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Essay: Threshold Multiple signature schemes

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Threshold Multiple signature schemes includes the various the striking features of threshold group-oriented signature and Multiple signature schemes so that ultimately it is able to derive a signature scheme that can provide a property by which various members of the software groups can collaborately sign an anonymous and arbitrary message for communication between different members of different groups.
The communication can be of two types :
‘ intergroup communication
‘ Intragroup communication
But when it is beingcompared to threshold group signatures, the individual members who sign the message are notcapable of remaining anonymous but are identified in public domain. The main objective of this project is to provide a secure and efficient multiple signature generation mechanism for group communication. This project shows that it is highly advanced, reliable and is prone to various adversary attacks that other systems are subjected to in their lifetime operation.
Multiple signature involves a distributed-key management infrastructure (DKMI), which consists of two processes:-
‘ distributed-key generation (DKG) protocol
‘ distributed-key redistribution/updating (DKRU) protocol
The use of this optimum distributed-key redistribution/updating (DKRU) protocol solves a major problem by giving an opportunity to various group users to identify share holders who are not correct, thus helps in avoiding again and again executions of multiple protocols.
In this project, java is used as the front end language and Mysql server is used as the back end server for database creation and integration .The IDE used to write java code was eclipse as it is an efficient platform to build java applications. For generation of public and private keys for individual users Elgamal algorithm is used. These keys are generated and stored in the database with the individual group keys that is generated by group members.
Now multiple signature is generated using this group key. After generation of these keys the message is encoded and transmitted over the network. When this message is received by the users they can decrypt this message using their public keys and hence they can read the message that was transmitted over the network.
Threshold Cryptosystems has ever since 1989 been successful in attracting people’s attention when it was first explained and illustrated by Desmedt and Frankel. Since then various international studies have been done in the field of threshold cryptography. Threshold signature cryptographic system is a very important field of threshold cryptography. It represents the overall research in the field of threshold cryptography. Li, Hwang and Lee were the three scientist who developed the RSA algorithm for threshold signature scheme. In simultaneous researches that were conducted, the scientist came out with a conclusion that sub secret share holders can be conspiring with an aim to retrieve the system secret and as a result the conspirators and adversaries can generate a group signature.
The report shows a method of group communication using multiple signature generation scheme where the group members sign the message and this message is sent over the network to the receiver and he decrypts it. The public and private key generation is totally based on elgamal algorithm which is accompanied with DKRU protocol. The method is much more advanced and reliable and can handle various attacks on the system.
L.Harn went a little forward and provided with a group oriented threshold signature scheme which dependent on Elgamal algorithm. In this system any x out of y users in a can be involved to sign the group signature. The advantage of this system is that the size and the verification time for the generation of group signature are totally equal to individual digital signature generation scheme. By using this scheme the signature verification process becomes easy as in this scheme we require only one group public key. In this method we have on advantage that the group signature is fully varifable by any outsider. Another advantage of this system is that the scheme does not require any help from mutually trusted parties. In this scheme each member has its individual secret key and in relation the unified the group public key is decided by all the group members in collaboration. Every member of the group has the ability to sign the message individually and sends it to the clerk. The clerk then performs validation on each individual signature into the unique group signature.
Li, Hwang and Lee made a new system by closing two (t, n) threshold signature schemes so that they can limit the attacks by the conspirators and adversaries. They developed two method first which requires tdc(trusted distribution centre), and other without trusted distribution centre . These two methods were successful in avoiding the attacks as it attached a random arbitrary number to all the keys of various members present in the database. By this method the protection of signature was successful against detecting sub keys of members. However these two schemes were unable to protect attack from the members who are the part of the systems as they can be involved in forging activities.
Wang, Lin and Chang developed two fresh and varied (x, y) threshold signature systems. These two systems do not need any arbitrary number to attach with the keys of group members. This was an advanced method which can handle attacks without the need of any random secret number with every key. The determination of the group key is in the same manner and hence is provided by all the members of that particular group.
