JP2003317019A - Quantum cash method, device and program - Google Patents

Abstract

(57) [Summary] [Problem] It has the impossibility of forgery based on the principle of quantum mechanics,
And reduce the amount of confidential information held in the bank. A random bit string a1, ..., generates an, secret function f _1, ..., for _{f m ci = f i (a1} ,
, An) (i = 1,..., M), and a secret random sequence B ^(v) = (b (v, 1),.
b (v, j) (or b (v, n + i)) = 0 for each bit of (v, n), b (v, n + 1), ..., b (v, n + m) And aj (or ci) is the basis Z, b (v, j) (or b (v, n + i)) = 1 and aj (or c
i) is coded into one of four quantum states by basis X to generate a quantum bit sequence | φ>, and (| φ>, v) is cash,
The retail store that has received the payment requests the bank to verify the (| φ ′>, v) received from the user, and the bank observes | φ> with B ^(v) of ^v , and the observed bit sequence a ′ 1,…,
a′n, c′1,..., c′m are c′i = f _i (a′1,
, A'n) are checked.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a quantum cash method, a quantum cash method in which a quantum state is used as cash on the basis of a principle of quantum mechanics as a basis for impossibility of forgery, a device thereof, and a program thereof.

[0002]

2. Description of the Related Art Various types of electronic cash have been proposed. These electronic cash have been secured by using tamper resistant media or digital signature technology. However, the tamper-resistant medium can be broken in principle if there are advanced printing technology and device technology. It is also known that the digital signature is also based on computational complexity, and can be broken if it takes a huge amount of calculation time, or if the quantum computer is completed in the future, it will be broken in a realistic calculation time.

Quantum cash is S. Wiesner: Conjugate Coding,
Manuscript written circa 1970, unpublished until i
t appeared in Sigact News, Vol.15, No.1 pp.78-88 (1
983). In Wiesner's quantum cash method, the non-clonable theorem of quantum mechanics is the basis for non-counterfeiting. This Wiesner method is briefly explained.
Confidential information K = {ID, (a1, b1), (a2, b2), ...
(An, bn)} is kept secret in the database of the bank device. Here, ID is a serial number attached to each cash,
(Ai, bi) (i = 1, ..., N) is randomly selected from {0, 1}. Quantum cash is a quantum state consisting of ID and n qubits | φ> = | Ψ _{a1, b1} >, | Ψ _{a2, b2} >,
…, | Ψ _{an, bn} >. Here, the qubit | Ψ _{ai, bi} > is one of the following four quantum states.

[0004]     │Ψ₀₀> = | 0 >     │Ψ_Ten> = | 1 > (1)     │Ψ₀₁> = (| 0 > + | 1 >) / √2     │Ψ₁₁> = (| 0 >-| 1 >) / √2 The value bi defines the basis. If bi is 0, ai is the basis Z
Encoded with (| 0>, | 1>), and if bi is 1, ai
Is the basis X (| 0 > + | 1 >) / √2, (| 0 >-|
1 >) / √2. For example, if you
When using (| 0> is 0 °, | 1> is 90 °, (|
0 > + | 1 >) / √2 is 45 °, (| 0 >-| 1
>) / √2 is 135 °, bi = 0, ai = 0
Then 0 °, if ai = 1 then 90 ° is encoded, bi = 1
If ai = 0, sign 45 °; if ai = 1, sign 135 °
Be converted.

When a user requests the bank to issue quantum cash, the bank retrieves one of the secret information K from the database, encodes its (ai, bi) sequence into the quantum state | φ>, and the quantum cash Issue (ID, | φ>) to the user. The user pays quantum cash at the retail store. The retail store sends the quantum cash to the bank for verification. The bank extracts K from the ID of the received quantum cash from the database, and according to its (ai, bi), has each quantum bit | Ψ _{ai, bi} > of quantum φ | φ>, and if bi is 0, the basis Observe at Z, and if bi is 1, observe at base X. Then, it verifies that the observation result is ai. (Ai, b
i) If at least one of (i = 1, ..., N) is different from ai, it is determined that the quantum cash is not valid.

