Cryptographic device having physical unclonable function

1. An electronic cryptographic device, the cryptographic device being configured for an enrollment phase and a later reconstruction phase, comprising:

a physically unclonable function (PUF) configured to produce a first noisy bit string during the enrollment phase and a second noisy bit string during the reconstruction phase,

a helper data creating unit configured to generate helper data from the first noisy bit string during the enrollment phase, the helper data allowing reconstruction of the first noisy bit string from the helper data and the second noisy bit string produced by the PUF during the reconstruction phase, wherein the helper data creating unit is configured to:

select a series of repetition code words of an error correcting repetition code, and

exclusive-or (XOR) each repetition code word of the series with a corresponding part of the first noisy bit string, thus obtaining at least part of the helper data, and

a statistical unit configured to execute a statistical test on the helper data during the enrollment phase for verifying correct functioning of the physical unclonable function, the statistical test being configured to verify that a bias of whether the physical unclonable function produces zero-bits or one-bits is within an allowable bias range, the statistical test computing a statistical parameter for the physical unclonable function, the statistical parameter being computed from the helper data, the statistical test determining correct functioning if the statistical parameter satisfies a criterion of the statistical test, wherein the statistical test includes:

for each repetition code word of the series of repetition code words, determining a Hamming weight of the exclusive-or of the repetition code word and the corresponding part of the first noisy bit string, and

determining from the determined Hamming weights if the bias of the physical unclonable function is within the allowable bias range.

2. The electronic cryptographic device as in claim 1 , configured to determine a cryptographic key, and further comprising

a key derivation unit configured to determine the cryptographic key from the second noisy bit string and the helper data during the reconstruction phase.

3. The electronic cryptographic device as in claim 1 , wherein the error correcting code is a concatenated error correction code for which the most inner code is a repetition code, the series of code words of an error correcting repetition code being selected by selecting one or more code words from the concatenated error correcting code.

4. The electronic cryptographic device as in claim 1 , wherein a first statistical test includes:

counting the number of determined Hamming weights that are above an upper Hamming weight threshold or below a lower Hamming weight threshold, and

determining if the bias of the physical unclonable function is within an allowable bias range if the counted number is within an allowed counted Hamming weight range.

5. The electronic cryptographic device as in claim 1 , wherein a first statistical test includes:

for each repetition code word of the series of repetition code words, determining a Hamming weight of the exclusive-or of the repetition code word and the corresponding part of the first noisy bit string,

for each Hamming weight w less than or equal to [n/2] wherein n is the bit length of the repetition code word, counting the number of determined Hamming weights equal to w or n−w, thus obtaining observed frequencies of Hamming weights,

applying a further statistical test for comparing an observed distribution to a theoretical distribution to the observed frequencies of Hamming weights and to specified frequencies of Hamming weights for the PUF, and

determining correct functioning of the PUF if the further statistical test for comparing an observed distribution to a theoretical distribution indicates that the observed frequencies of Hamming weights and the specified frequencies of Hamming weights for the PUF are closer than a distributional threshold.

6. An electronic cryptographic device, the cryptographic device being configured for an enrollment phase and a later reconstruction phase, comprising:

a physically unclonable function (PUF) configured to produce a first noisy bit string during the enrollment phase and a second noisy bit string during the reconstruction phase,

a helper data creating unit configured to generate helper data from the first noisy bit string during the enrollment phase, the helper data allowing reconstruction of the first noisy bit string from the helper data and the second noisy bit string during the reconstruction phase,

an error correcting unit configured to reconstruct, during the reconstruction phase, the first noisy bit string from the second noisy bit string and the helper data, and further configured to determine differences between the first and second noisy bit string, and

a statistical unit configured to execute a statistical test for verifying correct functioning of the physical unclonable function during the reconstruction phase, the statistical test computing a statistical parameter for the physical unclonable function, the statistical parameter including a total number of differences between the first noisy bit string and the second noisy bit string, the statistical test determining correct functioning if the total number of differences between the first noisy bit string and the second noisy bit string is at least a difference threshold number of bits.

7. The electronic cryptographic device as in claim 6 , wherein the statistical parameter includes at least one of:

the longest run of difference bits in the difference between the first and second noisy bit string, and

the longest run of non-difference bits in the difference between the first and second noisy bit string.

8. The electronic cryptographic device as in claim 6 , further comprising:

a random seed generating unit configured to generate a random seed by applying an entropy concentration function to a noisy bit string produced by the physically unclonable function only if the statistical test indicates correct functioning, wherein

the random seed generating unit is configured to apply the entropy concentration function to the second noisy bit string,

or, wherein

the physically unclonable function (PUF) is configured to produce a further noisy bit string during the reconstruction phase, the second noisy bit string being different from the further noisy bit string, and

the random seed generating unit is configured to apply the entropy concentration function to the further noisy bit string.

9. An electronic cryptographic device as in claim 8 , wherein the physically unclonable function (PUF) is memory based, and the second noisy bit string and the further noisy bit string are interleaved in the memory.

