have no roots modulo each of a predefined set of prime numbers;
- selecting, by the processing device, one or more input numbers;
- generating, by the processing device, a candidate number by applying one or more instances of the one or more polynomial functions to the one or more input numbers;
- determining, by the processing device, that the candidate number is a prime number, and
- using, by the processing device, the determined prime number to decrypt an input into the cryptographic operation.
A system to perform a cryptographic operation, the system comprising:
- a memory device;
- and
- a processing device communicatively coupled to the memory device, the processing device to:
- determine one or more polynomial functions that have no roots modulo each of a predefined set of prime numbers;
- select one or more input numbers;
- generate a candidate number by applying one or more instances of the one or more polynomial functions to the one or more input numbers;
- determine that the candidate number is a prime number;
- and
- use the determined prime number to decrypt an input into the cryptographic operation.
A non-transitory computer-readable medium storing instructions thereon, wherein the instructions, when executed by a processing device performing a cryptographic operation, cause the processing device to:
- determine one or more polynomial functions that have no roots modulo each of a predefined set of prime numbers;
- select one or more input numbers;
- generate a candidate number by applying one or more instances of the one or more polynomial functions to the one or more input numbers;
- determine that the candidate number is a prime number;
- and
- use the determined prime number to decrypt an input into the cryptographic operation.
Dependencies are inferred from the claim text.