[0006]

[Problems to be Solved by the Invention] 1. The basis of the non-counterfeiting of the conventional electronic cash method is based on the realistic assumption that the tamper resistant device is forced to be enforced, or the computational complexity assumption of the digital signature, and does not guarantee the security in principle. It was 2. In the conventional quantum cash method, the bank needs to store the secret information K for each quantum cash, and the database of the bank becomes huge. An object of the present invention is to provide a quantum cash method, an apparatus thereof, and a program thereof capable of solving the above problems 1 and 2 at the same time.

[0007]

In order to prevent copy in principle in this invention as well, the principle of quantum mechanics is used,
The use of quantum states for cash is similar to Wiesner's quantum cash, but according to the present invention, secret face value information for each face value is held, and a plurality of related information generation functions are kept secret and quantum cash is used. Generates random information for each issuance, generates related information using the random information as a variable, and encodes the random information and the related information with a basis of quantum states based on face value information to generate a quantum state | φ>, | Φ> and v
Is the quantum cash, and the verification of (| φ>, v) observes | φ> with the corresponding face value information, and checks whether the observation result holds the relationship between the original random information and the related information.

As a result, the information that is secretly stored in the bank device is only the type of face value of the quantum cash to be issued, and since the related information is generated by the function that is secretly retained, the data amount of each quantum cash is relatively small. Even if it keeps safety.

[0009]

BEST MODE FOR CARRYING OUT THE INVENTION A system to which the method of the present invention is applied is, for example, as shown in FIG. 1, a device (hereinafter, referred to as a bank device) 100 included in an institution (hereinafter, referred to as a bank) that issues quantum cash and a device (hereinafter, referred to as a bank device). , Those who are issued quantum cash (hereinafter,
A device (hereinafter referred to as a user device) 200 included in a user and a device (hereinafter referred to as a retail store device) included in an institution (hereinafter referred to as a retail store) that receives quantum cash 30
0 and 0 can communicate with each other through a communication path.

A face value v of quantum cash issued to the bank device 100, for example, 1 yen, 10 yen, 100 yen, 1000 yen, 1
For each 0000 yen, an n + m-bit denomination-specific random sequence consisting of 0 and 1, B ^(v) = (b (v, 1), ..., b (v, n), b (v, n + 1), ... , B
(v, n + m)) b (v, j), b (v, n + i) ε {0,1}, i = 1, ..., M, j
, 1, ..., N are secretly stored in the storage unit 101 (see FIG. 2). In other words, a random sequence of 0 and 1 of n + m bits may be generated for each face value v, and this may be secretly stored for each face value v. v is discriminated according to each denomination of 1 yen, 10 yen, ... If the number of types is 5, it may be represented by a 3-bit denomination identifier. Furthermore, m related information generation functions f ₁ , ..., F
_m is secretly stored in the storage unit 102. The function f ₁ ,
, F _m may be, for example, a hash function that compresses to 1 bit, and the calculation program thereof is the storage unit 10.
2 or the arithmetic unit itself is provided. Issuance of quantum cash When a user wants to issue quantum cash, the user device 200 transmits a quantum cash issuance request including the amount of money to be issued and user identification information to the bank device 100.

When the communication unit 103 of the bank device 100 receives the quantum cash issuance request, the random number generation unit 104 outputs n.
A cash-specific random sequence of bits A = (a1, ..., an), ajε {0,1}, j = 1,
, N is generated. This random sequence A is generated by the related information generation unit 105.
Calculates the respective related information generation function f _i as variable _{ci = f i (a1, ...} , an) (2) additional information consisting of m bits c = (c1, ..., cm ) for generating a.

A face value v corresponding to the amount of quantum cash to be issued, for example, a face value specific random sequence B for 1000 yen
^(v) is read from the storage unit 101, and the quantum state encoding unit 1
At 06, one bit each is taken out from the face value-specific random sequence B ^{(v) in the} order of the bit arrangement, and the bit sequence a1, ..., An of the random sequence A is related to the bit sequence c1 ,.
From the array of m, one bit each is taken out in the array order, and aj is encoded into a quantum state with a basis determined by _{b (v, j)} to generate a quantum bit | Ψ _{aj, b (v, j)} >. For example, assuming that four quantum states are equation (1), and if b (v, j) is 0, aj is encoded by the basis Z and b (v, j) is 1 as in the case of the prior art. Then, aj is encoded with the base X. ci is similarly coded by b (v, n + i).

