Problems of Information Transmission, Vol. 37, No. 1, 2001, pp. 80–85. Translated from Problemy Peredachi Informatsii, No. 1, 2001, pp. 89–94.
Original Russian Text Copyright
2001 by Arbekov.
Key Secrecy in a Quantum Cryptography System
Based on Error-Correcting Codes
I. M. Arbekov
Received March 27, 2000; in ﬁnal form, November 8, 2000
Abstract—In [Probl. Peredachi Inf., 1999, vol. 35, no. 1, pp. 100–109], an algorithm based on
error-correcting codes was proposed for generating a common key in information transmission
through a quantum communication channel. In the present paper, we study the application of
this algorithm in a quantum cryptography system where bits of key information are encoded by
two nonorthogonal photon polarizations. An estimate for the key secrecy with respect to the
“translucent” eavesdropping method is given in the form of a lower bound on the cardinality
of the set of admissible key values.
Using various methods of information transmission through a quantum communication channel
[2, 3], each of two parties, A (Alice) and B (Bob), form random binary sequences a and b,which
are their primary key material. Since the quantum channel is aﬀected by noise, the sequences a
and b have noncoincident bits; for practically realizable quantum channels, the error probability is
not greater than several percent . The channel is overheard by an eavesdropper E (Eve), who
may interfere with the channel operation.
After receiving the primary key material, A and B form a common key using a public matching
The matching algorithm considered in  consists in dividing the sequences a and b into blocks
of equal length (in each of the sequences) and interchanging the parities of these blocks through
a public channel. If the parities of a block coincide, the sequences in these blocks are assumed to
be the same; here, to make the public interchange bear no information, the last bit in a block is
cancelled. If the parities do not coincide, the last bit of a block is also cancelled, the block is divided
into two parts, and then the error is further searched and corrected. The procedure is repeated
several times, each time with randomizing the sequences according to some known permutation
and new dividing into blocks.
In , a new matching algorithm is proposed, where correcting codes are employed for error cor-
rection. An advantage of this algorithm consists in substantial reduction of information transmitted
over the public channel.
In the present paper, the matching algorithm proposed in  is analyzed for a quantum cryp-
tography system where, for encoding bits of the key information transmitted, two nonorthogonal
photon polarizations  are used. As an estimate for the key secrecy, we give a lower bound on the
cardinality of the set of admissible key values constructed as a result of the so-called “translucent”
2. GENERATION OF A COMMON KEY USING AN ERROR-CORRECTING CODE
In this section, the main idea of using error-correcting codes in the matching algorithm for key
sequences  is developed.
2001 MAIK “Nauka/Interperiodica”