Method for on-board prime number generation

1. Method to generate prime number on board a portable computing device, said method comprising the steps of, each time at least one prime number is requested:

store, by the portable computing device, a predefined number of pre-calculated prime numbers, said pre-calculated prime numbers being available to be output in case no other calculated prime number is available, wherein the predefined number of the pre-calculated prime numbers is determined depending on calculation resources of the portable computing device and generation duration constraints from an application requesting the generation;

when available, retrieve, by the portable computing device, results from previously performed derivation calculation or, if not, select a start point for derivation;

process, by the portable computing device, derivation calculation to converge towards a prime number;

if a prime number is found, store, by the portable computing device, the prime number and restart derivation calculation from a new start point;

stop, by the portable computing device, continuation of the derivation calculation after one or more iterations of the derivation calculation and after a predetermined amount of time;

store, by the portable computing device, intermediate results to be used a next time a prime number will be requested; and

output, by the portable computing device, a stored prime number different from the intermediate results.

2. Method according to claim 1 , said method being further implemented during non critical phases of functioning of the portable computing device even in absence of any request for a prime number.

3. Method according to claim 1 , further including using the prime numbers for the generation of cryptographic material.

4. Method according to claim 3 , wherein, cryptographic material being an RSA key pair and the generation of two prime numbers being requested, the predetermined amount of time is determined based on a double prime number generation.

5. Device configured to produce cryptographic material based on at least one prime number, said device comprising:

a timer;

a memory storing a predefined number of pre-calculated prime numbers, said pre-calculated prime numbers being available to be output in case no other calculated prime number is available, wherein the predefined number of the pre-calculated prime numbers is determined depending on calculation resources of the device and generation duration constraints from an application requesting the generation; and

computational hardware configured to cause the device to:

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 the prime number and restart derivation calculation from a new start point;

stop continuation of the derivation calculation after one or more iterations of the derivation calculation and after a predetermined amount of time;

store intermediate results to be used a next time a prime number will be requested; and

output a stored prime number different from the intermediate results.

6. Device according to claim 5 , said device belonging to the group constituted by smart cards, HSM, tokens, USB keys, and embedded secure elements.