Package paillierp

Provides the structures and methods to encrypt data with the Paillier encryption scheme with thresholding.

See:
Description

Class Summary

AbstractPaillier	An abstract class of the simple Paillier cryptosystem.
ByteUtils	A set of static utilities for manipulating Bytes.
Paillier	A simple implementation of the generalized Paillier encryption scheme CS1.
PaillierThreshold	A simple implementation of the threshold Paillier encryption scheme CS1.
PartialDecryption	A partial decryption in the Threshold Paillier encryption scheme with necessary data to proceed with the full decryption.

Package paillierp Description

Provides the structures and methods to encrypt data with the Paillier encryption scheme with thresholding. This package a simplified implementation of what is specified in the paper A Generalization of Paillier's Public-Key System with Applications to Electronic Voting by Damgård et al. Within this paper, the authors generalize the Paillier encryption scheme to permit computations modulo n^s+1, allowing block length for encryption to be chosen freely. In addition to this undertaking, Damgård et al. also constructed a threshold variant of the scheme.

This package provides the following features of the paper

• The degree of n is fixed to 1.
• A fully functional simple Paillier encryption scheme with separate key classes for easy keysharing.
• Proper Thresholding for an arbitrary number of decryption servers and threshold needed to decrypt.
• Non-interactive zero knowledge proofs to ensure proper encryption and decryption.

Of particular note, this implementation is simple as s is fixed to be 1. This allows for simplicity at this stage of the design. Further, we hope to have added methods which would make the actual use of this package to be easy and flexible.

Future features would include support for encrypting arbitrary length strings/byte arrays to avoid padding issues.

Primary Papers

• A Generalization of Paillier's Public-Key System with Applications to Electronic Voting by Damgård, Jurik, and Nielsen, 2000. This is the primary implementation design for this package.

  Notice of typo: There is a typo in the calculation of λ_0,i on both pages 17 and 19. The correct calculation of the Lagrange coefficient for interpolating the value of a polynomial is
  &lambda^S_j,i=Δ Π_i'∈S\i (j-i')/(i-i').
  The error is that the numerator of the fraction is j-i' not j-i. The corresponding calculation of λ^S_0,i must be corrected accordingly.

• Multiparty Computation from Threshold Homomorphic Encryption by Cramer, Damgård, and Nielsen, 2000. This is a secondary source for understanding threshold encryption and its requirements.

Related Papers

• Efficient Protocols based on Probabilistic Encryption using Composite Degree Residue Classes by Damgård and Jurik, 2000. This is an earlier version of A Generalization of Paillier...
• Sharing Decryption in the Context of Voting or Lotteries by Fouque, Poupard, and Stern, 2000.
• Practical threshold signatures by Shoup, 2000. The original threshold protocol, but applied to RSA. This has the best mathematical explanation of how it works.