10. An electronic cryptographic method comprising an enrollment phase and a later reconstruction phase,

the enrollment phase comprising:

producing a first noisy bit string with a physically unclonable function (PUF),

generating helper data from the first noisy bit string, the helper data allowing reconstruction of the first noisy bit string from the helper data and a second noisy bit string produced by the PUF during the reconstruction phase, wherein generating the helper data comprises:

selecting a series of repetition code words of an error correcting repetition code, and

exclusive-or′ing (XOR) each repetition code word of the series with a corresponding part of the first noisy bit string, thus obtaining at least part of the helper data,

executing a statistical test for verifying correct functioning of the physical unclonable function, the statistical test on the helper data for verifying correct functioning of the physical unclonable function, the statistical test being configured to verify that a bias of whether the physical unclonable function produces zero-bits or one-bits is within an allowable bias range, the statistical test computing a statistical parameter for the physical unclonable function, the statistical parameter being computed from the helper data, the statistical test determining correct functioning if the statistical parameter satisfies a criterion of the statistical test, wherein the statistical test includes:

for each repetition code word of the series of repetition code words, determining a Hamming weight of the exclusive-or of the repetition code word and the corresponding part of the first noisy bit string, and

determining from the determined Hamming weights if the bias of the physical unclonable function is within the allowable bias range,

the reconstruction phase including:

producing the second noisy bit string with the physically unclonable function (PUF).

11. A method as in claim 10 , wherein

the statistical test includes a first statistical test, the first statistical test being executed during the enrollment phase on the helper data generated from the first noisy bit string,

the enrollment phase further including:

discarding the helper data generated from the first noisy bit string if the first statistical test does not verify correct functioning of the physical unclonable function, and storing the helper data if the first statistical test does verify correct functioning.

12. An electronic cryptographic method comprising an enrollment phase and a later reconstruction phase,

the enrollment phase comprising:

producing a first noisy bit string with a physically unclonable function (PUF), and

generating helper data from the first noisy bit string, the helper data allowing reconstruction of the first noisy bit string from the helper data and a second noisy bit string produced by the PUF during the reconstruction phase,

the reconstruction phase including:

producing the second noisy bit string with the physically unclonable function (PUF),

reconstructing the first noisy bit string from the second noisy bit string and the helper data,

determining differences between the first and second noisy bit string, and

executing a statistical test for verifying correct functioning of the physical unclonable function, the statistical test computing a statistical parameter for the physical unclonable function, the statistical parameter including a total number of differences between the first noisy bit string and the second noisy bit string, the statistical test determining correct functioning if the total number of differences between the first noisy bit string and the second noisy bit string is at least a difference threshold number of bits.

13. A non-transitory computer readable medium, comprising a computer program, comprising computer program instructions configured to perform, when the computer program is run on a computer, an electronic cryptographic method comprising an enrollment phase and a later reconstruction phase,

the enrollment phase comprising:

producing a first noisy bit string with a physically unclonable function (PUF),

generating helper data from the first noisy bit string, the helper data allowing reconstruction of the first noisy bit string from the helper data and a second noisy bit string produced by the PUF during the reconstruction phase wherein generating the helper data comprises:

selecting a series of repetition code words of an error correcting repetition code, and

exclusive-or′ing (XOR) each repetition code word of the series with a corresponding part of the first noisy bit string, thus obtaining at least part of the helper data,

executing statistical test on the helper data for verifying correct functioning of the physical unclonable function, the statistical test being configured to verify that a bias of whether the physical unclonable function produces zero-bits or one-bits is within an allowable bias range, the statistical test computing a statistical parameter for the physical unclonable function from the helper data generated from the first noisy bit string, the statistical test determining correct functioning if the statistical parameter satisfies a criterion of the statistical test, wherein the statistical test includes:

for each repetition code word of the series of repetition code words, determining a Hamming weight of the exclusive-or of the repetition code word and the corresponding part of the first noisy bit string, and

determining from the determined Hamming weights if the bias of the physical unclonable function is within the allowable bias range,

the reconstruction phase including:

producing the second noisy bit string with the physically unclonable function (PUF).

14. A non-transitory computer readable medium, comprising a computer program, comprising computer program instructions configured to perform, when the computer program is run on a computer, an electronic cryptographic method comprising an enrollment phase and a later reconstruction phase,

the enrollment phase comprising:

producing a first noisy bit string with a physically unclonable function (PUF), and

generating helper data from the first noisy bit string, the helper data allowing reconstruction of the first noisy bit string from the helper data and a second noisy bit string produced by the PUF during the reconstruction phase,

the reconstruction phase including:

producing the second noisy bit string with the physically unclonable function (PUF),

reconstructing the first noisy bit string from the second noisy bit string and the helper data,

determining differences between the first and second noisy bit string, and

executing a statistical test for verifying correct functioning of the physical unclonable function, the statistical test computing a statistical parameter for the physical unclonable function, the statistical parameter including a total number of the differences between the first noisy bit string and the second noisy bit string, the statistical test determining correct functioning if the total number of differences between the first noisy bit string and the second noisy bit string is at least a difference threshold number of bits.

15. The electronic cryptographic device as in claim 1 , wherein the electronic cryptographic device is configured to discard during the enrollment phase the helper data generated from the first noisy bit string if the statistical test does not verify correct functioning of the physical unclonable function.

16. The electronic cryptographic device as in claim 15 , wherein the electronic cryptographic device is further configured to store the helper data if the statistical test does verify correct functioning.