Geometric realization of electronic elections based on threshold secret sharing

Abstract

Introduction. One of the tasks arising in cryptography is to ensure a safe and fair conduct of e-voting. This paper details the algorithm of electronic elections particularly that part which deals with the cryptographic security. Materials and Methods. The results are obtained on the basis of the following methodology: finite field theory, projective geometry, and linear algebra. The developed cryptosystem is based on the application of geometric objects from projective geometry over finite fields. Research Results. The invented algorithm relies on the ElGamal encryption and a new geometric way of secret sharing among election committees. The proposed method uses some features of affine spaces over finite fields to generate special geometric constructions and secret, search of which is a complex algorithmic task for an illegal intruder. The threshold secret sharing is used to prevent voter fraud on the part of the members of election committees. The probability to generate the right share of secret by an illegal intruder in case when he/she knows only a part of secret shares is determined. Discussion and Conclusions. The described scheme is useful for electronic voting and in other spheres where methods of threshold cryptography are applied.

Keywords

• cryptography
• public-key cryptosystem
• elgamal encryption system
• finite fields
• threshold cryptography
• secret sharing
• affine geometry
• projective spaces
• electronic voting
• diffie-hellman problem