WO2021137391A1

WO2021137391A1 - Blockchain generation method using secret sharing

Info

Publication number: WO2021137391A1
Application number: PCT/KR2020/012719
Authority: WO
Inventors: 신상호; 유수빈; 박윤하; 김대수; 전재현; 김지성; 조정화; 손애선
Original assignee: 재단법인 경주스마트미디어센터; 주식회사 우경정보기술; 주식회사 엘토브
Priority date: 2019-12-30
Filing date: 2020-09-21
Publication date: 2021-07-08

Abstract

The present invention relates to a blockchain generation method using secret sharing in a multiple-participant environment. Unlike the conventional manner in which a running time and an operation increase in proportion to the number of participants when a PKI or a hash function having a key is used to generate a blockchain, according to the blockchain generation method using secret sharing according to an embodiment of the present invention, the use of the secret sharing and finite field operation allows the running time and the operation to be maintained constant regardless of the number of participants. Accordingly, a blockchain node can be very efficiently generated in a multiple-participant environment, and an excellent effect in a spatial and a temporal aspect in hardware manufacturing can be also achieved in the future. In addition, separate key management is not required.

Description

How to Create a Blockchain Using Secret Sharing

The present invention relates to a method of creating a block chain using secret sharing in a multi-participant environment.

As a data storage technology in a distributed ledger environment, block chain provides high transparency and reliability to users in terms of data management because it is impossible to forge or falsify data stored in a specific block using a hash function. Since the connected blocks are distributed and stored, there is no need for a central administrator, and the maintenance cost for safe data storage and management is relatively low.

The existing block chain creation method is performed through widely known cryptographic techniques and distributed consensus. The encryption technique mainly uses a cryptographic hash function in which a secret key exists or a public key infrastructure (PKI).

The problems caused by this are as follows.

First, it is a problem that requires a large amount of computation when using PKI. PKI mainly uses digital signature and public key cryptographic algorithms such as DSA, RSA, ECC, or EC-DSA. The speed and the amount of computation are increasing exponentially. If the capacity of the data stored in the block increases, the time and amount of computation required for the operation increase accordingly, and as a result, separate software or hardware must be newly developed and constructed in the related field, thereby increasing the cost to solve this problem. will do In addition, in the case of ECC, there is a disadvantage that it cannot be used for storing nodes in the block chain right away because it has only recently entered the commercialization stage and checked various safety.

Second, it is a problem of managing various keys. When data in the block chain is stored through a hash function or PKI in which a private key exists, a new private key (a public key must also be issued if necessary) for participating users must be issued and safely distributed to users, and users must A key management policy and system that can properly address the loss or other issues are needed. In particular, in the case of a hash function in which a secret key exists, a secret key must exist for each authorized user for a specific block chain node. Therefore, if the number of block chain nodes and authorized users increases, the corresponding key will inevitably increase exponentially. , since a more complex type of key management policy must be introduced along with the additional requirement of a key management system, the cost to solve this problem increases. Since PKI is also performed based on digital signature and public key cryptography, key management is very important, and security measures must be prepared for this when designing a system.

Third, there is the issue of exposure of data stored in the blockchain. The existing block chain node creation technique can check the data stored in the block chain by using the participant's private key. However, if a participant loses the secret key or is attacked by a malicious attacker, sensitive information stored in the block chain node may be exposed as it is. Moreover, if the stored data in the block chain is a secret, managing it fundamentally depending on the secret key has a problem in that the cost of construction and maintenance in terms of the system increases.