By this encoding, a quantum state consisting of n + m quantum bit strings | φ> = (| Ψ _{a1, b (v, 1)} >, ..., | Ψ _{an, b (v, n)} >, |
Ψ _{c1, b (v, n + 1)} >, ..., | Ψ _{cm, b (v, n + m)} >) is obtained. The quantum state | φ> and the face value v are transmitted as quantum cash to the requested user device 200 from the communication unit 103, and the issue amount v is withdrawn from the user's account. The user device 200 stores the received quantum cash (| φ>, v) in the storage unit. In the bank device 100, the control unit 1 sequentially operates each unit for the quantum cash issuing process described above.
08.

The transmission of quantum cash (| φ>, v) is | φ>
May be performed by a quantum communication channel, v may be performed by a classical communication channel, or v may be converted into a code of a quantum state and transmitted through the quantum communication channel. Use of Quantum Cash When the user pays with quantum cash (| φ ′>, v), the user device 200 transmits the quantum cash (| φ ′>, v) to the retail store device 300. Verification of Quantum Cash The retail store apparatus 300 sends the quantum cash (|
When the payment by φ ′>, v) is received, the quantum cash (| φ ′>, v) is sent to the bank device 100 to request verification.

When the verification request is received by the communication unit 103, the bank device 100 retrieves the face value-specific random sequence B ^(v) from the storage unit 101 by the face value v, and the observation unit 111 uses each bit b (v, j). ) Φ ′ received on the basis determined by
Observe the quantum state of the corresponding qubit | Ψ _{aj, b ( v, j)} >of>. For qubit | Ψ _{ci, b (v, n + i)} >, b (v, n +
Observe by i). The bit strings read by this observation are defined as a'1, ..., a'n, c'1, ..., c'm. In the verification unit 112, a ′ in this observed bit string is
1, ..., a′n are used as variables, and related information generating function f ₁ ,
, F _m are calculated by the calculation unit 112a, and the calculation result c ″
_{i = f i (a'1, ...} , a'n) and the corresponding observation bit c'i
To see if it matches. That _{c "i = f i (a'1} , ..., a'n) = c'i (3) it is checked whether established, all i = 1, ..., if satisfied for m, the quantum cash If it is determined to be valid, and if even one is not established (| φ ′>, v), it is determined to be illegal quantum cash, and the determination result is sent from the communication unit 103 to the retail store apparatus 3
Notify 00.

When the retail store device 300 receives the notification, the retail store device 300 allows the user device 200 to pay the quantum cash (| φ ′>, v), and the quantum cash (| φ ′>, v). The bank device 100 is instructed whether to deposit v) into the account of the retail store of the bank or have (| φ ′>, v) returned and use it as own quantum cash. If the verification fails, the retail store device 300 does not allow payment by the (| φ ′>, v) of the user device 200. When the bank device 100 receives the deposit instruction to the account, after depositing the amount v into the account of the retail store, (| φ ′>, v)
And discard the quantum cash even if the verification fails,
If it is a return request, it will be returned.

When the number of issued quantum cash of the same par value increases, the par value specific random sequence B ^(v) may be known. From this point, it is preferable that the values of m and n are large,
For example, a value of 100 or more can be considered. Generally, n> m, but m = n may be used. In the above description, the issuance required amount is equal to one of the face values v, but if the required amount is 1,300 yen, for example, the face value is 10,000 yen (| φ>, v5) and the face value is 1,000 yen. (| Φ>, v4),
(| Φ>, v4), (| φ>, v4), (v5 is the face value 1
10,000 yen, v4 represents 1,000 yen of the face value, and each | φ> is different from each other).

