Efficient Key Integrity Verification for Quantum Cryptography Using Combinatorial Group Testing

In quantum cryptography, the key can be directly distributed to the communicating parties through the communication channel. The security is guaranteed by the quantum properties of the channel. However, the transmitted key may contain errors due to the noise of the channel. Key integrity verification is an indispensable step in quantum cryptography and becomes an important problem in higher speed systems. Computing only one hash value for the key string does not provide an effective solution as it may lead to dropping all the bits once the hash values on both sides do not agree. In this paper, we introduce a new idea of using the technique of combinatorial group testing, which seems to be an unrelated topic, to design a scheme to identify the error bits to avoid dropping all the bits. Our scheme can precisely locate the error bits if the number of error bits is within the maximum set by the scheme while the overhead is insignificant based on our experiments (additional bits: 0.1% of the key; time for computing the hash values: 16ms; verification time: 22 ms). Also, even if the number of error bits is higher than the maximum set by the scheme, only some correct bits may be misclassified as error bits but not the vice versa. The results show that we can still keep the majority of the correct bits (e. g. the bits discarded due to misclassification is only 5% of the whole string even if the number of error bits is 10 times of the maximum).