# US 2021/0243021 A1 · Method for generating on-board a cryptographic key using a physically unclonable function > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2021/0243021 A1 - Document ID: US20210243021A1 - Status: Published application - Kind: A1 - Application number: 17/050,582 - Filed: 2019-04-24 - Published: 2021-08-05 - Earliest claimed: 2018-04-26 - Assignees: Thales Dis Design Services SAS - Applicants: Thales Dis Design Services SAS - Inventors: Olivier FOURQUIN; Alexandre BERZATI; Benjamin DUVAL - Web page: https://patentgrep.com/patent/US20210243021A1 ## CPC - H04L 9/0869: {involving random numbers or seeds} - G06F 7/588: {Random number generators, i.e. based on natural stochastic processes} - H04L 9/0866: {involving user or device identifiers, e.g. serial number, physical or biometrical information, DNA, hand-signature or measurable physical characteristics} - H04L 9/3249: {using RSA or related signature schemes, e.g. Rabin scheme} - H04L 9/3278: {using physically unclonable functions [PUF]} - H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M) - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract A method, cryptographic device, and computer readable memory with instructions, for generating a cryptographic key from at least one prime number, by performing during runtime of the cryptographic device by obtaining from memory a challenge and at least one associated increment number, generating a seed by applying a Physically Unclonable function to said obtained challenge, generating at least one prime number from said generated seed by performing said cryptographic prime numbers generation algorithm and by performing therein as many incrementation steps as said obtained at least one increment number, and generating the cryptographic key from the generated prime number. ## Claims ### Claim 1 A method for generating a cryptographic key from at least one prime number, comprising the following steps performed at runtime by a cryptographic device comprising at least one hardware processor, a Physically Unclonable function and a memory storing at least one challenge and at least one associated increment number, said associated increment number being a number of incrementation steps to be performed in a predefined cryptographic prime numbers generation algorithm to generate said at least one prime number from a seed obtained from said challenge using said Physically Unclonable function: obtaining from said memory a challenge and at least one associated increment number, generating a seed by applying said Physically Unclonable function to said obtained challenge, generating said at least one prime number from said generated seed by performing said cryptographic prime numbers generation algorithm and by performing therein as many incrementation steps as said obtained at least one increment number, generating said cryptographic key from said generated prime number. ### Claim 2 (depends on 1) The method of claim 1, comprising the following steps performed by said cryptographic device during an enrollment phase: generating a seed by applying said Physically Unclonable function of the cryptographic device to a challenge, storing, in said memory of the cryptographic device, said challenge and at least one associated increment number defined as the number of incrementation steps to be performed in a cryptographic prime numbers generation algorithm for generating said prime number from said seed. ### Claim 3 (depends on 2) The method of claim 2 comprising further, performed by said cryptographic device, a step of reception of said challenge from a server connected to said cryptographic device and a step of transmission of said generated seed to said server. ### Claim 4 (depends on 3) The method of claim 3, comprising, during the enrollment phase, performed by said server: sending said challenge to the cryptographic device, receiving said generated seed from the cryptographic device, generating a prime number from said seed by performing several incrementation steps in a cryptographic prime numbers generation algorithm, sending, to said cryptographic device for storing in memory, said at least one increment number defined as the number of incrementation steps performed in said cryptographic prime numbers generation algorithm for generating said prime number. ### Claim 5 (depends on 2) The method of claim 2, comprising further, performed by said cryptographic device: generating said challenge, generating a prime number from said seed by performing several incrementation steps in a cryptographic prime numbers generation algorithm, and generating said at least one associated increment number defined as the number of incrementation steps performed in said cryptographic prime numbers generation algorithm for generating said prime number. ### Claim 6 (depends on 1) The method of claim 1 wherein said cryptographic prime numbers generation algorithm is among FIPS 186-4 appendix A.1.1.2 and ANS X9.31, rDSA. ### Claim 7 (depends on 1) The method of claim 1 wherein said cryptographic key is among a RSA key or an ECC key. ### Claim 8 (canceled) ### Claim 9 A non-transitory computer readable medium storing executable computer code that when