eVerification2 TSI-020100-2011-39 is a research project leaded by Scytl Secure Electronic Voting S.A., with the collaboration of CRISES research group from Universitat Rovira i Virgili, and supported by the Spanish Ministry of Industry, Commerce and Tourism (through the development program AVANZA I+D).
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You can find more information about the eVerification2 project in http://crises-deim.urv.cat/everification2
#TTP SmartCard-Based ElGamal Cryptosystem Using Threshold Scheme for Electronic Elections
As a result of this research project, CRISES group has studied the feasibility of developing ElGamal cryptosystem and Shamir’s secret sharing scheme into JavaCards, whose API gives no support for it.
In particular, the contributions of our work have been the design and development of the following building blocks for JavaCards: (i) ElGamal cryptosystem to generate the ElGamal key pair, (ii) Shamir’s secret sharing scheme to divide the private key in a set of shares, (iii) secure communication channels for the distribution of the shares, and (iv) a decryption function without reconstructing the private key. This solution can be useful for a typical e-voting system, specifically in the voting scheme presented by Cramer et al. [1].
You can find more information about these contributions and how they were designed and implemented in the conference paper.pdf presented in Foundations & Practice of Security 2011 called: TTP SmartCard-Based ElGamal Cryptosystem Using Threshold Scheme for Electronic Elections [2]. In the extendedpaper.pdf, you can find a description of an execution example.
##Software
This library implements the protocol described in the paper mentioned above and it is prepared to easily execute a configurable example with a maximum number of shares (n=5) and a threshold from 2 to the maximum of shares (n). To execute the following functions implemented in the library:
- Generate a set of shares from a SmartCard(SC) according to user configuration (number of shares, threshold and key size).
- Distribute the generated shares, public key, and other public parameters from that SC to the rest of SCs.
- Verify the received share from each SC.
- Encrypt a value using the public ElGamal parameters.
- Partial decrypt from each SC.
- Homomorphic Recount (in a voting context) through the aggregation of the set of partial decryptions.
The code is divided into two different parts: thresholdClient and thresholdLib code. The former part includes the GUI and the code related to manage of the protocol execution as a client. This part has been developed in Java programming language. The last part is the applet code placed/installed into each SC, which is written in JavaCard.
Once the applet has been installed in each SC, our application, following the protocol described in the paper, initiates the APDU communication, as detailed below:
1. The Applet has been selected and initialized. In this case, the applet identifier is 3132333433123450. The
key size of ElGamal cryptosystem is fixed here. The sent APDUs are as follows:
- Applet selection: CLA=00, INS=a4, P1=04, P2=00, Lc=08, DATA=aID=3132333433123450, Le=00.
- Applet initialization: CLA=80, INS=00, P1=0x, P2=00 (where x is the key size, it can be 2=512, 3=768,
4=1024, 5=1280, 6=1536, 7=1984 and 8=2048 bits).
2. In order to generate the following values, which are requiered by ElGamal cryptosystem initialization, into
the SC, the following APDUs are sent:
- p: CLA=90, INS=01, P1-P2=00, Lc=20 and data=p.
- q: CLA=90, INS=11, P1-P2=00, Lc=20 and data=q.
- g: CLA=90, INS=02, P1-P2=00, Lc=20 and data=g.
3. In order to securely build the private and public key, which are requiered by ElGamal cryptosystem, into the
SC, the APDUs are as follows:
- Pk: CLA=80, INS=03, P1-P2=00.
- Sk: CLA=80, INS=04, P1-P2=00.
- The SC generator takes the id=0, this is stored by APDU: CLA=80, INS=12, P1-P2=00, Lc=1, DATA=id, Le=00.
4. Once the private key is generated, it must be split in some shares. The following APDUs fix the shares and
threshold number, and their generation:
- Threshold and shares number storing: CLA=80, INS=1e, P1=2-5,P2=3-5 (where P1 and P2 are the threshold
and the shares number respectively).
- (t-1) coefficients generation: CLA=80, INS=05, P1-P2=00.
- (t-1) coefficient commitments generation: CLA=80, INS=06, P1-P2=00.
- Evaluation values generation: CLA=80, INS=07, P1-P2=00.
- (N) shares generation: CLA=80, INS=08, P1-P2=00.
- (N) shares commitments generation: CLA=80, INS=09, P1-P2=00.
5. The client gets, from the SC, the public parameters generated by threshold scheme, coefficient commitment and
Pk:
- Coefficient commitment getting: CLA=80, INS=1B, P1-P2=00.
