Lightweight group signature system and method with short signature

A lightweight group signature system and method with short signatures according to the exemplary embodiments of the present invention can provide security characteristics similar to group signature mechanisms providing the existing known controllable linkability but can make a revocation method simple by outputting a short signature and providing excellent operation efficiency at the time of signature generation, signature verification, and revocation on smart terminals, and can be widely applied to various anonymity-based application environments, making by making operation efficiency excellent at the time of signature generation and verification and outputting very short signature lengths.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to and the benefit of Korean Patent Application No. 10-2011-0103670 filed in the Korean Intellectual Property Office on Oct. 11, 2011, the entire contents of which are incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to a lightweight group signature system and method with short signatures, and more particularly, to a lightweight group signature system and method with short signatures, which can be effectively operated on a lightweight smart terminal.

BACKGROUND ART

A group signature mechanism, which is one of the very important cryptographic authentication mechanisms for protecting user's privacy, has been widely researched and has been considerably developed since the concept thereof is first proposed by Chaum and Heyst in 1991. Various security requirements, formal models, and detailed mechanisms have been proposed. Recently, a group signature mechanism providing controllable linkability by extending typical group signature mechanisms has been researched.

Typical authentication mechanisms, such as an ID/password authentication mechanism, a real-name based PKI authentication mechanism, and an i-Pin mechanism, and the like, have many disadvantages, such as personal information exposure due to a registration and identification process of personal information, leakage due to excessive personal information collection and management carelessness of a service provider, a wide range of activity trace, and the like. As a result, a group signature mechanism providing controllable linkability as an effective anonymous authentication mechanism that can replace the above-mentioned mechanisms has been actively researched recently.

The group signature mechanism providing controllable linkability additionally has controllable linkability capable of identifying that group signatures are linked with each other (that is, the group signatures are generated by one signer or a signer key) when a special linking key is provided, by extending the typical group signature mechanisms simply handling anonymity using a dichotomical structure that conceals/recovers identity information or ID of a signer. Therefore, the anonymity can be controlled to various levels according to the desired policy.

Using the characteristics, a service provider can obtain user related effective information from various anonymity based services, for example, web based personalized anonymous authentication service or in the case of data mining, anonymous authentication data, while maintaining anonymity of identity information.

Existing group signature mechanisms providing various security characteristics such as the known controllable linkability, and the like, cannot be widely adopted in various application environments due to structural complexity. Currently, user storage costs and operation costs are very cheap. Therefore, costs of resources for designing the system greatly depends on communication costs and therefore, the group signature mechanism providing controllable linkability with short signatures is urgently required in low resource application environments such as a radio Internet based service market.

Recently, application mechanisms for enhancing privacy protection by performing anonymous authentication between the smart terminals by using short range communication environment, and the like, have been researched and developed.

As an example, a method for transmitting information using multi-dimensional codes such as a QR code has been greatly interested as one method of short range communications. A device with a built-in camera capable of recognizing the multi-dimensional code can obtain information through the multi-dimensional codes any time and therefore, the user can process information using the corresponding devices without separate communication networks (thus, without charging communication costs). The method for recognizing multi-dimensional codes through a camera is performed by a contactless type and therefore, does not require devices such as a separate connection cable, and the like.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present inventors have developed the lightweight group signature mechanism, and the like, that is excellent in terms of performance, in particular, outputs short signatures and has the excellent security characteristics while providing excellent operation efficiency at the time of signature generation and signature verification on the smart terminals.

The present invention has been made in an effort to provide a lightweight group signature system and method with short signatures capable of providing excellent operation efficiency at the time of signature generation, signature verification, and revocation on smart terminals while providing security characteristics similar to group signature mechanisms providing the existing known controllable linkability but outputting the short signatures.

An exemplary embodiment of the present invention provides a lightweight group signature system with short signatures, may include: a signature control unit configured to generate a group public key, issue a signature key to a user device, store the signature key in a signature key management list, and update related information including the signature key management list when validity of a join request generated from the user device is verified, identify whether two signatures are linked and manage a revocation list to perform revocation and generate a signer identification proof when a valid signature is; a user device configured to generate a signature using a signature key issued from the signature control unit; a signature verifying unit configured to verify a signature generated from the user device; signer identification proof evaluating unit configured to evaluate the validity of the signer identification proof generated from the signature control unit.

The signature control unit may include: a key issuing unit configured to generate a group public key, a master issuing key, a master opening key, and a master linking key based thereon, issue the signature key to the user device when a join of the user device is requested, and manage a revocation list so as to be used to update the signature key when the revocation of the issued signature key is performed; a signer identifying unit configured to identify the validity of a signature key generating a signature and generate the signer identification proof by using the master opening key when the valid signature is given; and a signature linking unit configured to identify whether two signatures are linked with each other by using the master linking key when two valid signatures are present.