The present invention provides a method of creating a block chain using secret sharing, which has no restrictions on participants using secret sharing, does not require management of a private key (or public key) for each participant, and can reduce block chain creation time and computational amount aim to do

A block chain generation method using secret sharing according to an embodiment of the present invention,

The number of participants (n) related to the block data to be stored in the block chain, the identifiers of the participants (P _i , 1≤i≤n), and the irreducible polynomial (f() x)) a pre-processing step to set; The identifier (P _i ) is input into the reduced polynomial (f(x) _{) to generate a secret fragment value (f(P i} )), and the identifier (P _i ) and the secret fragment value (f(P _i )) Distributing the ordered pair (P _i , f(P _i )) to the participants, respectively, and an additional identifier (P _n+1 ) and an additional secret fragment value (f(P _n+1 )) other than the identifiers of the participants. and a secret sharing step of storing the ordered pair (P _n+1 , f(P _{n+1 )) in the node.}

In the method of generating a block chain using secret sharing according to an embodiment of the present invention, the ordered pair (P _i , f(P _i _{)) of the identifier (P i} ) and the secret fragment value (f(P _i )) is calculated using Lagrange information. An additional secret fragment value generated by inputting a snack-based formula to derive a reduced polynomial (f'(x)), and inputting the additional identifier (P _{n+1 ) to the derived reduced polynomial (f'(x))} The method may further include a proof-of-work step of performing proof-of-work by comparing (f'(P _n+1 )) with an additional secret fragment value f(P _{n+1 ) stored in the node.}

In the block chain generation method using secret sharing according to an embodiment of the present invention, the irreducible polynomial (f(x)) may be defined by the following equation (1).

Formula (1):

(Here, t is the threshold, a _j is the coefficient value inserted in bits after binarizing and parsing the original data as a part of the block data to be inserted into the block chain, and mod is the remainder to obtain the remainder of arbitrary division. function, GF is a polynomial belonging to Galois feild, and k means the number of bits)

In the block chain generation method using secret sharing according to an embodiment of the present invention, at least a part of block data to be inserted into the block chain cannot be inserted as _{a coefficient value (a j ) in the irreducible polynomial (f(x)).} In this case, by additionally setting another irreducible polynomial (g(x), h(x), ...), the above secret sharing step can be performed repeatedly until all transformed binary data are inserted as coefficient values. have.

In the block chain generation method using secret sharing according to an embodiment of the present invention, the irreducible polynomial (f'(x)) may be defined by the following Equation (2).

Equation (2):

(where x is the variable of the polynomial f'(x), x _o is the identifier (P _o ), x _j is the identifier (P _j ), y _j is the secret fragment value (f(P _j )), Π is a function that means product)

In the block chain generation method using secret sharing according to an embodiment of the present invention, the additional identifier (P _n+1 ) is at least one of a nonce and a time stamp in the block chain system. It can be specified according to the operation policy of the blockchain system.

In the block chain generation method using secret sharing according to an embodiment of the present invention, a threshold (t) for starting the proof-of-work step is set in the pre-processing step, and the threshold value (t) or more among n participants is collusion Thus, proof-of-work can be performed by submitting the ordered pair (P _i , f(P _i )) of its identifier (P _i ) and the secret fragment value (f(P _{i )) to the blockchain system.}

In the method of generating a block chain using secret sharing according to an embodiment of the present invention, the threshold value t may be set to a higher stake for a certain participant than other participants.

The present invention is a finite body coupled with a computing device, and input values are the number of participants (n) related to block data to be stored in the block chain, the identifiers of the participants (P _i , 1≤i≤n), and the identifiers of the participants. A preprocessing step of setting the irreducible polynomial (f(x)) on (Finite Field); The identifier (P _i ) is input into the reduced polynomial (f(x) _{) to generate a secret fragment value (f(P i} )), and the identifier (P _i ) and the secret fragment value (f(P _i )) Distributing the ordered pair (P _i , f(P _i )) to the participants, respectively, and an additional identifier (P _n+1 ) and an additional secret fragment value (f(P _n+1 )) other than the identifiers of the participants. A secret sharing step of storing the ordered pair (P _n+1 , f(P _{n+1 )) in the node;} By inputting the ordered pair (P _i , f(P _i )) of the identifier (P _i ) and the secret fragment value (f(P _i )) into the equation using the Lagrange interpolation equation, the reduced polynomial (f'(x)) is derived. and the additional secret fragment value (f'(P _n+1 _{)) generated by inputting the additional identifier (P n+1} ) to the derived irreducible polynomial (f'(x)) and the additional secret fragment stored in the node In order to execute the proof-of-work step of performing proof-of-work by comparing the values f(P _{n+1 ), it may be implemented as a computer program stored in a computer-readable recording medium.}