In today’s modern life things have changed on a drastic note. First people used to communicate using telegram, telegraph etc but now we use telephones, email etc. with modernisation we have risked ourselves to various attacks. In this report the focus is laid on the communication process between different people electronically. With the advent of emails, there also came a risk of data authenticity and integrity. So to make communication between people secure this system has been designed which encrypts the messages that are sent over the network and when the specified person receives the message heshe can decrypt it. The whole technique in this communication process is termed as Cryptography.
Cryptography is the study of various techniques for securing network communication. It makes communication more reliable in the presence of various other users (adversaries)
that are present over the network by encrypting and decrypting the message that is to be communicated between members. In a more general sense, it is about analyzing different protocols that overcome the influence of various attacks by attackers and which are related to many aspects in data and network security such as authenticated data, data confidentiality and data integrity. The best advantage of using distributed cryptographic system is that the code which contains the secret while transmitting data over the network is never subjected to computation, reconstruction, and is never stored in a single location hence as a result the secret code becomes more difficult to attack by attackers.
A Group signature scheme is a procedure for which allows a user or participant of a group to sign a particular message for the entire group. In a group communication there is a group administrator who accepts a request of a new member into the group and can also remove the person from the group. He also has the ability to reveal who is the original sender or signer of the messages.
Threshold-multi signature scheme allows group members to sign a arbitrary message in collaboration which they then can send over the network. They can sign this message individually or as a group also. In comparison with the threshold group signatures, when individual signers sign a message they do not remain anonymous anymore, as they are identifiable publicly by the data that is present in valid and true threshold multi signature scheme.
This Secure Multiple signature Generation for Group Communication is divided into 3 modules:-
‘ Signature generation
‘ Cryptography
‘ Message transmission
Fig 1. Classification of multiple signature generation into it’s components
The objective of this report is to make a secure and efficient threshold-multi signature scheme for effective group communication.
1.1 Benefits of Multi signature
The various benefits of using Multi signature scheme is are listed below:-
‘ This routing is used to decrease to the latency
‘ It increase the throughputs on the network
‘ It is highly cost efficient.
‘ It reduces the administrative costs heavily.
‘ Lower down the error rate ratio.
‘ It enhances profitability by high margins.
‘ It provides good services to various clients.
1.2 Properties of Multi signature
The secure Multi signature schemes should provide with following advantages:-
1.2.1 Publicly verifiable
All Multi signatures on an anonymous message, that are generated by authentic set of group members, can be subjected to easy verification by any non authentic user V (with respect to the group). This shows that the group-oriented generation of signature can be verified publicly.
1.2.2 Threshold property
This property is maintained by the fact that only authorised/authentic group users can sign a message individually or collaborately and as a result they can only generate valid signatures required for communication. This property hence includes unforgeability.
1.2.3 Traceability
Any user who is not the member of the group can identify the identity of individual signers without interacting to any group member or manager. This shows that the signers of message can be publicly identified and are traceable with public information. Traceability results in accountability, where the individual signers can be held responsible in the group oriented communication.
1.3.4 Coalition-resistance
By this property the system becomes more reliable and secure. Using this property system includes framing-resistance, which means that any set of group members cannot have the potential to sign a message in place of any other subset of group members.
1.4.5 Break-resistance
This is the most important property for multiple signature generation in group communication by which it becomes highly secure and reliable. By this property if an adversary by some reason gets a secret share still it cannot generate a valid signature. Hence though the cryptographic system has been broken still the adversary can’t reach the transmitted message.
2.1 Existing System
Threshold Multiple signature schemes is a combination of threshold group-oriented signature schemes and various multiple signature schemes. Multiple signature schemes are also referred to as threshold signature schemes with traceability factor in it. The combination of different properties gives the signature verifier an assurance that at least x members participated in group oriented signature generation and the identity of various signers can be identified easily. Most of the existing multiple signature schemes are variants of single signatory which uses elgamal algorithm and are extended to group orientation for communication.
