CN109921900A - A kind of algorithm of distributed key generation - Google Patents

Abstract

The invention discloses a kind of algorithms of distributed key generation, comprising the following steps: node users P_iGenerate random number d_i, by d_iIt is converted into P_iPublic key d_iG, and by d_iG is broadcasted, and receives the d of other users_iG；All P_iMultiple key generator polynomial coefficients are generated at random, and generate Lagrange interpolation polynomial, each P_iPolynomial value is calculated, and is sent to the corresponding P of i_i；All P_iKey generator polynomial coefficient is converted to key format, obtains multinomial coefficient public key, by coefficient public key broadcasts；All P_iThe polynomial value and key generator polynomial coefficient public key that receive are verified；All P_iAccording to the polynomial value and the value oneself being calculated for receiving other users, distributed user share private key t is calculated_i；All P_iAccording to the public key d for the transmission for receiving other node users_iG calculates distributed public key Q, and Q is broadcasted to network.

Description

A kind of algorithm of distributed key generation

Technical field

The present invention relates to block chain technical fields, and in particular to a kind of algorithm of distributed key generation.

Background technique

In certain important events, a document needs multi people signatures to guarantee the safety of data, such as high confidential document Using or the transaction of electronic money in.For problems, relatively common solution is to be divided into the private key of user More parts, give the data distribution after segmentation to multiple participants, when needing to be signed using private key, multiple divided data It can restore the private key of user, and then generate signature.Once any individual side can be at other however, private key is resumed Participant generates signature in the case where being unaware of.Especially in the case where two sides need one contract of signature jointly or agreement, If the side in two sides obtains original signature private key, can be to contract at discretion in the case where agreeing to without other side It signs, generates the stolen risk of private key for user.

In the prior art, there is the algorithm signed by distributed cipher key, this algorithm, which realizes, is not restoring private key Under the premise of sign to the information of node users, but existing algorithm cannot achieve the node users on block chain and become When dynamic, under the premise of not restoring distributed private key, user's share private key of all node users is updated.

Summary of the invention

The object of the present invention is to provide a kind of algorithms of distributed key generation, in the premise for not restoring distributed private key Under, update user's share private key of all node users.

An embodiment provides a kind of algorithms of distributed key generation, comprising the following steps:

1) quantity for defining all nodes on block chain is n, and G is to generate ellipse used in algorithmic formula used in public key The basic point of curve point group, all node users P on block chain_iGenerate original random number d_i, i is the sequence number value of Pi, and by d_iTurn Turn to P_iPublic key d_iG, and by d_iG is broadcasted, while receiving the d that other node users are sent on block chain_iG；

2) all P_iMultiple key generator polynomial coefficient a are generated at random_{I, 1}.......a_{I, k-1}, the value range of k be [1, N], and Lagrange interpolation polynomial is generated, polynomial format are as follows:

f_i(x_i)=d_i+a_{I, 1}x_i+…+a_{I, k-1}x_i ^k-1 (1)

x_iFor P in formula (1)_iSequence number value pass through the obtained numerical value of Hash operation；

Each P_iCalculate each x_iCorresponding f_i(x_i) numerical value, and by f_i(x_i) it is sent to the corresponding P of i_i；

3) all P_iBy a_{I, 1}.......a_{I, k-1}It is converted to key format, obtains multiple multinomial coefficient public key a_{I, 1}G.......a_{I, k-1}G, and multiple multinomial coefficient public keys are broadcasted；

4) all P_iReceive the f that other all node users are sent_i(x_i) and key generator polynomial coefficient public key, and To f (x_i) and key generator polynomial coefficient public key verified with following formula:

f_i(x_i) G=d_iG+a_{I, 1}x_iG+…+a_{I, k-1}x_i ^k-1G (2)

I is the sequence number value of other all node users in formula (2)；

If verifying does not pass through, other node users that can't pass is requested to retransmit d_iG、f_i(x_i) and a_{I, 1}G......a_{I, k-1}G information gives oneself；

5) and 6) if verification result passes through, the step of progress；

5) all P_iAccording to the f for the transmission for receiving other all node users_i(x_i) and the f that oneself is calculated_i(x_i), Calculate distributed user share private key t_i, calculation formula are as follows:

t_i=f₁(x_i)+f₂(x_i)+…+f_n(x_i) (3)

6) all P_iAccording to the public key d for the transmission for receiving other all node users_iG calculates distributed public key Q, Calculation formula are as follows:

Q=d₁G+d₂G+…+d_nG (4)

And Q is broadcasted to block chain network.