executed by a cryptographic device comprising at least one hardware processor, the hardware processor implementing with a Physically Unclonable function and comprising a memory # storing at least one challenge and at least one associated increment number, said associated increment number being a number of incrementation steps to be performed in a predefined cryptographic prime numbers generation algorithm to generate said at least one prime number from a seed obtained from said challenge using said Physically Unclonable function, wherein the executable computer code, when executed by the hardware processor, causes the hardware processor to: obtain from said memory a challenge and at least one associated increment number, generate a seed by applying said Physically Unclonable function to said obtained challenge, generate said at least one prime number from said generated seed by performing said cryptographic prime numbers generation algorithm and by performing therein as many incrementation steps as said obtained at least one increment number, generate said cryptographic key from said generated prime number. ### Claim 10 A cryptographic device comprising: at least one hardware processor implementing a Physically Unclonable function; and a memory storing at least one challenge and at least one associated increment number, said associated increment number being a number of incrementation steps to be performed in a predefined cryptographic prime numbers generation algorithm to generate said at least one prime number from a seed obtained from said challenge using said Physically Unclonable function, wherein the executable computer code, when executed by the hardware processor, causes the hardware processor to: obtain from said memory a challenge and at least one associated increment number, generate a seed by applying said Physically Unclonable function to said obtained challenge, generate said at least one prime number from said generated seed by performing said cryptographic prime numbers generation algorithm and by performing therein as many incrementation steps as said obtained at least one increment number, generate said cryptographic key from said generated prime number. ### Claim 11 (depends on 9) The non-transitory computer readable medium storing executable computer code of claim 9, wherein the executable code further causes the hardware processor, during an enrollment phase, to: generate a seed by applying said Physically Unclonable function of the cryptographic device to a challenge, storing, in said memory of the cryptographic device, said challenge and at least one associated increment number defined as the number of incrementation steps to be performed in a cryptographic prime numbers generation algorithm for generating said prime number from said seed. ### Claim 12 (depends on 11) The non-transitory computer readable medium storing executable computer code of claim 11, wherein the executable code further causes the hardware processor, during an enrollment phase, to: generating said challenge; generating a prime number from said seed by performing several incrementation steps in a cryptographic prime numbers generation algorithm, and generating said at least one associated increment number defined as the number of incrementation steps performed in said cryptographic prime numbers generation algorithm for generating said prime number. ### Claim 13 (depends on 9) The non-transitory computer readable medium storing executable computer code of claim 9 wherein said cryptographic prime numbers generation algorithm is among FIPS 186-4 appendix A.1.1.2 and ANS X9.31, rDSA. ### Claim 14 (depends on 9) The non-transitory computer readable medium storing executable computer code of claim 9 wherein said cryptographic key is among a RSA key or an ECC key. ### Claim 15 (depends on 10) The cryptographic device of claim 10, wherein the executable code further causes the hardware processor, during an enrollment phase, to: generate a seed by applying said Physically Unclonable function of the cryptographic device to a challenge, storing, in said memory of the cryptographic device, said challenge and at least one associated increment number defined as the number of incrementation steps to be performed in a cryptographic prime numbers generation algorithm for generating said prime number from said seed. ### Claim 16 (depends on 15) The cryptographic device of claim 15, wherein the executable code further causes the hardware processor, during an enrollment phase, to: generating said challenge; generating a prime number from said seed by performing several incrementation steps in a cryptographic prime numbers generation algorithm, and generating said at least one associated increment number defined as the number of incrementation steps performed in said cryptographic prime numbers generation algorithm for generating said prime number. ### Claim 17 (depends on 10) The cryptographic device of claim 10, wherein said cryptographic prime numbers generation algorithm is among FIPS 186-4 appendix A.1.1.2 and ANS X9.31, rDSA. ### Claim 18 (depends on 10) The cryptographic device of claim 10, wherein said cryptographic key is among a RSA key or an ECC key.