2.2 Proposed System
This project is developed with an objective of a new Multiple signature scheme with effective group communication and is without a trusted third party (TTP). This project is based on a publicly verifiable Distributed Key Generation ( DKG ) protocol. The project can be easily modified to incorporate a TTP but in this project the assistance of a TTP is not presented.
The proposed discrete logarithm-based Multiple signature scheme which is used in the project is also highly secure, as it allows a new access structure every time and mitigate various attacks from an active adversary. This proposed discrete logarithm-based Multiple signature scheme is made highly secure by various processes such as
‘ Periodically updating secrets.
‘ It allows changes in group membership as it allows an authorized set of existing group members to redistribute their secret shares to new access mechanisms or structures.
This project is a much advanced project as it resist the various attacks that other similar systems are unable to do. It also accomplishes all the properties of multi signature schemes.
2.3 Efficiency Analysis
The efficiency of Multiple signatures schemes depends on the following four basic criteria:-
2.3.1Group Public Key Length
The Multiple signature scheme has the capability to avoids the different threat attacks without even attaching a secret to messages. The group public key primarily depends on the number of group members present in a particular group. The reason for this is that the signature verifier needs values of all group members on individual basis which he uses to compute one subgroup public key for that group that is required to verify the signature. Sometimes difficulty can be experienced with this scheme when we feel the need for a trustworthy authority to distribute the various key the on their behalf.
An authentication system is very essential to make a distributed system secure against active adversaries over the network and it also ensures traceability of different users. The proposed scheme uses the private keys of the members of different groups, which helps in avoiding from various conspiracy attacks irrespective of the fact that colluding handles the group secret. As a result of this procedure of different members attaching their private keys in their individual signatures the scheme becomes more and more secure. The single public key of the group is a abstract derived from individual public key of the group members.
As the group public key is seen to depend on the group size, this scheme does not introduce any extra storage requirements since keys that are used in the calculation of secret is publicly known and is easily traceable. This key is basically required for authentication purposes.
2.3.2 Group-related Signature Size
The most important contribution to the two processes which are listed below:-
‘ communication
‘ post signature generation
is totally dependent on the size of the group. The size of signature in Multiple signature schemes is totally dependent on the threshold’s parameter value. This can be seen from traceability property of various multiple signature schemes, which means that any outsider (who is not the member of the system) to the system must have the potential ability to retrieve the identity of the individual signers from their particular threshold signature.
The threshold signature hence is totally linked to the information explicitly which is further linked to each of the signers that in collaboration generated the threshold signature.
In this scheme, the information related or associated is the identities of the individual signers of the message. The individual identities should be chosen carefully so that the size of multiple signature reduces.
2.3.4 Communication and Networking Cost
In form of communication cost, both the individual as well as the threshold signature generation mechanisms of all the present Multiple signature schemes and this proposed scheme are almost equal. Multiparty signature schemes that are made using ElGamal type (discrete logarithm-based) signature variants are highly interactive.
Firstly, each participant has the duty to generates it’s commitment and secondly, the very participant generates an individual signature on a particular arbitrary message . Thirdly, the signers then send their contribution to a controller which then constructs the threshold signature.
For example, assume that the authorized set group members come together to collaborate on to sign a particular message. This then yields a protocol for various schemes, which requires broadcasting messages and unicasting messages. This proposed Multiple signature generation scheme, is the best according to my analysis. This also eliminates the need for combination. For example, the group contains one malicious participant, then the proposed protocol will definitely require three rounds and if individual signatures are verified then only two rounds will be required.
