Permutation method for correcting bit error in quantum key distribution protocol

1. A method for reconciling bit errors in a sifted key generated through a quantum key distribution (QKD) protocol, at least one application-specific integrated circuit (ASIC) to implement the method comprising: repeatedly performing a reconciliation step comprising the substeps of:

receiving a signal for dividing a bit string subject to bit error reconciliation into one or more blocks each having a predetermined length of a block;

searching for, in response to the received signal, a block containing an odd number of bit errors among the divided one or more blocks by performing a parity check on each of the divided one or more blocks; and

reconciling the bit errors by performing a predetermined operation according to a reconciliation protocol on the block containing the odd number of the bit errors,

wherein the method further comprises:

changing at least one of the length (n) of the bit string and the predetermined length (a) of the block for a subsequent reconciliation step to satisfy gcd(n,a)=1,

wherein the bits in the bit string reconciled in a previous reconciliation step are permuted before the subsequent reconciliation step by performing a linear modulo operation without using random numbers,

the bits in the bit string through a step of permuting the bits are rearranged such that all bits in a same block in the previous reconciliation step are dispersed to different blocks in the subsequent reconciliation step to thereby disperse continuous error bits occurred from said all bits in the same block into the different blocks,

wherein the ASIC perform the linear modulo operation based on (i) a length of the reconciled bit string and (ii) the predetermined length of the block to be used for the subsequent reconciliation step,

wherein the linear modulo operation is given by F: x→ax+b (mod n), where ‘x’ denotes the location of a bit, ‘a’ denotes the predetermined length of the block to be used for the subsequent reconciliation step, ‘b’ denotes an arbitrary integer, and ‘n’ denotes the length of the bit string.

2. The permutation method of claim 1 , wherein the ASIC is configured to

determine whether the length of the bit string which is subject to bit error reconciliation is an even number or an odd number, and

permute the bits in the string when the length of the bit string which is subject to bit error reconciliation is an odd number.

3. The permutation method of claim 2 , wherein the ASIC is configured to

remove a last bit of the bits to thereby change the bit string to an odd number length when the length of the bit string which is subject to bit error reconciliation is an even number, and

permute bits in the changed bit string.

4. The method of claim 1 , wherein the reconciliation step comprises:

determining whether the length of the bit string which is subject to bit error reconciliation is an even number or an odd number; and

permuting the bits in the string when the length of the bit string which is subject to bit error reconciliation is an odd number.

5. The method of claim 4 , wherein the reconciliation step comprises:

removing a last bit of the bits to thereby change the bit string to an odd number length when the length of the bit string which is subject to bit error reconciliation is an even number; and

permuting bits in the changed bit string.

6. The method of claim 1 ,

wherein the changing of at least one of ‘n’ and ‘a’ comprises changing ‘n’ into an odd number if ‘a’ is a power of 2.

7. The method of claim 1 , wherein the quantum key reconciliation protocol is a scheme for dividing a bit string resulting from each reconciliation step into blocks, and performing a predetermined operation on each block.

8. The method of claim 6 , wherein the changing ‘n’ into an odd number includes removing a last bit from the bit string obtained from the previous reconciliation step.

9. A non-transitory computer-readable medium having instructions stored thereon, which, when executed by at least one application-specific integrated circuit (ASIC), cause the ASIC to perform permutation operations for reconciling bit errors in a quantum key reconciliation protocol performing an iterative reconciliation process, the permutation operations comprising:

receiving a signal for a bit string obtained through a previous reconciliation step;

permuting, in response to the received signal, bits in the bit string obtained from the previous reconciliation step before a subsequent reconciliation step by performing a linear modulo operation without using random numbers;

rearranging the bits in the bit string through a step of permuting the bits such that all bits in a same block in the previous reconciliation step are dispersed to different blocks in the subsequent reconciliation step to thereby disperse continuous error bits occurred from said all bits in the same block into the different blocks; and

providing the rearranged bit string to the subsequent reconciliation step,

wherein the permutation operations further comprises:

changing at least one of the length (n) of the bit string and the predetermined length (a) of the block for the subsequent reconciliation step to satisfy gcd(n,a)=1,

wherein the ASIC perform the linear modulo operation based on (i) a length of the bit string and (ii) the predetermined length of the block to be used for the subsequent reconciliation step,

wherein the linear modulo operation is given by F: x→ax+b (mod n), where ‘x’ denotes the location of a bit, ‘a’ denotes the predetermined length of the block to be used for the subsequent reconciliation step, ‘b’ denotes an arbitrary integer, and ‘n’ denotes the length of the bit string.

10. The non-transitory computer-readable medium of claim 9 , wherein the changing of at least one of ‘n’ and ‘a’ comprises changing ‘n’ into an odd number if ‘a’ is a power of 2.

11. The non-transitory computer-readable medium of claim 9 , wherein the quantum key reconciliation protocol is a scheme for dividing a bit string resulting from each reconciliation step into blocks, and performing a predetermined operation on each block.

12. The non-transitory computer-readable medium of claim 9 , wherein the permutation operations comprises:

determining whether the length of the bit string which is subject to bit error reconciliation is an even number or an odd number; and

permuting the bits in the string when the length of the bit string which is subject to bit error reconciliation is an odd number.

13. The non-transitory computer-readable medium of claim 12 , wherein the permutation operations comprises:

removing a last bit of the bits to thereby change the bit string to an odd number length when the length of the bit string which is subject to bit error reconciliation is an even number; and

permuting bits in the changed bit string.