Further, when node users change on block chain, under the premise of not restoring q, all nodes are updated The t of user_i, comprising the following steps:

7.1) all P_iBy t_iIt is converted into t_iG, and broadcasted to block chain network；

7.2) all P_iMultiple key updating multinomial coefficient b are generated at random_{I, 1}......b_{I, k-1}, and generate Lagrange Interpolation polynomial, polynomial format are as follows:

f_i(x_i)=t_i+b_{I, 1}x_i+…+b_{I, k-1}x_i ^k-1 (6)

x_iFor P in formula (6)_iSequence number value pass through the obtained numerical value of Hash operation；

Each P_iCalculate each x_iCorresponding f_i(x_i) numerical value, and by f_i(x_i) it is sent to the corresponding P of i_i；

7.3) all P_iBy b_{I, 1}......b_{I, k-1}It is converted to key format, it is public to obtain multiple key updating multinomial coefficients Key b_{I, 1}G......b_{I, k-1}G, and multiple key updating multinomial coefficient public keys are broadcasted；

7.4) all P_iReceive the f that other all node users are sent_i(x_i) and key updating multinomial coefficient public key, And to f (x_i) and key updating multinomial coefficient public key verified with following formula:

f_i(x_i) G=t_iG+b_{I, 1}x_iG+…+b_{I, k-1}x_i ^k-1G (7)

I is the sequence number value of other all node users in formula (7)；

If verifying does not pass through, other node users that can't pass is requested to retransmit t_iG、f_i(x_i) and b_{I, 1}G......b_{I, k-1}G information gives oneself；

If verification result passes through, the step of progress 7.5)；

7.5) all P_iAccording to the f for the transmission for receiving other all node users_i(x_i) and the f that oneself is calculated_i (x_i), calculate new distributed user share private key t_i, calculation formula are as follows:

t_i=f₁(x_i)+f₂(x_i)+…+f_n(x_i) (8)。

Compared with prior art, distributed key generation provided by the invention and the algorithm of update have the advantages that

Under the premise of not restoring distributed private key, user's share private key of all node users is updated.Pass through intelligent conjunction About, q is calculated automatically, is avoided centralization facility personnel and is cheated the risk done evil,

Detailed description of the invention

Fig. 1 show the flow diagram of one embodiment of the algorithm of distributed key generation of the invention.

Fig. 2 show the flow diagram of one embodiment of the algorithm updated after distributed key generation of the invention.

Specific embodiment

To make the object, technical solutions and advantages of the present invention clearer, below in conjunction with the specific embodiment of the invention and Technical solution of the present invention is clearly and completely described in corresponding attached drawing.

In the description of the present invention, authentication center (CA-Certificate Authority) is as authority, believable , the just third-party institution, be responsible for digital certificate needed for providing and managing the entities traded on all participation chains specially.It As an authoritative institution, key is effectively managed, certificate proves the validity of key, and public-key cryptography is same Some entity (consumer, trade company, bank) links together.It is responsible for generating, distribute and managing all participation network informations Digital certificate needed for exchanging each side, therefore be the core of safe electronic information exchange.

With reference to Fig. 1, in one embodiment of the invention, the algorithm of distributed key generation includes step 100~600:

100: the quantity for defining all nodes on block chain is n, and G is ellipse used in algorithmic formula used in generation public key The basic point of circular curve point group, all node users P on block chain_iGenerate original random number d_i, i is the sequence number value of Pi, and by d_i It is converted into P_iPublic key d_iG, and by d_iG is broadcasted, while receiving the d that other node users are sent on block chain_iG；

200: all P_iMultiple key generator polynomial coefficient a are generated at random_{I, 1}......a_{I, k-1}, the value range of k is [1, n], and Lagrange interpolation polynomial is generated, polynomial format are as follows:

f_i(x_i)=d_i+a_{I, 1}x_i+…+a_{I, k-1}x_i ^k-1 (1)

x_iFor P in formula (1)_iSequence number value pass through the obtained numerical value of Hash operation；

Each P_iCalculate each x_iCorresponding f_i(x_i) numerical value, and by f_i(x_i) it is sent to the corresponding P of i_i；

300: all P_iBy a_{I, 1}......a_{I, k-1}It is converted to key format, obtains multiple multinomial coefficient public key a_{I, 1}G......a_{I, k-1}G, and multiple multinomial coefficient public keys are broadcasted；

400: all P_iReceive the f that other all node users are sent_i(x_i) and key generator polynomial coefficient public key, And to f (x_i) and key generator polynomial coefficient public key verified with following formula:

f_i(x_i) G=d_iG+a_{I, 1}x_iG+…+a_{I, k-1}x_i ^k-1G (2)

I is the sequence number value of other all node users in formula (2)；

If verifying does not pass through, other node users that can't pass is requested to retransmit d_iG、f_i(x_i) and a_{I, 1}G......a_{I, k-1}G information gives oneself；

If verification result passes through, carry out 500 and 600 the step of；

500: all P_iAccording to the f for the transmission for receiving other all node users_i(x_i) and the f that oneself is calculated_i (x_i), calculate distributed user share private key t_i, calculation formula are as follows:

t_i=f₁(x_i)+f₂(x_i)+…+f_n(x_i) (3)

600: all P_iAccording to the public key d for the transmission for receiving other all node users_iG calculates distributed public key Q, Its calculation formula is:

Q=d₁G+d₂G+…+d_nG (4)

And Q is broadcasted to block chain network.