2.3.5 Computational cost
To strike a comparison between the computational cost of this Multiple signature scheme and other similar schemes it is ought to assume that the various system parameters are selected to provide the same time complexity for various operations like:-
‘ Exponentiations
‘ Multiplications
‘ Summations
Although summations and, multiplications contribute insignificantly to the overall time complexity, we still include these operations to make the system complete.
Values which remain constant over time between various signature can be computed beforehand and are hence are not being included in the analysis. The computational cost of the schemes is calculated in terms of minimum members that are needed to sign an arbitrary message collaborately. The computational problems that is most difficult is the number of exponentiations that is related to individual signature verification and multiple signature verification and hence this problem takes large amount of time verification complexity.
If we concentrate critically at the verification processes it is justified by the fact that a signature is normally generated only once, but is subjected to verification many times. For an ElGamal type signature generation the optimal number of exponentiations operations is two. hence it can be said that this Multiple signature scheme is far more advanced and superior to previously existing schemes as it only requires two exponentiations for Multiple signature verification.
But for individual signature verification process, three exponentiations operations are required. The additional exponentiation is used to make the break resistance property even much more stronger.
3.1 Hardware Specification
Processor : Pentium processors.
Ram : 64 Mb or more.
Hard Disk : 10 GB or more.
Input device : Keyboard and Mouse.
Output device : High Resolution Monitor.
3.2 Software Specification
Operating System : Windows xp or higher.
Programming language : java
Techniques : JDK 1.5
Database server : My sql server
Ide : Eclipse
4.1 Java Features
‘ A machine compiles and runs code for the machine only.
‘ A “virtual” always have and runs its own type of binary data.
‘ The Java Virtual Machine (JVM) is a program that runs on each architecture.
‘ It takes Java Byte code as its input language.
‘ When non-native machine code is used as the only input to the machine, it is called “interpreting”.
Fig 1 Java Platform Description
Sun Microsystems developed JDBC which is an acronym for Java Database Connectivity. Java database connectivity provides a standard SQL database access mechanism which can be interfaced to different types of RDBMSs present. This interfacing is achieved by the use of a ‘plug-in’ database connection modules or drivers. If the database provider wishes to provide JDBC support, he must also provide the driver for each other platform available on which the database and Java runs on.
To use Java database connectivity on a larger scale, Sun Microsystem launched JDBC’s framework on Open Database Connectivity(ODBC). ODBC can be used on a number of different platforms. Using JDBC on ODBC framework will provide an opportunity to spread JDBC drivers to market at a more faster rate than developing a new connectivity.
TCP and UDP Connection
TCP is connection-oriented protocol while UDP (User Datagram Protocol) is a connectionless protocol.
IP datagram’s
The IP layer is connectionless and provides unreliable data networking interface. It takes into account each of the datagram independent of the others present. Any type of combination or association between different datagram must be provided by the other higher layers. After receiving the data IP layer adds a checksum that includes header of itself. This header is the main element in communication as it contains the source and destination addresses of communicating users. The IP layer also handles data packet transmission through the Internet. It is considered responsible for splitting up of large datagram packets into smaller ones so that it can be transmitted much more easily and efficiently and hence reassembling can be performed on a faster rate.
UDP is again a connectionless protocol. It is generally considered unreliable. It adds a checksum to the ip address for the information present in the datagram and its port numbers. Hence this provides a client/server architecture model.
TCP is a connection-oriented protocol which provides application logic. It also provides a type of virtual circuit by which two or more processes running can use to communicate with each other.
Internet addresses
To find the machine the Internet uses a particular address for different machines so that it can be use to know their location. Internet address is a 32 bit integer which provides the IP address of a system. It codes a network ID and address. The network ID are divided into different types of classes depending on the size of network address.
Fig 3 Total Address
A socket is a data structure that is used by the pc to handle and work out with network connections. Socket creation is done by the use of a call socket the call socket. It then return back an integer that relates to a file descriptor. In Windows, it can be handled using read and write operations. When two processes wishes to transmit a message or establishes a type of communication over a network they create a socket each.