The key issuing unit may provide the generated group public key to all the participants including the user device.

The key issuing unit may define the master issuing key by using (algebraic) bilinear groups and a bilinear map associated with the bilinear groups.

The key issuing unit may verify the validity of a join request message when receiving the join request message from the user device to be registered in the lightweight group signature system and then, issues the signature key to the user device.

The join request message may include personal key ownership verification information and verification information related to key issuance.

A security channel for authentication may be formed between the key issuing unit and the user device.

The key issuing unit may change a session at the time of generating a revocation list of issued signature keys and make public the revocation list to be used to update the group public key and a user secret key.

The signer identifying unit may output a proof identifying who is a signer by using the master opening key when the valid signature is given.

Another exemplary embodiment of the present invention provides a lightweight group signature method, including: generating a group public key and generating a master secret key, a master opening key, and a master linking key based thereon; verifying the validity of user information after receiving user information required to join a signature group from a user device when a join is requested from the user device, issuing a signature key by using the master secret key when the verification is valid, and generating the signature; and searching registration information including a public key of the user device, calculating validity of the signature by using the master opening key, the signature, and related information, and determining whether revocation of the signature is performed according to whether the calculating results are present in the revocation list.

The generating of the signature may further include: verifying the validity of the join request message by receiving a join request message from the user device; receiving a signature for the join request message of which the validity is verified from the user device; generating a secret signature key corresponding to a group public key in the user device by verifying the validity of the signature and registering the user device; and providing the generated group public key to the user device registered in the group signature system.

The determining whether the revocation of the signature is performed may further include identifying whether two signatures are linked with each other by using the master linking key when two valid signatures are given.

The determining whether the revocation of the signature is performed may further include providing the identifying result of the revocation to the user device when the revocation identification for the given signature is requested

The master issuing key may be defined by using bilinear groups, a bilinear map associated with the bilinear groups, and a hash function.

The join request message may include a personal key ownership verification information.

The lightweight group signature system and method with short signatures according to the exemplary embodiments of the present invention can make the revocation method simple and can be widely applied to various anonymity-based application environments such as the multi-dimensional code based authentication, and the like, by providing the excellent operation efficiency at the time of the signature generation and verification and outputting the very short signature length.

The lightweight group signature system and method with short signatures according to the exemplary embodiments of the present invention can provide unforgeability, traceability, non-frameability, controllable anonymity, and controllable linkability to systemically control the degree of anonymity.

The lightweight group signature system and method with short signatures according to the exemplary embodiments of the present invention can be used for applications to which the existing group signature mechanisms, such as anonymous authentication for traffic network, future Internet anonymous packet authentication, and the like, are applied, and various next-generation IT applications such as anonymous based web services, medical information security, cloud computing authentication, and the like, and can be used on the smart terminals.

DETAILED DESCRIPTION

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. First of all, we should note that in giving reference numerals to elements of each drawing, like reference numerals refer to like elements even though like elements are shown in different drawings. In describing the present invention, well-known functions or constructions will not be described in detail since they may unnecessarily obscure the understanding of the present invention, and terms described in the singular form may include a plural concept. Hereinafter, exemplary embodiments of the present invention will be described, but the spirit of the present invention is not limited thereto and may be changed and modified in various ways by those skilled in the art.

FIG. 1shows a configuration of a lightweight group signature system with short signature lengths according to an exemplary embodiment of the present invention.

Referring toFIG. 1, a lightweight group signature system according to an exemplary embodiment of the present invention includes a signature control unit100including a key issuing unit110, a signer identifying unit120, and a signature linking unit130, a signature verifying unit150, and a signer identification proof evaluating unit160. Here, each component of the signature control unit100can be implemented by a software algorithm that outputs special values for given input values. However, each component is not limited thereto and a role of participants may be flexibly separated or integrated based on definition of a new subject according to a designed method. If necessary, it is possible to add new components for linking with known real-name authentication mechanisms. Herein, examples of the integration may also include the integration of the key issuing unit110and the integration of the signer identifying unit120or the integration of the signer identifying unit120and the signature linking unit130.

The key issuing unit110initially generates the group public key as a trusted subject and generates a master issuing key (mik), a master opening key (mok), and a master linking key (mlk) corresponding thereto.

The key issuing unit110performs an interactive protocol when receiving a join request from a new user device140and then, issues a signature key to the user device.