When using a hash function or PKI in which a key exists to create an existing block chain, the time required and the amount of computation increase in proportion to the number of participants, but in the block chain generation method using secret sharing according to the embodiment of the present invention, According to the report, using secret sharing and finite-body operation, the required time and amount of computation are constant regardless of the number of participants, so it is very efficient when creating a block chain node in a multi-participant environment, It has an excellent effect. In addition, there is an effect that separate key management is not required.

1 is a block diagram illustrating a block chain system according to an embodiment of the present invention.

2 is a flowchart illustrating a block chain generation method using secret sharing according to an embodiment of the present invention.

FIG. 3 is a diagram for explaining a process in which _{coefficient values a j} of the irreducible polynomial (f(x)) are generated from original data in the step of performing secret sharing according to an embodiment of the present invention.

_{4 is an identifier (P i} _{) of the identifier (P i} ) and the secret fragment value (f(P _i )) by inputting the identifier (P i ) into the irreducible polynomial (f(x)) in the step of performing secret sharing according to an embodiment of the present invention; It is a diagram for explaining the process of distributing the ordered pairs (P _i , f(P _{i )) to the participants, respectively.}

5 is a diagram for explaining a work proof step according to an embodiment of the present invention.

6 is a diagram illustrating a computing device according to an embodiment of the present invention.

Since the present invention can apply various transformations and can have various embodiments, specific embodiments are illustrated and described in detail in the detailed description. However, this is not intended to limit the present invention to specific embodiments, and it should be understood to include all modifications, equivalents, and substitutes included in the spirit and scope of the present invention.

The terms used in the present invention are only used to describe specific embodiments, and are not intended to limit the present invention. The singular expression includes the plural expression unless the context clearly dictates otherwise. In the present invention, terms such as 'comprising' or 'having' are intended to designate that the features, numbers, steps, operations, components, parts, or combinations thereof described in the specification exist, but one or more other features It should be understood that this does not preclude the existence or addition of numbers, steps, operations, components, parts, or combinations thereof. Hereinafter, a block chain generation method using secret sharing according to an embodiment of the present invention will be described with reference to the drawings.

1 is a block diagram showing a block chain system.

Referring to FIG. 1 , the block chain system may be a decentralized network 100 system composed of a plurality of nodes 200 . The nodes 200 constituting the decentralized network 100 may be electronic devices having an arithmetic function, a communication function, a storage function, etc., such as a computer, a server, and a mobile terminal.

The decentralized network 100 can store and refer to information commonly known to all participating nodes in a connected bundle of blocks called a block chain. The plurality of nodes 200 can communicate with each other and can be divided into a full node that stores, manages, and propagates the block chain and a light node that can simply participate in transactions.

Each block connected to the block chain contains block data to be stored in the block chain. The block data may be transaction details within a certain period, that is, a transaction. The nodes 200 manage transactions by creating, storing, or verifying a block chain according to their respective roles.

A transaction may represent various types of transactions. For example, a transaction may correspond to a financial transaction for indicating the ownership status of virtual currency and its change. Also, in another example, the transaction may correspond to a physical transaction for indicating the ownership status of the object and its change. In addition, a transaction may be a work jointly created by a plurality of participants. These are only examples, and the type of block data is not limited thereto.

As shown in FIG. 2 , the method for generating a block chain using secret sharing according to an embodiment of the present invention (hereinafter also referred to as a “block chain generating method”) includes a pre-processing step (S100) and a secret sharing step (S200). ), a proof-of-work step (S300), and a block chain storage step (S400). The above steps ( S100 to S400 ) may be performed by a computing device that performs an arithmetic function, which will be described later with reference to FIG. 6 .

S100: pre-processing step

First, in the preprocessing stage, the number of participants (n) related to the block data to be stored in the blockchain, the identifiers of the participants (P _i ~ P _n ), the irreducible polynomial in the finite field (f(x)), and the proof of work Set a threshold value (t) for In the following description, “participant” may mean a participant terminal.