- Pk getting: CLA=80, INS=1A, P1-P2=00.
6. Finally, the SC must verify the correctness generation of his own share and share commitment (remember that
generator SC may also participate in the secret reconstruction step):
- Share verification: CLA=80, INS=A0, P1-P2=00.
- Share commitment verification: CLA=80, INS=B0, P1-P2=00.
Share Distribution between generator SC and receiver SC (this step must be repeated in each receiver SC).
Steps 1 and 2 from shares generation process are repeated here.
3. The public parameters of threshold scheme, generated by generator SC for each different receiver SC, are
recovered by sending the following APDUs to generator SC:
- Share getting: CLA=80, INS=19, P1= smart card identifier,P2=00.
- Share commitment getting: CLA=80, INS=1C, P1= smart card identifier, P2=00.
Note that SC identifier must be different in each receiver SC since there is no equal share.
4. The threshold parameters generated in the generation step, including the corresponding share and share
commitment, are stored in the receiver SC:
- Threshold and shares number storing: the APDU is: CLA=80, INS=1e, P1=2-5,P2=3-5
- Coefficient commitment storig: CLA=90, INS=16, P1-P2=00.
- Card identifier storing: CLA=80, INS=12, P1-P2=00, Lc=01 and data=id_card.
- (own)Share storing: CLA=90, INS=14, P1-P2=00, Lc=20 and data=share.
- (own)Share commitment storing: CLA=90, INS=17, P1-P2=00, Lc=20 and data=share commitment.
- Public key storing: CLA=90, INS=15, P1-P2=00, Lc=20 and data=public key.
- Evaluation values generation: CLA=80, INS=07, P1-P2=00.
5. Once the receiver SC has stored its own share and share commitment, it must verify the correctness generation
made by generator SC.
- Share verification: CLA=80, INS=A0, P1-P2=00.
- Share commitment verification: CLA=80, INS=B0, P1-P2=00.
Step 1 from shares generation process is repeated here.
2. Once the receiver SC has stored its own share and share commitment, it must verify the correctness generation
made by generator SC.
- Share verification: CLA=80, INS=A0, P1-P2=00.
- Share commitment verification: CLA=80, INS=B0, P1-P2=00.
Steps 1 and 2 (if they are not performed before) from shares generation process are repeated here.
3. The data to encrypt are sent to SC and they are encrypted with APDU: CLA=90, INS=0C, P1-P2=00, Lc=20,
Data=message to encrypt.
4. ElGamal encryption result is recovered by sending the APDU: CLA=90, INS=0D, P1-P2=00.
Once elections have been concluded, a set of at least t-members of the electoral board is necessary to decrypt
votes successfully.
At this point, votes have been aggregated thanks to the use of a homomorphic properties of ElGamal.
- By using the lagrange coefficients, the evaluations values and the aggregated votes computed before in the
client side, each of t-SCs compute securely and internally its partials Y1:
Step 1 from shares generation process is repeated here.
2. Lagrange coefficient sending: CLA=90, INS=13, P1= card identifier, P2=00, Lc=20 and data=Lagrange
coefficient.
3. Data to decrypt sending: CLA=90, INS=1D, P1-P2=00, Lc=20 and data=Y2+Y1.
4. Partial decryption: CLA=80, INS=0F , P1-P2=00.
Once all partial decryptions have been recovered, the final decryption is computed in the client side by
following the steps described in the paper.
You can find more information about the implementation in the Development Details section of the extendedpaper.pdf
##License
This software is released under BSD 3-clause license, which is contained in the file LICENSE.
##Future Work
As future work concerns, we are working on a non-trusted third party (Non-TTP) solution with a distributed generation of the shares. In addition, we would like to improve the efficiency, time and storage of the protocol in smartcards (i.e., using ElGamal on elliptic curves).
#Bibliography
[1] Cramer, R., Gennaro, R., Schoenmakers, B.: A secure and optimally e�cient multi-authority election scheme. In: Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques. pp. 103{118. EUROCRYPT'97, Springer-Verlag, Berlin, Heidelberg (1997), http://portal.acm.org/citation.cfm?id=1754542.1754554
[2] J. Pujol-Ahullo, R. Jardi-Cedo, J. Castella-Roca, O. Farràs , "TTP SmartCard - based ElGamal Cryptosystem using Threshold Scheme for Electronic Elections ", Foundations & Practice of Security 2011 - FPS 2011, Paris, France, May 2011. http://crises2-deim.urv.cat/docs/publications/conferences/656.pdf