The signer identifying unit120updates related information including a revocation list when a revocation phenomenon occurs. If the signer identifying unit120identifies whether revocation is performed, by using the updated revocation list and the master opening key when the revocation identification request is received from the signature verifying unit150and then, returns the identified results to the signature verifying unit150.

The signer identifying unit120uses the master opening key to output the verification information for identifying a signer when a valid signature is given. Anyone can publicly identify the output verification information.

The signature linking unit100can identify a linking relationship of two signatures by using the master linking key when two valid signatures are given. That is, it can be appreciated whether a single signer generates two signatures.

The user device140may be joined in a member of a valid group to receive a signature key from the key issuing unit110. In this case, the user device140and the key issuing unit110perform an interactive protocol.

Thereafter, the user device140generates a group signature for a given message by using an issued signature key. The signature verifying unit150identifies validity of a signature for the given signature. The signer identification proof evaluating unit160evaluates the validity of the signer identification proof generated from the signer identifying unit120.

The key issuing unit110defines a group public key (gpk) and makes public the defined group public key to components of the lightweight group signature system and all the systems linked with the lightweight group signature system.

FIG. 2is an operational control flow chart of allowing the key issuing unit110according to an exemplary embodiment of the present invention to generate an initial group public key (gpk), the master issuing key (mik) corresponding to the initial group public key, the master opening key (mok), and the master linking key (mlk).

Hereinafter, referring toFIG. 2, an operational process of the key issuing unit10(110) according to the exemplary embodiment of the present invention will be described in detail.

Initially, the key issuing unit110receives a security parameter k as an input to generate bilinear groups G1and G2, a bilinear map e:G1×G2→GTcoupled therewith, and a hash function H:{0,1}→Zp′. Here, the number of groups is set to be a decimal p. The key issuing unit110performs the followings so as to generate parameters for generating the keys according to each group signature mechanism.

Elements h1ε G2and g, g1, g2, u ε G1and θεZp* and η, ξεZp* are selected uniformly at random. After hθ=h1θ, w=uη, d=uξis calculated, mik=θ is defined as the master issuing key, mok=(η, ξ) is defined as the master opening key, and mlk=L=h1ξis defined as the master linking key, respectively (S200).

The key issuing unit110transfers the master opening key mok=(η, ξ) to an identifier server and transfers the master linking key mlk=L=h1ξto a linker unit130(S202).

FIG. 3shows an operational control flow of allowing the key issuing unit110to interactively generate a signature key with the user device140according to the exemplary embodiment of the present invention.

Hereinafter, the process of generating the signature key of the key issuing unit110according to the exemplary embodiment of the present invention will be described in detail with reference toFIG. 3.

The user device140and the key issuing unit110interactively perform the following operations according to the group signature mechanism to be used. Authentication and security channels are formed between the user device140and the key issuing unit110that are two participants.

The user device140selects secret value ziεZp* and generates its own public key Ci=wZiwhen being newly joined in the group. The user device140provides a join request message and user information (IDi, uZi, Ci=wZi, POP(w, Ci), ZK-Eq(u, uZi, w, Ci)) to the key issuing unit110(S300). Herein, it is assumed that the fact that C is a public key generated in a user IDican be publicly verified. It is assumed that all the C values are defined as different values for each user. If necessary, two assumptions may be easily implemented by using a binary search. When more than two users want to use the same public key value, the user joined later is not allowed to join and allows the use of other public key values.

The key issuing unit110verifies that the user IDiknows zi=logwCiby using POP(w, Ci) and also verifies loguYi=logwCiby using zero-knowledge verification of knowledge ZK-Eq(u, Zi=uZi, w, Ci). If the verifications succeed, the key issuing unit110selects xi, yi←rp*, calculates Ai=(g1g2−yiCi−1)1/(θ−xi)=(g1g2−yiwzi)1/(θ+xi)by using the master issuing key θ and transfers (Ai, xi, yi) to the user device140(S302).

The user device140verifies the validity of (Ai, xi, yi) and stores a secret key usk[i]=(Ai, xi, yi, zi) of a group member (S304).

The key issuing unit110additionally registers registration information REGi=[gyi, IDi, Ci=wzi, POP(w, Ci), Xi=h1xi, Yi=g2yi] in a user registration list register (REG) (S306).

The methods may support a simultaneous join when using a non-interactive zero-knowledge verification of knowledge.

FIG. 4is an operational control flow of allowing the valid user device140to generate a group signature for given messages according to an exemplary embodiment of the present invention.

Hereinafter, a process of generating the group signature by the valid user device according to the exemplary embodiment of the present invention will be described in detail with reference toFIG. 4.

The user device140receives the given group public key (gpk), a user secret signature key usk[i]=(A, x, z, y) corresponding to the group public key, and a message M (S400). Then, the user device140generates a signature a for the input as follows.