The quantum state that each qubit can take is given by
Not limited to (1), │Ψ₀₀> = | Ψ_x> │Ψ_Ten> = | Ψ ′_x> │Ψ₀₁> = | Ψ_y> │Ψ₁₁> = | Ψ ′_y> 4 states may be used. │Ψ_x> And | Ψ_x'> Are orthogonal to each other
, Ψ_y> And | Ψ_y′> Are also orthogonal to each other
Is | Ψ_x> And | Ψ_y> Is non-orthogonal. b (v, j), b
If (v, n + i) is 0, the basis X (| Ψ_x>, | Ψ_x′ ＞)
If 1, then base Y (| Ψ _y> And | Ψ_y′ ＞)
Encode j, ci.

In the above, if the expression (4) is not satisfied even for one i, it is judged as a failure. However, if the expression (4) is 90% or more, it may be judged as a success. By doing this, some false detections and malfunctions are allowed,
It becomes possible to operate at such a high speed or to configure at a low cost. Furthermore, the element b (v,
j) and b (v, n + i) are not limited to binary cases of 0 or 1, and b (v, j), b (v, n + i) ε {0,1, ... q −1} and q may be integers of 2 or more, that is, q may be 3 or more. Similarly, ajε {0, 1, ... P-1}, and p may be an integer of 2 or more. _Qubit | Ψ _{aj, b (v, j)} ＞, | Ψ _{ci, b (v, n + 1)}
> Is one of q × p kinds of quantum states.

FIG. 3 shows an example of the processing procedure of the bank device 100. When a quantum cash issuance request is received from the user device 200 (S1), a random sequence A consisting of n elements is generated (S2), and the random sequence A is used as an n variable to generate related information generating functions f ₁ , ..., F. _The relevant information c = (c1,
, Cm) is generated (S3), and a quantum denomination specific random sequence B ^(v) consisting of n + m elements of the denomination v corresponding to the amount requested to be issued is retrieved from the storage unit 101 (S4),
Each element of the random sequence A and the related information c is sequentially encoded in the order of the elements of the denomination-specific random sequence B ^(v) into one of the quantum states with a basis according to the element to generate a quantum bit, and the quantum bit sequence is generated. To obtain a quantum state | φ> (S5). The | φ> and v are transmitted to the user device 200 as quantum cash (S6).

Next, it is checked whether or not a verification request is received from the retail store apparatus 300 (S7), and if it is received, the storage unit 1 is determined by the face value v of the received quantum cash (| φ '>, v).
The random facet-specific random sequence B ^(v) is read from 01 (S
8), using the elements b (v, j) and b (v, n + i) as a basis reference, observe corresponding quantum bits in the quantum state | φ ′> by sequentially observing the quantum states. Find element sequence (S
9). Its associated parts corresponding to the random sequence A under observation element sequence as the variable information generating function f _1, ..., by calculating _{f m c "1, ...,} c" seek m this observation element c'1,
,, c′n is verified to match (S1
0) If the coincident ones are equal to or higher than the predetermined rate, the quantum cash (| φ ′>, v) is determined to be valid, the result is notified to the retail store apparatus 300, and the process returns to step S1 (S1).
1).

If the issuance request has not been received in step S1, the process proceeds to step S7, and if the verification request has not been received in step S7, the process returns to step S1. The bank device 100 shown in FIG. 2 can also be made to function by executing a program by a computer. In that case, for example, a bank device processing program for causing a computer to execute the processing procedure shown in FIG. 3 is installed in the computer from a recording medium such as a CD-ROM or a flexible magnetic disk,
Alternatively, the program may be downloaded via a communication line and the computer may execute the program.

[0023]

As described above, according to the present invention, since the information which has the forgery by the principle of quantum mechanics and which is secretly stored in the bank device is only the random sequence for each face value, The storage capacity can be significantly reduced as compared with the case where each piece of information corresponding to all quantum cash is stored. Further, since the secret related information generation function is used, safety can be obtained even if the number of elements of the cash random sequence A generated for each issuance of quantum cash is relatively small. The quantity is small.

[Brief description of drawings]

FIG. 1 is a diagram showing a minimum configuration example of a system to which the method of the present invention is applied.

FIG. 2 is a diagram showing a functional configuration example of a bank device according to the present invention.

