BB84
Encyclopedia
BB84 is a quantum key distribution scheme developed by Charles Bennett
and Gilles Brassard
in 1984. It is the first quantum cryptography
protocol
. The protocol is provably secure, relying on the quantum property that information gain is only possible at the expense of disturbing the signal if the two states we are trying to distinguish are not orthogonal (see no cloning theorem
). It is usually explained as a method of securely communicating a private key from one party to another for use in one-time pad
encryption.
s,
and 
, each 
bits long. She then encodes these two strings as a string of 
qubit
s,
and 
are the 
bits of 
and 
, respectively. Together, 
give us an index into the following four qubit states:
Note that the bit
is what decides which basis 
is encoded in (either in the computational basis or the Hadamard basis). The qubits are now in states which are not mutually orthogonal, and thus it is impossible to distinguish all of them with certainty without knowing 
.
Alice sends
over a public quantum channel
to Bob. Bob receives a state
, where 
represents the effects of noise in the channel as well as eavesdropping by a third party we'll call Eve. After Bob receives the string of qubits, all three parties, namely Alice, Bob and Eve, have their own states. However, since only Alice knows 
, it makes it virtually impossible for either Bob or Eve to distinguish the states of the qubits. Also, after Bob has received the qubits, we know that Eve cannot be in possession of a copy of the qubits sent to Bob, by the no cloning theorem, unless she has made measurements. Her measurements, however, risk disturbing a particular qubit with probability ½ if she guesses the wrong basis.
Bob proceeds to generate a string of random bits
of the same length as 
, and then measures the string he has received from Alice, 
. At this point, Bob announces publicly that he has received Alice's transmission. Alice then knows she can now safely announce 
. Bob communicates over a public channel with Alice to determine which 
and 
are not equal. Both Alice and Bob now discard the qubits in 
and 
where 
and 
do not match.
From the remaining
bits where both Alice and Bob measured in the same basis, Alice randomly chooses 
bits and discloses her choices over the public channel. Both Alice and Bob announce these bits publicly and run a check to see if more than a certain number of them agree. If this check passes, Alice and Bob proceed to use privacy amplification and information reconciliation techniques to create some number of shared secret keys. Otherwise, they cancel and start over.
Charles H. Bennett (computer scientist)
Charles H. Bennett is an IBM Fellow at IBM Research. Bennett's recent work at IBM has concentrated on a re-examination of the physical basis of information, applying quantum physics to the problems surrounding information exchange...
and Gilles Brassard
Gilles Brassard
Gilles Brassard was born in Montreal, Canada, in 1955. He received a Masters degree from the Université de Montréal in 1975, and obtained his Ph.D. in Computer Science from Cornell University in 1979, working in the field of cryptography with John Hopcroft as his advisor...
in 1984. It is the first quantum cryptography
Quantum cryptography
Quantum key distribution uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages...
protocol
Quantum cryptography protocol
A quantum cryptography protocol is a protocol for quantum cryptography.The first quantum cryptography protocol, BB84, was defined in 1984.SARG04 is a recent quantum cryptography protocol...
. The protocol is provably secure, relying on the quantum property that information gain is only possible at the expense of disturbing the signal if the two states we are trying to distinguish are not orthogonal (see no cloning theorem
No cloning theorem
The no-cloning theorem is a result of quantum mechanics that forbids the creation of identical copies of an arbitrary unknown quantum state. It was stated by Wootters, Zurek, and Dieks in 1982, and has profound implications in quantum computing and related fields.The state of one system can be...
). It is usually explained as a method of securely communicating a private key from one party to another for use in one-time pad
One-time pad
In cryptography, the one-time pad is a type of encryption, which has been proven to be impossible to crack if used correctly. Each bit or character from the plaintext is encrypted by a modular addition with a bit or character from a secret random key of the same length as the plaintext, resulting...
encryption.
Description
In the BB84 scheme, Alice wishes to send a private key to Bob. She begins with two strings of bitBit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
s,
and , each bits long. She then encodes these two strings as a string of qubitQubit
In quantum computing, a qubit or quantum bit is a unit of quantum information—the quantum analogue of the classical bit—with additional dimensions associated to the quantum properties of a physical atom....
s,
and are the bits of and , respectively. Together, give us an index into the following four qubit states:Note that the bit
is what decides which basis is encoded in (either in the computational basis or the Hadamard basis). The qubits are now in states which are not mutually orthogonal, and thus it is impossible to distinguish all of them with certainty without knowing .Alice sends
over a public quantum channelQuantum channel
In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit...
to Bob. Bob receives a state
, where represents the effects of noise in the channel as well as eavesdropping by a third party we'll call Eve. After Bob receives the string of qubits, all three parties, namely Alice, Bob and Eve, have their own states. However, since only Alice knows , it makes it virtually impossible for either Bob or Eve to distinguish the states of the qubits. Also, after Bob has received the qubits, we know that Eve cannot be in possession of a copy of the qubits sent to Bob, by the no cloning theorem, unless she has made measurements. Her measurements, however, risk disturbing a particular qubit with probability ½ if she guesses the wrong basis.Bob proceeds to generate a string of random bits
of the same length as , and then measures the string he has received from Alice, . At this point, Bob announces publicly that he has received Alice's transmission. Alice then knows she can now safely announce . Bob communicates over a public channel with Alice to determine which and are not equal. Both Alice and Bob now discard the qubits in and where and do not match.From the remaining
bits where both Alice and Bob measured in the same basis, Alice randomly chooses bits and discloses her choices over the public channel. Both Alice and Bob announce these bits publicly and run a check to see if more than a certain number of them agree. If this check passes, Alice and Bob proceed to use privacy amplification and information reconciliation techniques to create some number of shared secret keys. Otherwise, they cancel and start over.See also
- SARG04SARG04SARG04 is a quantum cryptography protocol derived from the first protocol of that kind, BB84.-Origin:Researchers built SARG04 when they noticed that by using the four states of BB84 with a different information encoding they could develop a new protocol which would be more robust when attenuated...
- E91 - Quantum CryptographicQuantum cryptographyQuantum key distribution uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages...
communication protocol