A regression on a prime-indexed-prime finite difference generator function is used to predict prime numbers. It is emphasized that this abstract is provided to comply with the rules requiring an abstract that will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.

The present invention relates to a method for generating a prime number and using it in a cryptographic application, comprising the steps of: a) determining at least one binary base B with a small size b=log.sub.2(B) bits and for each determined base B at least one small prime p.sub.i such that B mod p.sub.i=1, with i an integer, b) selecting a prime candidate Y.sub.P, c) decomposing the selected prime candidate Y.sub.P in a base B selected among said determined binary bases : Y.sub.P=y.sub.jB.sup.id) computing a residue y.sub.PB from the candidate Y.sub.P for said selected base such that y.sub.PB=.sub.yje) testing if said computed residue y.sub.PB is divisible by one small prime pi selected among said determined small primes for said selected base B, f) while said computed residue y.sub.PB is not divisible by said selected small prime, iteratively repeating above step e) until tests performed at step e) prove that said computed residue y.sub.PB is not divisible by any of said determined small primes for said selected base B, g) when said computed residue y.sub.PB is not divisible by any of said determined small primes for said selected base B, iteratively repeating steps c) to f) for each base B among said determined binary bases, h) when, for all determined bases B, said residue y.sub.PB computed for a determined base is not divisible by any of said determined small primes for said determined base B, executing a known rigorous probable primality test on said candidate Y.sub.P, and when the known rigorous probable primality test is a success, storing said prime candidate Y.sub.P and using said stored prime candidate Y.sub.P in said cryptographic application.

Aspects of the present disclosure involve a method, a system and a computer readable memory to perform a cryptographic operation that includes identifying a first set of mutually coprime numbers, obtaining a second set of input numbers coprime with a corresponding one of the first set of mutually coprime numbers, obtaining an output number that is a weighted sum of the second set of input numbers, each of the second set of input numbers being taken with a weight comprising a product of all of the first set of mutually coprime numbers except the corresponding one of the first set of mutually coprime numbers, and performing the cryptographic operation using the output number.

Methods and systems for wave-based computation are provided. In one aspect, a wave-based computer includes an input circuit configured to receive a dividend and generate a plurality of prime waves and a dividend wave based on the received dividend, and a transmission circuit configured to receive the prime waves and the dividend wave from the input circuit. The wave-based computer further includes an output circuit configured to receive the prime waves and the dividend wave from the transmission circuit, detect zero-crossings of each of the prime waves and the dividend wave, and determine prime factors of the dividend based on the detected zero-crossings.

The present invention relates to a method to generate prime numbers on board a portable device, said method comprising the steps of, each time at least one prime number is requested: when available, retrieve results from previously performed derivation calculation or, if not, select a start point for derivation; process derivation calculation to converge towards a prime number; if a prime number is found, store it and restart derivation calculation from a new start point; stop the derivation calculation after a predetermined amount of time; store intermediate results to be used a next time a prime number will be requested; output a stored prime number.

A regression on a prime-indexed-prime finite difference generator function is used to predict prime numbers. It is emphasized that this abstract is provided to comply with the rules requiring an abstract that will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.

A system generating a prime number comprising a prime number generator (PNG) module and a pseudorandom number generator (PRNG) module which is configured to: initialise the pseudorandom number generator (PRNG) module; receive a request from the PNG module, the request containing a bit length of the pseudorandom number required; generate the required bit length of pseudorandom number; transmit a response containing the generated bit length of pseudorandom numbers to the PNG module. The PNG module is configured to: transmit the request containing the bit length of the pseudorandom numbers required; receive the response from the PRNG module; assign the pseudorandom numbers in the response to form raw data PPP; set a least significant bit (LSB) and most significant bit (MSB) of PPP as 1 to obtain a first big odd number denoted as PP; and execute an algorithm to determine a first big prime number starting from odd number PP.

The present description concerns a method of checking a first data element, executed by an electronic device comprising a processor and a memory, wherein the first data element is divided in N second data elements being stored in the memory, and first data element being equal to the sum, modulo the dimension of a space comprising the first data element, of the N second data elements, wherein an image of the first data element by a LCG function is stored in the memory, and the method comprising a step of checking if the image of the first data element by the LCG function is equal to the sum, modulo the module of the LCG function, of a product of an integer varying from 0 to N?1 and an image of the dimension by the LCG function, and of the images of the second data elements by the LCG function.

The arrangements disclosed herein relate to systems, apparatus, methods, and non-transitory computer readable media for generating, using a Quantum Random Number Generator (QRNG), an initial random number and a secondary random number, generating, using a Prime Number Generator (PGN), a random prime number using the initial random number and the secondary random number, and generating an encryption key using the random prime number, wherein the encryption key is used to encrypt first data or decrypt second data.

Generation of a message m of order (n) for a test of the integrity of the generation of a pair of cryptographic keys within the multiplicative group of integers modulo n=p.Math.q, including: key pair generation including, to generate p and q: a random selection of candidate integers; and a primality test; a first search of the multiplicative group of integers modulo p for a generator a; a second search of the multiplicative group of integers modulo q for a generator b; a third search for a number y, as message m, verifying: 1n1, where =a mod p and =b mod q, the first or second search being performed during the primality test.