In one embodiment of the invention, further include the steps that generating distributed private key q, specifically:

The no less than node users of k value quantity send t_iTo cipher key center management organization, calculates and generates distributed private key q, Its calculation formula is:

J indicates the sequence number value of other all node users different from i in formula (5).

In one embodiment of the invention, further include the steps that generating distributed private key q, specifically:

Committee's node disposes administrative center's intelligence contract, all node users P on block chain_iSend t_iInto management Intelligence energy contract, the code of administrative center's intelligence contract calculates q according to formula rule automatically, and q is stored in administrative center In the database of intelligent contract；The calculation formula of q are as follows:

Further, when node users change on block chain, this algorithm further includes step 700, is not restoring q's Under the premise of, update the t of all node users_i, step 700 the following steps are included:

701: all P_iBy t_iIt is converted into t_iG, and broadcasted to block chain network；

702 all P_iMultiple key updating multinomial coefficient b are generated at random_{I, 1}......b_{I, k-1}, and generate Lagrange and insert It is worth multinomial, polynomial format are as follows:

f_i(x_i)=t_i+b_{I, 1}x_i+…+b_{I, k-1}x_i ^k-1 (6)

x_iFor P in formula (6)_iSequence number value pass through the obtained numerical value of Hash operation；

Each P_iCalculate each x_iCorresponding f_i(x_i) numerical value, and by f_i(x_i) it is sent to the corresponding P of i_i；

703: all P_iBy b_{I, 1}......b_{I, k-1}It is converted to key format, it is public to obtain multiple key updating multinomial coefficients Key b_{I, 1}G......b_{I, k-1}G, and multiple key updating multinomial coefficient public keys are broadcasted；

704: all P_iReceive the f that other all node users are sent_i(x_i) and key updating multinomial coefficient public key, And to f (x_i) and key updating multinomial coefficient public key verified with following formula:

f_i(x_i) G=t_iG+b_{I, 1}x_iG+…+b_{I, k-1}x_i ^k-1G (7)

I is the sequence number value of other all node users in formula (7)；

If verifying does not pass through, other node users that can't pass is requested to retransmit t_iG、f_i(x_i) and b_{I, 1}G......b_{I, k-1}G information gives oneself；

If verification result passes through, the step of carrying out 705；

705: all P_iAccording to the f for the transmission for receiving other all node users_i(x_i) and the f that oneself is calculated_i (x_i), calculate new distributed user share private key t_i, calculation formula are as follows:

t_i=f₁(x_i)+f₂(x_i)+…+f_n(x_i) (8)。

In one embodiment of the invention, d is generated_iG, Q or t_iThe algorithm of G are as follows: elliptic curve Elliptic-curve Diffie-Hellman (ECDH) algorithm.

In one embodiment of the invention, node users P_iSerial number i generation process are as follows: all P_iOn block chain Dispose user management intelligence contract, after node users are registered in user management intelligence contract, the generation of user management intelligence contract Code distributes specific user's serial number according to the time sequencing of registration.

Although being made that detailed description to the present invention with above-mentioned preferred embodiment, not limited with above-described embodiment The present invention.Those skilled in the art is not it should be recognized that departing from technical characteristic given by technical solution of the present invention and range In the case where, to made by technical characteristic increase, with the replacement of some same contents in this field, protection model of the invention should all be belonged to It encloses.

Claims (6)

1. a kind of algorithm of distributed key generation, which comprises the following steps:

1) quantity for defining all nodes on block chain is n, and G is to generate elliptic curve used in algorithmic formula used in public key The basic point of point group, all node users P on block chain_iGenerate original random number d_i, i is the sequence number value of Pi, and by the d_iTurn Turn to P_iPublic key d_iG, and by d_iG is broadcasted, while receiving the d that other node users are sent on block chain_iG；

2) all P_iMultiple key generator polynomial coefficient a are generated at random_i,1……a_i,k-1, the value range of the k is [1, n], And Lagrange interpolation polynomial is generated, the polynomial format are as follows:

f_i(x_i)=d_i+a_{I, 1}x_i+…+a_{I, k-1}x_i ^k-1 (1)

x_iFor P in formula (1)_iSequence number value pass through the obtained numerical value of Hash operation；