FIG. 3 is a flowchart showing an example of a processing procedure of a bank device.

Claims (9)

[Claims] 1. A device (hereinafter, referred to as a bank device) of a quantum cash issuing institution (hereinafter, referred to as a bank) secretly holds face value specific information for each face value and secretly holds a plurality of related information generation functions. When a quantum cash issuance request is received from a device (hereinafter, referred to as a user device) held by a person who holds the quantum cash (hereinafter referred to as a user), quantum cash unique information is generated, and the quantum cash unique information is generated. The plurality of related information generation functions are respectively calculated using information as variables to generate a plurality of related information, and the quantum cash specific information and the related information are generated based on the requested face value of the quantum cash and the corresponding face value specific information. Is encoded into a quantum state, and the quantum state and the requested face value information are sent to the user device as quantum cash. 2. When a user uses quantum cash, the user device transfers the quantum cash to a device (hereinafter referred to as a retail store device) of an institution (hereinafter referred to as a retail store) that receives the quantum cash. Sending, the retail store device sends the received quantum cash to the bank device and requests verification of its legitimacy, and when the bank device receives the request for the legitimacy verification, it uses the face value information and corresponding face value specific information, Examine whether the received quantum state holds the relationship between the quantum cash specific information and the related information, and verify the validity of the quantum cash,
The quantum cash method according to claim 1, wherein the verification result is transmitted to a retail store device. 3. An institution that issues quantum cash (hereinafter referred to as a bank)
U) has a device (hereinafter referred to as a bank device) at face value v
And face-specific random columns B^(v) = (B (v, 1), ..., b (v, n), b (v, n + 1), ..., b
(v, n + m)) b (v, j), b (v, n + i) ε {0,1, ..., q-1}, j =
1, ..., N, i = 1, ..., M, q are integers of 2 or more Keep secretly in the memory, Function f₁,, f_mKeep secretly in the memory, There is a person who issues quantum cash (hereinafter referred to as a user)
Issuing quantum cash from a device (hereinafter referred to as user device)
Random column for quantum cash upon receipt of request A = (a1, ..., an) aj? {0,1, ..., p-
1}, p is an integer of 2 or more, Produces A function f with this random sequence unique to quantum cash as a variable₁，
…, F_mAnd calculate related information c = (c1, c2, ..., cm), ci = f_i(A1,
…, An) And generate Random sequence A and related information c
B according to the face value v of money ^(v) By the basis corresponding to each element of
, Each of which is one of q × p quantum states
Quantum state consisting of n + m elements | Φ> = (| Ψ_{a1, b (v, 1)}>, ..., | Ψ_{an, b (v, n)}>, |
Ψ_{c1, b (v, n + 1)}>,…, Ψ_{cm, b (v, n + m)}＞) │φ ＞ ＝ ｜ φ₁>, | Φ₂>, ..., | φ> Encoded to The bank device uses this | φ> and v as quantum cash (v, | φ>)
And then sending it to the user device. 4. When a user uses quantum cash, the user device has (v, | φ>) as a device (hereinafter, referred to as a retail store) of an institution (hereinafter referred to as a retail store) that receives quantum cash. Retail device), the retail device sends the received quantum cash to the bank device to request the justification verification, and when the bank device receives the request for the justification verification, the face value v
, The denomination-specific random sequence B ^(v) is taken out, and the quantum state | φ> received at the basis corresponding to each element is observed, and the observation result, a′1, ..., a′n, c′1, ..., c′m is obtained, and the related information generating function c ″ i = f _i (a′1, ..., a′m) is calculated using (a′1, ..., a′n) in the observation result as a variable, c ″ i =