For example, if the block data is a joint work by a plurality of participants, the number of participants (n) who participated in the joint work is set.

And, for each participant, a participant's unique identifier (P _i ~ P _n ) is set. The identifiers P _i to P _n may be set to an arbitrary number.

Then, in the work proof step (S300) to be described later, the minimum number of participants required for work proof is set as the threshold value (t). For example, when the number of participants n is 10, the threshold value t may be set to 5. Alternatively, a particular participant may have a higher stake than another participant. That is, a general participant is counted as 1, while a specific participant may be counted as 2 or more.

Then, an arbitrary irreducible polynomial (f(x)) on a finite field is set.

A finite field is a field that has only a finite number of elements and forms an algebraic structure. It means a field in which the result of operation (addition, multiplication, etc.) of elements in a finite field set is again within the set.

An irreducible polynomial is a polynomial that cannot be factored any further. Depending on the finite field range, the reduced polynomial can be different. For example, if f(x) = x ² - 2 and g(x) = x ² + 2, if the finite body is a set of rational numbers, then f(x) and g(x) are irreducible polynomials because they are not factored. If the finite body is a set of real numbers, f(x) = x ² - 2 is factored into f(x) = (x - √2)(x + √2), so f(x) cannot be a reduced polynomial, g(x) becomes a reduced polynomial.

The reduced polynomial (f(x)) on the finite field set in this step is, for example, the following equation (1).

Formula (1):

Here, t is a threshold value, mod is a remainder function that finds the remainder of an arbitrary division, and GF is a polynomial belonging to Galois feild. k means the number of bits, generally 8 or 16 is selected, and up to 64 can be selected depending on the amount of data to be stored in the block chain.

S200: Steps to perform secret sharing

In this step, an identifier (P _i ) is input into the reduced polynomial (f(x)) of Equation (1 _{) to generate a secret fragment value (f(P i} )), and an identifier (P _i ) and its corresponding secret Secret sharing is performed by distributing ordered pairs (P _i , f(P _i )) of the fragment values (f(P _i )) to the participants, respectively. Here, “secret sharing” means a state in which the secret fragment value f(P _i ) is distributed to several participants, respectively.

The identifier (Pi) performs a function similar to a kind of public key, and the secret fragment value (f(Pi)) performs a function similar to the private key (or private key). However, if the existing private key is exposed for various reasons, the corresponding block data may be hacked, but even if the secret fragment value f(Pi) of the present invention is exposed, since the secret is shared among the participants, Hacking is impossible and block data can be hacked only when t or more of the secret fragment value (f(P _i )) are exposed. However, in the real environment, the secret fragment value (f(P _i )) is the threshold value of t t pieces. Since there is almost no case of abnormal exposure, the secret sharing method is superior to the existing public key or symmetric key in terms of safety.

In Equation (1), the coefficient value of the polynomial a _j (j is 0 ~ t-1) is a part of the block data to be inserted into the actual block chain. After binarizing and parsing the original data, the coefficient value a _j insert into The predetermined unit may be, for example, 8 bits or 16 bits, and may be the k size ^{of GF(2 k ) in Equation (1).} The original data can be obtained by summing all the coefficient values a _{j .}

The coefficient value a _j will be described with reference to FIG. 3 . FIG. 3 is a diagram for explaining a process in which _{coefficient values a j} of the irreducible polynomial (f(x)) are generated from original data in the step of performing secret sharing according to an embodiment of the present invention.

As shown in FIG. 3 , original data is converted into binary data by the computing device of the present invention. The converted binary data is divided into a certain bit unit, and this is inserted as _{a coefficient value a j of the reduced polynomial (f(x)).} All the converted binary data is divided into a predetermined bit unit and inserted as _{a coefficient value a j of the reduced polynomial (f(x)).} Therefore, if all coefficient values a _j are summed, it can become binary data of the original data, and the original data can be extracted by transforming it again.