Each P_iCalculate each x_iCorresponding f_i(x_i) numerical value, and by f_i(x_i) it is sent to the corresponding P of i_i；

3) all P_iBy a_i,1……a_i,k-1It is converted to key format, obtains multiple multinomial coefficient public key a_i,₁G……a_i,k-1G, And the multiple multinomial coefficient public key is broadcasted；

4) all P_iReceive the f that other all node users are sent_i(x_i) and key generator polynomial coefficient public key, and to institute State f (x_i) and key generator polynomial coefficient public key verified with following formula:

f_i(x_i) G=d_iG+a_{I, 1}x_iG+…+a_{I, k-1}x_i ^k-1G (2)

I is the sequence number value of other all node users in formula (2)；

If verifying does not pass through, other node users that can't pass is requested to retransmit d_iG、f_i(x_i) and a_i,1G……a_i,k-1G letter It ceases to oneself；

5) and 6) if verification result passes through, the step of progress；

5) all P_iAccording to the f for the transmission for receiving other all node users_i(x_i) and the f that oneself is calculated_i(x_i), Calculate distributed user share private key t_i, calculation formula are as follows:

t_i=f₁(x_i)+f₂(x_i)+…+f_n(x_i) (3)

6) all P_iAccording to the public key d for the transmission for receiving other all node users_iG calculates distributed public key Q, Calculation formula are as follows:

Q=d₁G+d₂G+…+d_nG (4)

And Q is broadcasted to block chain network.

2. the algorithm of distributed key generation according to claim 1, which is characterized in that further include generating distributed private key The step of q, specifically:

The no less than node users of k value quantity send t_iTo cipher key center management organization, calculates and generates distributed private key q, Its calculation formula is:

J indicates the sequence number value of other all node users different from i in formula (5).

3. the algorithm of distributed key generation according to claim 2, which is characterized in that node users occur on block chain When variation, under the premise of not restoring q, the t of all node users is updated_i, comprising the following steps:

7.1) all P_iBy t_iIt is converted into t_iG, and broadcasted to block chain network；

7.2) all P_iMultiple key updating multinomial coefficient b are generated at random_i,1……b_i,k-1, and it is more to generate Lagrange's interpolation Item formula, the polynomial format are as follows:

f_i(x_i)=t_i+b_{I, 1}x_i+…+b_{I, k-1}x_i ^k-1(6)

x_iThe numerical value obtained for the sequence number value of Pi in formula (6) by Hash operation；

Each P_iCalculate each x_iCorresponding f_i(x_i) numerical value, and by f_i(x_i) it is sent to the corresponding P of i_i；

7.3) all P_iBy b_i,1……b_i,k-1It is converted to key format, obtains multiple key updating multinomial coefficient public key b_{i, 1}G……b_i,k-1G, and the multiple key updating multinomial coefficient public key is broadcasted；

7.4) all P_iReceive the f that other all node users are sent_i(x_i) and key updating multinomial coefficient public key, and it is right F (the x_i) and key updating multinomial coefficient public key verified with following formula:

f_i(x_i) G=t_iG+b_{I, 1}x_iG+…+b_{I, k-1}x_ik^-1G (7)

I is the sequence number value of other all node users in formula (7)；

If verifying does not pass through, other node users that can't pass is requested to retransmit t_iG、f_i(x_i) and b_i,1G……b_i,k-1G letter It ceases to oneself；

If verification result passes through, the step of progress 7.5)；

7.5) all P_iAccording to the f for the transmission for receiving other all node users_i(x_i) and the f that oneself is calculated_i (x_i), calculate new distributed user share private key t_i, calculation formula are as follows:

t_i=f₁(_xi)+f₂(x_i)+…+f_n(x_i) (8)。

4. the algorithm of distributed key generation according to claim 1 or 3, it is characterised in that: the generation d_iG, Q or t_iG Algorithm are as follows: elliptic curve Elliptic-curve Diffie-Hellman (ECDH) algorithm.

5. the algorithm of distributed key generation according to claim 1, which is characterized in that all node users P_i's The generation process of serial number i are as follows: all P_iUser management intelligence contract is disposed on the block chain, the node users are described After registering in user management intelligence contract, the code of the user management intelligence contract is specific according to the time sequencing distribution of registration User's serial number.

6. the algorithm of distributed key generation according to claim 1, which is characterized in that further include calculating distributed private key The step of q, specifically:

Committee's node disposes administrative center's intelligence contract, all node users P on block chain_iSend t_iInto the management Intelligence energy contract, the code of administrative center's intelligence contract calculates q according to formula rule automatically, and q is stored in management In the database of center intelligence contract；The calculation formula of the q are as follows: