CN111934858B - Supervised random public key derivation method - Google Patents
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- H—ELECTRICITY
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- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
- H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds
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- H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
- H04L9/3006—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters
- H04L9/3033—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters details relating to pseudo-prime or prime number generation, e.g. primality test
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Abstract
The invention discloses a supervised random public key derivation method, which provides optional supervision functions and comprises the following steps: (1) a system parameter generation algorithm; (2) a user initial key generation algorithm; (3) a user tracking key generation algorithm; (4) a user tracking key verification algorithm; (5) a user derived public key generation algorithm; (6) a user derived private key generation algorithm; (7) a user derived public key tracking algorithm; steps (1) to (7) are executed when the supervision function is selected, and steps (1), (2), (5), (6) are executed when the supervision function is not selected. The method of the invention realizes that only one public key needs to be initially registered by the receiver, and simultaneously provides an optional supervision function.
Description
Technical Field
The invention relates to the technical field of public key derivation, in particular to a supervised random public key derivation method.
Background
In the era of the rapid development of current information technology, the advanced data acquisition and transmission technologies such as 5G, the Internet of things and the like will bring data streams with richer contents, stronger timeliness and larger volume, wherein countless private data are wrapped. In the era of the flood of data, whether the individual user is safe to enjoy the service or the enterprise explores an emerging business model, it is important to implement privacy protection.
At present, most key derivation methods are derivation methods based on symmetric keys, and the derivation method for public keys is only a random public key derivation method based on double public keys proposed by Cryptonote protocol in 2012. The method is mainly used for enhancing the anonymity of the data receiving party. In the Cryptonote protocol, when a and B are transacted, the sending party a (if the initial public key of B is known) can derive a random public key according to the initial public key pair of the receiving party B without interaction, and declare that the formulation is transferred to the user corresponding to the random public key. Since only receiver B can compute the specified private key, only B can own the asset and others cannot deduce the identity of B.
However, this method requires each receiver to initially register two public keys for derivation, and therefore, two public key certificates need to be registered, which not only increases the cost of applying for the initial certificate, but also increases the cost of storing the certificate. And the key derived in the method has no managed function.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: in view of the above existing problems, a policeable random public key derivation method is provided that requires only the initial registration of a public key by the recipient, while also providing optional policing functionality.
The technical scheme adopted by the invention is as follows:
a policeable random public key derivation method, comprising:
when the participating party comprises a user A and a user B, the user A is a sender, and the user B is a receiver, the execution flow of the random public key derivation method is as follows in sequence: the method comprises the following steps of (1), (2), (5) and (6), wherein the step (1) is executed by a third party organization or is executed by a user A and a user B together; step (5) is executed by the user A, and steps (2) and (6) are executed by the user B;
when the participating party comprises a monitoring party, a user A and a user B, the user A is a sending party, and the user B is a receiving party, the execution flow of the random public key derivation method is as follows in sequence: steps (1) to (7); wherein, the steps (1), (4) and (7) are executed by a supervisor, the step (5) is executed by a user A, and the steps (2), (3) and (6) are executed by a user B;
wherein the steps (1) to (7) are as follows:
(1) system parameter generation algorithm Pub ← (1)λ)：
Input of safety parameters 1λWherein λ is a positive integer, and outputting and generating a system parameter Pub;
(2) user initial key generation algorithm (PK)0,SK0)←Pub：
Inputting system parameter Pub, outputting user B initial public and private key Pair (PK)0,SK0)；
(3) User tracking key generation algorithm TK ← (Pub, SK)0)：
Inputting system parameter Pub and user B initial private key SK0Outputting a tracking key TK of the user B;
(4) user tracking key validation algorithm (Y/N) ← (Pub, PK)0,TK)：
Inputting system parameter Pub, user B initial public key PK0User B keeps track of the secret TK, if TK is indeed the user B's initial public key PK0If not, outputting Y, otherwise, outputting N;
(5) user-derived public key generation algorithm (PK)R,R)←(Pub,PK0)：
Inputting system parameter Pub, user B initial public key PK0Exporting user B derived Public Key (PK)R,R)；
(6) User derived private key generation algorithm (SK)R,R)←(Pub,SK0,PKR,R)：
Inputting system parameter Pub and user B initial private key SK0User derived Public Key (PK)RR), output user B derived private key SKR；
(7) User-derived public key tracking algorithm (Y/N) ← (Pub, PK)0,PKR,R,TK)：
Inputting system parameter Pub, user B initial public key PK0User B derived Public Key (PK)RR), user B tracks the key TK if the derived public key is indeed the initial public key PK by user B0Deriving then outputs Y, otherwise outputs N.
Further, the step (1) comprises:
(1.1) input of safety parameters 1λWherein λ is a positive integer;
(1.2) run 1λGenerating prime p, group G1、G2And a computable bilinear pairing operation e;
(1.3) outputting the system parameter Pub, { P ═ P1，P2，G1，G2，GT，ê，Zp，H}；
Wherein G is1，G2For an elliptic curve addition cyclic group of order p, GTFor multiplication loop groups of elliptic curves of order p, ZpIs a group of integers of order P, P1Is a group G1Is generated from P2Is a group G2A generator of (2); h is a hash function G of collision resistanceT→Zp(ii) a E is a computable bilinear pairing operation e: g1×G2→GT(ii) a Satisfies the following conditions:
1) bilinear; for arbitrary U1∈G1，U2∈G2Any integer a, b ∈ ZpAll have "A" "U1，b·U2)＝ê(ab·U1，U2)＝ê(U1，ab·U2)＝ê(U1，U2)ab；
2) Non-degradability; e (P)1，P2)≠1。
Further, the step (2) comprises the following steps:
(2.1) random selection of SK0∈Zp；
(2.2) calculation of PK0←SK0·P1∈G1。
Further, the step (3) comprises:
(3.1) calculating TK ← SK0·P2∈G2。
Further, the step (4) comprises the following steps:
(4.1) if [ E (P)1，TK)＝＝ê(PK0，P2) Outputting Y;
and (4.2) otherwise, outputting N.
Further, the step (5) comprises:
(5.1) randomly selecting r ∈ Zp；
(5.2) calculating R ← R. P1∈G1；
(5.3) calculation of RK ← E (PK)0，r·P2)∈GT；
(5.4) calculation of PKR←H(RK)·P1+PK0∈G1。
Further, the step (6) comprises:
(6.1) calculating RK ← E (R, SK)0·P2)∈GT；
(6.2) calculating R ← R. P1∈G1；
(6.3)SKR←H(RK)+SK0∈Zp。
Further, the step (7) comprises:
(7.1) calculation of RK ← E (R, TK). epsilon.GT；
(7.2)PKR′←H(RK)·P1+PK0∈G1；
(7.3) if PKR′＝PKROtherwise, outputting Y, and otherwise, outputting N.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
the method of the invention realizes that only one public key needs to be initially registered by the receiver, and simultaneously provides an optional supervision function.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
Fig. 1 is a flow chart diagram of a random public key derivation method of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
Aiming at the problem that in the existing method, each receiver needs to initially register two public keys to derive, so that two public key certificates need to be registered, which not only increases the cost of applying for the initial certificate, but also increases the cost of storing the certificate. Also, the key derived in this existing method does not have a managed function. The invention provides a supervised random public key derivation method based on bilinear pairing technology, which only needs a receiver to initially register a public key and simultaneously provides an optional supervision function. Thus, as shown in fig. 1, a policeable random public key derivation method of the present invention includes:
when the participating party comprises a user A and a user B, the user A is a sender, and the user B is a receiver, the execution flow of the random public key derivation method is as follows in sequence: steps (1), (2), (5) and (6), wherein step (1) is executed by a third mechanism or is executed by a user A and a user B together; step (5) is executed by the user A, and steps (2) and (6) are executed by the user B;
when the participating party comprises a monitoring party, a user A and a user B, the user A is a sending party, and the user B is a receiving party, the execution flow of the random public key derivation method is as follows in sequence: steps (1) to (7); wherein, the steps (1), (4) and (7) are executed by a supervisor, the step (5) is executed by a user A, and the steps (2), (3) and (6) are executed by a user B;
wherein the steps (1) to (7) are as follows:
(1) system parameter generation algorithm Pub ← (1)λ)：
Input of safety parameters 1λWherein λ is a positive integer, and outputting and generating a system parameter Pub;
(2) user initial key generation algorithm (PK)0,SK0)←Pub：
Inputting system parameter Pub, outputting user B initial public and private key Pair (PK)0,SK0)；
(3) User tracking key generation algorithm TK ← (Pub, SK)0)：
Inputting system parameter Pub and user B initial private key SK0Outputting a tracking key TK of the user B;
(4) user tracking key validation algorithm (Y/N) ← (Pub, PK)0,TK)：
Inputting system parameter Pub, user B initial public key PK0User B keeps track of the secret TK, if TK is indeed the user B's initial public key PK0If not, outputting Y, otherwise, outputting N;
(5) user-derived public key generation algorithm (PK)R,R)←(Pub,PK0)：
Inputting system parameter Pub, user B initial public key PK0Exporting user B derived Public Key (PK)R,R)；
(6) User derived private key generation algorithm (SK)R,R)←(Pub,SK0,PKR,R)：
Inputting system parameter Pub and user B initial private key SK0User B derived Public Key (PK)RR), output user B derived private key SKR；
(7) User-derived public key tracking algorithm (Y/N) ← (Pub, PK)0,PKR,R,TK)：
Inputting system parameter Pub, user B initial public key PK0User B derived Public Key (PK)RR), user B tracks the key TK if the derived public key is indeed the initial public key PK by user B0Deriving then outputs Y, otherwise outputs N.
The features and properties of the present invention are described in further detail below with reference to examples.
Let G1，G2For an elliptic curve addition cyclic group of order p, GTFor multiplication loop groups of elliptic curves of order p, ZpIs a group of integers of order P, P1Is a group G1Is generated from P2Is a group G2A generator of (2); h is a hash function G of collision resistanceT→Zp(ii) a E is a computable bilinear pairing operation e: g1×G2→GT(ii) a Satisfies the following conditions:
1) bilinear; for arbitrary U1∈G1，U2∈G2Any integer a, b ∈ ZpAll have "A" "U1，b·U2)＝ê(ab·U1，U2)＝ê(U1，ab·U2)＝ê(U1，U2)ab；
2) Non-degradability; e (P)1，P2)≠1。
1. When the supervision function is not needed
Namely: when the participating party comprises a user A and a user B, the user A is a sender, and the user B is a receiver, the execution flow of the random public key derivation method is as follows in sequence: the method comprises the following steps of (1), (2), (5) and (6), wherein the step (1) is executed by a third party organization or is executed by a user A and a user B together; step (5) is executed by the user A, and steps (2) and (6) are executed by the user B;
the execution flow of the random public key derivation method is as follows:
(1) (performed by a third-party authority, or jointly by user a and user B) generates the system parameters algorithm Pub ← (1)λ)：
(1.1) input of safety parameters 1λWherein λ is a positive integer;
(1.2) run 1λGenerating prime p, group G1、G2And a computable bilinear pairing operation e;
(1.3) outputting the system parameter Pub, { P ═ P1，P2，G1，G2，GT，ê，Zp，H}。
(2) (user B execution) user initial Key Generation Algorithm (PK)0,SK0)←Pub：
(2.1) random selection of SK0∈Zp；
(2.2) calculation of PK0←SK0·P1∈G1(ii) a Then (5) is executed;
(5) (user A execution) user-derived public key generation algorithm (PK)R,R)←(Pub,PK0)：
(5.1) randomly selecting r ∈ Zp；
(5.2) calculating R ← R. P1∈G1；
(5.3) calculation of RK ← E (PK)0，r·P2)∈GT；
(5.4) calculation of PKR←H(RK)·P1+PK0∈G1。
(6) (performed by user B) user-derived private Key Generation Algorithm (SK)R,R)←(Pub,SK0,PKR,R)：
(6.1) calculating RK ← E (R, SK)0·P2)∈GT；
(6.2) calculating R ← R. P1∈G1；
(6.3)SKR←H(RK)+SK0∈Zp。
2. When the supervision function is required to be used
Namely: when the participating party comprises a monitoring party, a user A and a user B, the user A is a sending party, and the user B is a receiving party, the execution flow of the random public key derivation method is as follows in sequence: steps (1) to (7); wherein, the steps (1), (4) and (7) are executed by a supervisor, the step (5) is executed by a user A, and the steps (2), (3) and (6) are executed by a user B;
the execution flow of the random public key derivation method is as follows:
(1) (supervisor execution) generating System parameter Algorithm Pub ← (1)λ)：
(1.1) input of safety parameters 1λWhere λ ∈ Z+；
(1.2) run 1λGenerating prime p, group G1、G2And a computable bilinear pairing operation e;
(1.3) outputting the system parameter Pub, { P ═ P1，P2，G1，G2，GT，ê，Zp，H}。
(2) (user B execution) user initial Key Generation Algorithm (PK)0,SK0)←Pub：
(2.1) random selection of SK0∈Zp；
(2.2) calculation of PK0←SK0·P1∈G1。
(3) (user B performs) user tracking key generation algorithm TK ← (Pub, SK)0)：
(3.1) calculating TK ← SK0·P2∈G2；
(4) (supervisor execution) user tracking Key verification Algorithm (Y/N) ← (Pub, PK)0,TK)：
(4.1) if [ E (P)1，TK)＝＝ê(PK0，P2) Outputting Y;
and (4.2) otherwise, outputting N.
(5) (user A execution) user-derived public key generation algorithm (PK)R,R)←(Pub,PK0)：
(5.1) randomly selecting r ∈ Zp；
(5.2) calculating R ← R. P1∈G1；
(5.3) calculation of RK ← E (PK)0，r·P2)∈GT；
(5.4) calculation of PKR←H(RK)·P1+PK0∈G1。
(6) (performed by user B) user-derived private Key Generation Algorithm (SK)R,R)←(Pub,SK0,PKR,R)：
(6.1) calculating RK ← E (R, SK)0·P2)∈GT；
(6.2) calculating R ← R. P1∈G1；
(6.3)SKR←H(RK)+SK0∈Zp。
(7) (supervisor execution) user-derived public key tracking algorithm (Y/N) ← (Pub, PK)0,PKR,R,TK)：
(7.1) calculation of RK ← E (R, TK). epsilon.GT；
(7.2)PKR′←H(RK)·P1+PK0∈G1；
(7.3) if PKR′＝PKROtherwise, outputting Y, and otherwise, outputting N.
Through the process, the user B sends the tracking key TK of the user B to the supervisor, and the supervisor can supervise all transactions of the user B, so that single-user tracking can be achieved. If user B does not send his tracking key TK to the supervisor, RK ← E (R, SK) for each specific derivation0·P2)∈GTAnd the transaction is sent to a supervisor, and the supervisor can only supervise the transaction, so that single transaction tracking can be realized.
In the random public key derivation methods, the tracking key is generated by the user according to the private key of the user and is sent to the supervision party, so that the supervision mode belongs to user-selectable supervision. If strong supervision is to be realized, each user is required to send the tracking key of the user to the supervisor by force, and after the supervisor receives the tracking key from the user, the correctness of the tracking key can be verified through the public key of the user, so that the situation that the supervisor cannot perform correct tracking because the user sends a wrong tracking key to escape supervision is avoided.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (5)
1. A policeable random public key derivation method, comprising:
when the participating party comprises a user A and a user B, the user A is a sender, and the user B is a receiver, the execution flow of the random public key derivation method is as follows in sequence: the method comprises the following steps of (1), (2), (5) and (6), wherein the step (1) is executed by a third party organization or is executed by a user A and a user B together; step (5) is executed by the user A, and steps (2) and (6) are executed by the user B;
when the participating party comprises a monitoring party, a user A and a user B, the user A is a sending party, and the user B is a receiving party, the execution flow of the random public key derivation method is as follows in sequence: steps (1) to (7); wherein, the steps (1), (4) and (7) are executed by a supervisor, the step (5) is executed by a user A, and the steps (2), (3) and (6) are executed by a user B;
wherein the steps (1) to (7) are as follows:
(1) system parameter generation algorithm Pub ← (1)λ)：
Input of safety parameters 1λWherein λ is a positive integer, and outputting and generating a system parameter Pub;
(2) user initial key generation algorithm (PK)0，SK0)←Pub：
Inputting system parameter Pub, outputting user B initial public and private key Pair (PK)0，SK0)；
(3) User tracking key generation algorithm TK ← (Pub, SK)0)：
Inputting system parameter Pub and user B initial private key SK0Outputting a user tracking key TK;
(4) user tracking key validation algorithm (Y/N) ← (Pub, PK)0，TK)：
Inputting system parameter Pub, user B initial public key PK0The user keeps track of the secret TK, if the TK is indeed the user B initial public key PK0If not, outputting Y, otherwise, outputting N;
(5) user-derived public key generation algorithm (PK)R，R)←(Pub，PK0)：
The parameters of the system are input to the Pub,user B initial public key PK0Exporting user B derived Public Key (PK)R，R)；
(6) User derived private key generation algorithm (SK)R，R)←(Pub，SK0，PKR，R)：
Inputting system parameter Pub and user B initial private key SK0User B derived Public Key (PK)RR), output user B derived private key SKR；
(7) User-derived public key tracking algorithm (Y/N) ← (Pub, PK)0，PKR，R，TK)：
Inputting system parameter Pub, user B initial public key PK0User B derived Public Key (PK)RR), user B tracks the key TK if the derived public key is indeed the initial public key PK by user B0If the derivation is carried out, Y is output, otherwise, N is output;
the step (1) comprises the following steps:
(1.1) input of safety parameters 1λWherein λ is a positive integer;
(1.2) run 1λGenerating prime p, group G1、G2And a calculable bilinear pairwise operation
(1.3) outputting the system parameter Pub,
wherein G is1，G2For an elliptic curve addition cyclic group of order p, GTFor multiplication loop groups of elliptic curves of order p, ZpIs a group of integers of order P, P1Is a group G1Is generated from P2Is a group G2A generator of (2); h is a hash function G of collision resistanceT→Zp；
For computable bilinear pairings
G1×G2→GT(ii) a Satisfies the following conditions:
1) bilinear; for arbitrary U1∈G1，U2∈G2Any integer a, b ∈ ZpAll are provided with
2) Non-degradability;
the step (2) comprises the following steps:
(2.1) random selection of SK0∈Zp；
(2.2) calculation of PK0←SK0·P1∈G1；
The step (5) comprises the following steps:
(5.1) randomly selecting r ∈ Zp；
(5.2) calculating R ← R. P1∈G1；
(5.3) calculation of
(5.4) calculation of PKR←H(RK)·P1+PK0∈G1。
2. A policeable random public key derivation method according to claim 1, wherein step (3) comprises:
(3.1) calculating TK ← SK0·P2∈G2。
3. A policeable random public key derivation method according to claim 2, wherein step (4) comprises:
(4.1) if
Outputting Y;
and (4.2) otherwise, outputting N.
4. A policeable random public key derivation method according to claim 3, wherein step (6) comprises:
(6.1) calculation of
(6.2) calculating R ← R. P1∈G1；
(6.3)SKR←H(RK)+SK0∈Zp。
5. A policeable random public key derivation method according to claim 4, wherein step (7) comprises:
(7.1) calculation of
(7.2)PKR′←H(RK)·P1+PK0∈G1；
(7.3) if PKR′＝PKROtherwise, outputting Y, and otherwise, outputting N.
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