When the coefficient value a _j _{is determined from the original data, a secret piece value (f(P i} )) is generated by _{inputting an identifier (P i} ) consisting of a random number into the reduced polynomial (f(x)) of Equation (1). can Create and this secret piece value generated as (f (P _i)) to the input of identifiers (P _i) and the pair with ordered pairs _{_{(P i, f (P i}} )), the ordered pairs (P _i, f (P _i )) is distributed to the participants (participant terminals) of the corresponding identifier (P _{i ).} (See Fig. 4)

In Figure 4, the identifier (P _i ) is input to the irreducible polynomial (f(x)) in this secret sharing step, and an ordered pair (P _i , f( _{) of the identifier (P i} ) and the secret fragment value (f(P _{i ))} The _{process of distributing P i} )) to each participant is shown.

Finally, in this step, a secret fragment value (f(P _n+1 )) to be temporarily stored in the blockchain node is additionally created. The secret fragment value (f(P _n+1 )) temporarily stored in the node is called the additional secret fragment value. The additional secret piece value f(P _n+1 ) is generated by inputting the additional identifier P _n+1 into equation (1). The additional identifier (P _n+1 ) uses values such as nonce and time stamp within the block chain system and may be separately specified according to the operation policy of the block chain system.

The additional secret fragment value f(P _n+1 ) is stored in the node for proof-of-work in the proof-of-work step to be described later.

S300 :　Proof of work step

This step is the process of verifying the data through proof of work of the additional secret fragment value (f(P _{n+1 )) temporarily stored in the blockchain node.} The proof-of-work step will be described with reference to FIG. 5 . 5 is a diagram for explaining a work proof step according to an embodiment of the present invention.

Proof-of-work is a collusion of more than a threshold (t) among n participants, _{and an ordered pair (P i} , f(P _i )) of _{its own identifier (P i} ) and secret fragment value (f(P _i )) is created in the blockchain system. , and the blockchain system automatically initiates the proof-of-work process when more than the threshold of t people are colluded.

The process of proof-of-work is the same as the restoration process of shared secret, and is performed using Lagrange interpolation. The interpolation method is a method of estimating the value of the interval using discrete data, and the Lagrange interpolation method is a method of creating an nth-order polynomial with (n+1) coordinates.

When t participants conspire and t ordered pairs (P _i , f(P _i )) are submitted to the blockchain system, the reduced polynomial f'(x) is derived through the following equation (2) using Lagrange interpolation. (See Fig. 5A)

Equation (2):

where x is the variable of the polynomial f'(x), x _o is the identifier (P _o ), x _j is the identifier (P _j ), y _j is the secret fragment value (f(P _j )), Π is a function that means product.

The additional secret fragment value (f'(P _n+1 )) _{by inputting the additional identifier (P n+1} ) stored in the node in step S200 into the reduced polynomial (f'(x)) derived through Equation (2) create Next, when the same, by comparing the added value of the newly generated secret piece _{(f '(P n + 1} )) and adding a secret piece of value _{(f (P n + 1)} ) stored in the node exit the proof-of-work. (See Fig. 5B)

If the newly created additional secret fragment value (f'(P _n+1 )) and the additional secret fragment value stored in the node (f(P _n+1 )) are different, the value stored in the block chain by a malicious attacker Detects that the ordered pair (P _i , f(P _i )) of this altered or collusive participant is not correct.

When the proof-of-work is finished, the binary data of the original data is created by summing all the _{coefficient values a j , and the original data can be extracted by transforming it again.} (See Fig. 5C)

S400: Blockchain storage phase

After the proof of work is completed, _{a hash value is generated using SHA-3 for the additional secret fragment value (f(P n+1} )) temporarily stored in the block chain, and it is stored in the block chain node. SHA-3 is a cryptographic hash function announced in August 2015 by the US National Institute of Standards and Technology to replace SHA-2.

In addition to the additional secret fragment value (f(P _n+1 )) stored temporarily to generate as a hash value, the hash value of the node before the block chain to generate a block in the form of a chain, a Nonce (or time stamp), and other block chains For maintenance, various values that are policy-specified within the blockchain system are designated as input to SHA-3. This completes the process of creating a new type of block chain using secret sharing.