FIG. 5is an operational control flow chart of verifying a group signature for a message, which is generated by valid user devices140, by the signature verifying unit150according to the exemplary embodiment of the present invention.

Hereinafter, a process of verifying the signature verifying unit150according to the exemplary embodiment of the present invention will be described in detail with reference toFIG. 5.

It is assumed that the signature for the message M is previously generated (S500). The signature verifying unit150for the given signature calculates R1←usoD1−c, R3←gsydsαD3−c, and R2←e(D2, h1)sxe(w, hθ)−sαe(w, h1)−sye(g2, h1)sz(e(D2, hθ)/e(g1, h1))c. The signature verifying unit150calculates a hash function value c′=H(M, D1, D2, D3, R1, R2, R3) and then, identifies whether c is equal to c′ (S502). As the identified result, if two values are equal to each other, the signature verifying unit150outputs 1 representing that the given signature is valid. If not, 0 is output (S504).

FIG. 6is an operational control flow chart of generating a signer identification proof identifying who is a real signer of a group signature for a message generated by the valid user device140by using the master opening key and verifying the validity of the signer identification proof by using the signer identification proof evaluating unit160according to the exemplary embodiment of the present invention.

Hereinafter, a process of verifying the validity of the verification information by the signer identification proof evaluating unit160according to the exemplary embodiment of the present invention will be described in detail with reference toFIG. 6.

It is assumed that a valid signature σ=(D1, D2, D3, c, sα, sx, sγ, sy) for the message M is previously given (S600). The signer identifying unit120generates the verification information τ by using the master opening key mok=(η, ξ) as follows.

Then, the signer identifying unit120searches a user index i and information REGi=[gyi, IDi, Ci=wzi, POP(w, Ci), Xi=h1xi, Yi=g2yi] corresponding thereto by the binary search in the user registration list REG by using gy. Herein, upk[i]=Ci=wziis information registered by the public key of the signer when the signer is joined (S604). The signer identifying unit120calculates K=D1η=uαηand Ai=Aiuηα(uα)−η=D2K−1and verifies that Equation e(Ai, Xih0)=e(g1Yi−1Ci−1, h1) is established (S606). If the verification equation is valid, the signer identifying unit120selects r←p* and calculates copen=H(Mopen, σ, g, K, ur, D1r) and sopen=r−copenη (mod p). Here, Mopenis a message for identifying the signer. The signer identifying unit120outputs the signer identification proof τ=(K, sopen, copen) corresponding to the IDi, the public key Ci=wzi, and the signature σ of the signer (S608).

The signer identification proof evaluating unit160evaluates if the valid signature σ=(D1, D2, D3, c, sα, sx, sγ, sy) for the given message M, the signer identification proof upk[i]=Ci=wziand τ=(K, sopen, copen), and the public key upk[i] of the given signer meets the following conditions.

(1) The signer identification proof evaluating unit160calculates W1=usopenwcopen=ur, W2=D1sopenKropen=D1r, and the hash function value copen′=H(Mopen, σ, g, K, W1, W2) and identifies that copen′=copenis established and also identifies that (2) c(D2K−1, Xihθ)=c(g1g2−yiCi−1, h1) is established.

If both of the Equations (1) and (2) are established, the signer identification proof evaluating unit160outputs 1 representing the validity. If not, 0 is output (S608).

FIG. 7is an operational control flow chart of confirming whether the group signatures are linked with each other by using a master linking key for two group signatures generated by the valid user device140according to the exemplary embodiment of the present invention.

Hereinafter, a process of identifying on the linking of group signatures of two group signatures according to the exemplary embodiment of the present invention will be described in detail with reference toFIG. 7.

FIG. 8is an operational control flow chart of allowing the signer identifying unit120to update the related information in the revocation list (RL) when the revocation is generated and outputting results when the revocation is requested, according to the exemplary embodiment of the present invention.

Hereinafter, the process of outputting processed results at the time of receiving the revocation identification request by the signer identifying unit120will be described in detail with reference toFIG. 8, according to the exemplary embodiment of the present invention.

The valid signature σ=(D1, D2, D3, c, sα, sx, sγ, sy) for the message M is previously given as an input (S800). The signer identifying unit120identifies whether the revocation of the key generating the signature given as follows is performed by using the master opening key mok=(η, ξ).

The signer identifying unit120calculates LI=D3D1−ξ=gyuξα·(uα)−ξ=gy(S802). The signer identifying unit120identifies whether the calculated value is present in the revocation list (RL). The signer identifying unit120outputs the ‘revocation’ when the calculation value is present and outputs ‘valid’ when the calculation value is not present (S804).