5.1 Design Overview
This system is designed so that it is able to identify different classes and their relations with each other. They are examined to see how much collaboration they hold with each other. In context of object wise classification the classes are classified as:-
‘ Entity classes
‘ Interface classes
‘ Control associating classes
The Software Engineering tools that are found in the market do not provide any type of help in transition. The various CASE tools that are available can only lift the benefits of meta data modelling which can only be helpful once the class diagrams are completed.
This Multiple signature project works on a multiparty extension of the ElGamal type signature variant: GES. This scheme of multiple signature generation can use ElGamal type signature scheme for efficient functioning..
The reason for which GES algorithm is used is to reduce the computational cost for signature generation and verification.
In this Multiple signature scheme, all the properties of threshold multiple signature system are fulfilled and satisfied. This system is high in terms of efficiency and is less prone to various attacks.
5.2 Module description
In this section it is seen how to generate signatures for the various group members. The signatures are created with Participants generated private key. This is done and then members sends the messages and their signature to all other members. The message encryption with the secret for members is done with a publicly verified encryption scheme
This modules divided into 2 modules
‘ Signature Generation on individual basis
‘ Multiple Signature by group members for a particular group
5.2.1 Signature Verification
This is a verification module where a group member’s signature is verified against the already generated signatures. When all the signatures have been received, the public key set is used for authentication of the identity of the individual signer. If the result is negative then the transmission do not occurs as signature is not generated because of the false member’s presence. When that member is removed then the real and true member forms a set and performs individual signature generation. If there are less number of members present then the known number to the system, the result is that the system quits
The reciever can than use the public key that was sent with the message is computed and it is determined whether the messages has been sent by the claimed sender .So it’s like the sender is the private-key holder and is signing the message; then the recipient can use that sender’s public information to verify that the sender did *indeed* send (and sign) that message.
5.3 Cryptography
In this project encryption is mainly used for security purpose. Here we are message convert to unknown format. Then only intermediate person can’t understand the message. The messages that are to be transmitted are first encrypted using members private key and public key is appended with this message. After this process that data or message is transmitted over the network with the associated public key.
5.4 Decryption
It is the process of retrieving the original format from the encrypted message. After the Decryption we can read the message by using public key. This key is deliberately attached with the message that is encrypted. After decrypting this message can be read by users.
5.5 Message transmission
In this very module we transmit the message (encrypted) for two type of transmission
‘ Intragroup transmission
‘ Intergroup transmission
Then this encrypted message will be transmitted and decrypted by the receiver at the receiving end after signature verification.
. In most of these applications involved, users generally receive identical information from single or multiple senders.
The system’s message transmission is divided having two sub modules they are
‘ Unicasting
‘ Multicasting
‘ Unicasting module is used to transfer our message from one to only one recipient present in database.
‘ Multicasting module is used to transfer our message from one sender to many recipient present in database.
5.6 Data Flow Diagram
The DFD stands for Data Flow Diagram. It is a way to graphically represent the various inputs, the processing involved with the data and the related output to the different inputs.
Fig3 Generating keys using elgamal algorithm
Fig 4 Comparing private key with received key
Fig 5 Message encryption
Fig6 Message decryption
Fig 7 Unicasting
Fig 8 Multicasting
The aim of software testing is to find different errors present in software system application. Software Testing is the procedure of discovering every possible errors or malfunctions in a working software. It provides a way to check the different functions that various components are intended to perform, and whether the complete software is providing the desired results. There are numerous types of test available to test a software. Each test focuses on a specific testing requirement for the software that is being tested. But all these test has only one common function that is to find the errors in intended software functioning.
6.1.1 Unit test
Unit testing includes the design of different test cases that can validate whether the internal programming logic is functioning in a proper manner or not. It checks whether the program gives the desired output or not. All the decision branches or the program and internal data flow structure is subjected to validation. It is testing of segregated software components of the application software. It is always done before the integration of software.