If, because the amount of block data to be stored in the block chain is large, the secret sharing operation step S200 is not completed with the coefficient values in one reduced polynomial (f(x)), another reduced polynomial (g(x), h( x), ...) are additionally set, and the secret sharing operation step (S200) is repeatedly performed until all the converted binary data are inserted as coefficient values. _{In this case, step S200 is completed while additional secret fragment values g(P n+1} ), h(P _n+1 ), ...) are stored in the node as many as the number of reduced polynomials.

According to the block chain generation method using secret sharing according to an embodiment of the present invention as described above, when using a hash function or PKI having a key to create an existing block chain, the time required and the amount of computation are proportional to the number of participants. Unlike this increase, using secret sharing and finite-body operation, the required time and amount of computation are constant regardless of the number of participants, so it is very efficient when creating a block chain node in a multi-participant environment, and space and It has an excellent effect in terms of time. In addition, there is an effect that separate key management is not required.

6 is a diagram illustrating a computing device according to an embodiment of the present invention. The computing device TN100 of FIG. 6 may be a computing device that performs operations S100 to S400 described above.

In the embodiment of FIG. 6 , the computing device TN100 may include at least one processor TN110 , a transceiver device TN120 , and a memory TN130 . In addition, the computing device TN100 may further include a storage device TN140 , an input interface device TN150 , an output interface device TN160 , and the like. Components included in the computing device TN100 may be connected by a bus TN170 to communicate with each other.

The processor TN110 may execute a program command stored in at least one of the memory TN130 and the storage device TN140. The processor TN110 may mean a central processing unit (CPU), a graphics processing unit (GPU), or a dedicated processor on which methods according to an embodiment of the present invention are performed. The processor TN110 may be configured to implement procedures, functions, methods, and the like described in connection with an embodiment of the present invention. The processor TN110 may control each component of the computing device TN100 .

Each of the memory TN130 and the storage device TN140 may store various information related to the operation of the processor TN110 . Each of the memory TN130 and the storage device TN140 may be configured as at least one of a volatile storage medium and a non-volatile storage medium. For example, the memory TN130 may include at least one of a read only memory (ROM) and a random access memory (RAM).

The transceiver TN120 may transmit or receive a wired signal or a wireless signal. The transceiver TN120 may be connected to a network to perform communication.

Meanwhile, the present invention may be implemented as a computer program. The present invention may be implemented as a computer program stored in a computer-readable recording medium in order to execute the block chain generation method using secret sharing according to the present invention in combination with hardware.

The methods according to the embodiment of the present invention may be implemented in the form of a program readable by various computer means and recorded in a computer readable recording medium. Here, the recording medium may include a program command, a data file, a data structure, etc. alone or in combination.

The program instructions recorded on the recording medium may be specially designed and configured for the present invention, or may be known and available to those skilled in the art of computer software.

For example, the recording medium includes magnetic media such as hard disks, floppy disks and magnetic tapes, optical recording media such as CDROMs and DVDs, and magneto-optical media such as floppy disks. optical media), and hardware devices specially configured to store and execute program instructions, such as ROM, RAM, flash memory, and the like.

Examples of program instructions may include not only machine language such as generated by a compiler, but also a high-level language that can be executed by a computer using an interpreter or the like.

Such hardware devices may be configured to operate as one or more software modules to perform the operations of the present invention, and vice versa.

In the above, although an embodiment of the present invention has been described, those of ordinary skill in the art can add, change, delete or add components within the scope that does not depart from the spirit of the present invention described in the claims. The present invention may be variously modified and changed by, etc., and this will also be included within the scope of the present invention.