If the matching rate is equal to or more than a predetermined value, it is determined that the quantum cash is valid, and the bank device transmits the determination result to the retail store device. Cash method. 5. The q and the p are both 2, and the kinds of the quantum states are | Ψ ₀₀ > = | Ψ _x > | Ψ ₁₀ > = | Ψ ′ _x > | Ψ ₀₁ > = | Ψ _y >. | Ψ ₁₁ > = | Ψ ′ _y >, and | Ψ _x > ⊥ | Ψ ′ _x >, | Ψ _y > ⊥ | Ψ ′
_y >, and | Ψ _x > and | Ψ _y > are non-orthogonal, and A ⊥
B represents that A and B are in an orthogonal state, and the encoding to the above quantum state is such that if b (v, j) and b (v, n + i) are 0, aj and ci are set to the basis X (| Ψ _x ＞, ｜ Ψ ′
_x >), and if b (v, j) and b (v, n + i) are 1, encode aj and ci with the basis Y (| Ψ _y >, | Ψ ′ _y >), respectively. The quantum cash method according to claim 3 or 4, characterized in that. 6. The type of the quantum state is | Ψ ₀₀ > = | 0> | Ψ ₁₀ > = | 1> | Ψ ₀₁ > = (| 0> + | 1>) / √2 | Ψ ₁₁ > = ( | 0> − | 1>) / √2, and the basis Z is (| 0>, | 1 >) And the base X
Is ((| 0> + | 1 >) / √2, (| 0>-| 1>) /
6. The quantum cash method according to claim 5, wherein if the verification of validity is established for i = 1, ..., M equal to or more than a predetermined value, the quantum cash is determined to be valid. 7. A face value-specific random sequence for each face value v B^(v) = (B (v, 1), ..., b (v, n), b (v, n + 1), ..., b
(v, n + m)) b (v, j), b (v, n + i) ε {0,1}, i = 1, ..., N, i
= 1, ..., m A storage unit that secretly stores Related information generation function f₁,, f_mMemorize secretly
Department, Quantum cash specific random sequence A = (a1, ..., an), ajε {0,1} A random sequence generator that generates Related information generation function value with the random sequence A as a variable ci = f (a1, ..., an) To generate related information c = (c1, ..., cm)
A related information generator, Quantum states │Ψ₀₀> = | 0 > │Ψ_Ten> = | 1 > │Ψ₀₁> = (| 0 > + | 1 >) / √2 │Ψ₁₁> = (| 0 >-| 1 >) / √2 If b (v, j) and b (v, n + i) are 0, then a
Let j, ci be the basis Z (| 0 >, | 1 >), And b
If (v, j) and b (v, n + i) are 1, then aj and ci are the basis X
((| 0 > + | 1 >) / √2, (| 0 >-| 1 ＞)
It is composed of n + m qubit strings encoded with / √2)
Quantum state | Φ> = (| Ψ_{a1, b (v, 1)}>, ..., | Ψ_{an, b (v, n)}>, |
Ψ_{c1, b (v, n + 1)}>, ..., | Ψ_{cm, b (v, n + m)}＞) A quantum state encoding unit that generates Communication means, The communication means receives the quantum cash issuance request from the user device.
And the above-mentioned quantum
Generate a cash unique random sequence A and its related information c,
Face value specific random sequence B according to the face value v requested to be issued
^(v) To the quantum state coding unit,^(v) By that
The generated A and c are coded, and the quantum is
State | φ> and face value v are transmitted to the user device as quantum cash
Bank device of quantum cash method, comprising: 8. An observation unit for observing each quantum bit of the quantum state | φ ′> by a basis based on the corresponding element of the denomination-specific random sequence B ^(v) of the denomination v to read out the bit sequence A ′, and the bit sequence A. , A'n in ′ are used as variables to calculate related information generating functions f ₁ , ..., F _m , and c ″ i = f _i
(a′1, ..., a′n) is obtained, and it is checked whether c ″ i matches the observed corresponding bit ci, and if all of these i match, the quantum cash | φ ′> is judged to be valid. When the verification unit for performing the verification and the communication means receive a request from the retail store apparatus for verification of validity of the quantum cash | φ ′> and its face value v, the face value v
Of the denomination peculiar random sequence B ^(v) , the observation unit is caused to observe the quantum state | φ ′> by this B ^(v) , and the verification unit performs the above verification on the read bit string A ′. The bank device of the quantum cash method according to claim 7, further comprising: a control unit that causes the communication unit to transmit the verification result to the retail store device. 9. A bank device processing program for causing a computer to function as the bank device according to claim 7.