Unit tests also ensure each components of the software performs its documented functions accurately when tested to various inputs.
6.1.2 Integration test
Integration tests are used to test integrated software to determine if they are running as one program with the desired results. Integration Testing is event driven and dedicated to the outcome on screens. Integration tests performs testing on integrated software after unit testing is performed successfully. Hence Integration testing is aimed at finding the problems that comes from the combination and integration of various software components.
6.1.3 Functional test
Functional Test is a systematic illustration in which various functions are checked according to their business and technical requirements of the software.
6.1.4 System Test
System testing checks whether the entire integrated software application meets the requirements. It tests different configurations according to known and predictable results. System testing is fully based on data and process flows, and mainly emphasizes on integration points of different components.
6.1.5 White Box Testing
White Box Test is a software testing procedure in the person who test’s the software hs the inner knowledge of the software’s working, it’s structure and its coded. The person who performs the testing should also know the purpose of the software for which it has been developed. It is designed to test various parts of software that cannot be accessed by black box tests.
6.1.6 Black Box Testing
Black Box Test involves test of software application in which the software testing person do not have any knowledge of the inner structure and working of various components os the software application. Black box tests must be written from a definitive and specific source document, such as specification and requirements document. It is a test in which the software that is being tested is being assumed as a black box hence a person cannot know its internal structure. The software is tested to various inputs and the outputs are noted without taking into account how the system is providing the desired functions.
Acceptance Testing
User Acceptance Testing is an important step in testing for any project and is basicaaly dependent on participation by the end user. It fully takes into account that the software that is being tested meets the all the functional requirements that is been listed in the specification sheet. This checks whether the users is satisfied with the software working or not.
Test Results: All the test that were listed above were performed with utmost success. No defects were confronted.
Member login page. This page contains member’s login and new members signup fields where new users can sign up in particular groups of the systems.
Text message sender’s page where a sender can create a message and send it to another person in that group.
Group view of various users present in a particular group. This group view shows who all group members are present in a particular group.
Message send to a user in group 1 by amod. The message is successfully delivered to amod2
Encrypted message send over the network. These messages are encrypted using members private keys and then transmitted over the network
Decrypted message received by the receiver with secret key. This message is decrypted using their public keys and hence they are able to read that encrypted messages
New user sign up page where the users enter their information and chooses the group whose membership he or she wants and sends the information to the group controller for acceptance.
New users send its registration request to group controller to sign up with this proposed system
Group controller accepts new user’s request. When group administrator accepts the new member it data is simultaneously added in its requested database group table and a particular private key is generated.
The main goal/objective of this project is to accomplish and develop a secure multiple signature scheme for effective and secure group communication. To complete this project ElGamal algorithm which is an asymmetric key encryption algorithm for generation of public and private keys for various group members was used so that they can encrypt their messages using their private key and other user can decrypt that same messages using their own public key. This algorithm is based on Diffie-Hellman protocol for key exchange. Data Encryption Standard (DES) algorithm is a symmetric key algorithm which was included to encrypt the electronic messages. This algorithm is highly useful and beneficial in cryptographic systems.
The proposed and developed Multi signature scheme was tested and is satisfied all of the specified security requirements. It accomplishes the stronger security requirement property in group communication over the network. The Multi signature scheme hence is fully secure, even if the threshold cryptographic system has been broken apart, i.e., the group or individual secret set by the group members are known to the adversary and as a result he can access the secret over the network.
The efficiency testing has showed that this Multi signature scheme is far better than the various existing scheme and hence is optimal both threshold signature verification and individual signature.
Inclusion and use of DKRU protocol makes the fully distributed Multiple signature scheme more secure and relaible. It also allows for quick group membership for different users, and also gives the group members the capacity of variation in the security by distributing the existing access protocol to a new protocol. Hence the algorithm is considered ideal in this case.

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