Claims

A method of creating a block chain that is performed by a computing device and consists of a plurality of nodes,

The number of participants (n) related to the block data to be stored in the block chain, the identifiers of the participants (P i , 1≤i≤n), and the irreducible polynomial (f() x)) a pre-processing step to set;

The identifier (P i ) is input into the reduced polynomial (f(x) ) to generate a secret fragment value (f(P i )), and the identifier (P i ) and the secret fragment value (f(P i )) Distributing the ordered pair (P i , f(P i )) to the participants, respectively, and an additional identifier (P n+1 ) and an additional secret fragment value (f(P n+1 )) other than the identifiers of the participants. A secret sharing step of storing the ordered pair (P n+1 , f(P n+1 )) in the node;

A method of creating a blockchain using secret sharing, including
The method according to claim 1,

By inputting the ordered pair (P i , f(P i )) of the identifier (P i ) and the secret fragment value (f(P i )) into the equation using the Lagrange interpolation equation, the reduced polynomial (f'(x)) is derived. and,

The additional secret fragment value (f'(P n+1 )) generated by inputting the additional identifier (P n+1 ) into the derived irreducible polynomial (f'(x)) and the additional secret fragment value stored in the node ( A proof-of-work step that performs proof-of-work by comparing f(P n+1 ))

A method of creating a block chain using secret sharing further comprising a.
The method according to claim 1,

The irreducible polynomial (f(x)) is a block chain generation method using secret sharing, which is defined by the following equation (1).

Formula (1):

(Here, t is the threshold, a j is the coefficient value inserted in bits after binarizing and parsing the original data as a part of the block data to be inserted into the block chain, and mod is the remainder to obtain the remainder of arbitrary division. function, GF is a polynomial belonging to Galois feild, and k means the number of bits)
4. The method according to claim 3,

When at least a part of block data to be inserted into the block chain cannot be inserted as a coefficient value (a j ) in the reduced polynomial (f(x)), other reduced polynomials (g(x), h(x), .. .) to perform the secret sharing step repeatedly until all transformed binary data are inserted as coefficient values.

How to create a blockchain using secret sharing.
3. The method according to claim 2,

The irreducible polynomial (f'(x)) is a block chain generation method using secret sharing, which is defined by the following equation (2).

Equation (2):

(where x is the variable of the polynomial f'(x), x o is the identifier (P o ), x j is the identifier (P j ), y j is the secret fragment value (f(P j )), Π is a function that means product)
The method according to claim 1,

The additional identifier (P n+1 ) is specified according to the operation policy of the block chain system using at least one of a nonce and a time stamp in the block chain system.

How to create a blockchain using secret sharing.
The method according to claim 1,

In the pre-processing step, a threshold value (t) for starting the proof-of-work step is set, and the threshold value (t) or more among n participants is collusive, so that the identifier (P i ) and the secret fragment value (f(P i )) ) by submitting the ordered pair (P i , f(P i )) to the blockchain system to perform proof-of-work.

How to create a blockchain using secret sharing.
8. The method of claim 7,

The threshold value (t) is set to a higher stake than other participants for a specific participant.

How to create a blockchain using secret sharing.
coupled to the computing device;

The number of participants (n) related to the block data to be stored in the block chain, the identifiers of the participants (P i , 1≤i≤n), and the irreducible polynomial (f() x)) a pre-processing step to set;

The identifier (P i ) is input into the reduced polynomial (f(x) ) to generate a secret fragment value (f(P i )), and the identifier (P i ) and the secret fragment value (f(P i )) Distributing the ordered pair (P i , f(P i )) to the participants, respectively, and an additional identifier (P n+1 ) and an additional secret fragment value (f(P n+1 )) other than the identifiers of the participants. A secret sharing step of storing the ordered pair (P n+1 , f(P n+1 )) in the node;

By inputting the ordered pair (P i , f(P i )) of the identifier (P i ) and the secret fragment value (f(P i )) into the equation using the Lagrange interpolation equation, the reduced polynomial (f'(x)) is derived. and the additional secret fragment value (f'(P n+1 )) generated by inputting the additional identifier (P n+1 ) to the derived irreducible polynomial (f'(x)) and the additional secret fragment stored in the node A proof-of-work step that performs proof-of-work by comparing values (f(P n+1 )).

A computer program stored in a computer-readable recording medium to execute the computer program.