A Secure and Optimally Efficient Multi-Authority Election Scheme

Abstract

Abstract. In this paper we present a new multi-authority secret-ballot election scheme that guarantees privacy, universal verifiability, and robustness. It is the first scheme for which the performance is optimal in the sense that time and communication complexity is minimal both for the individual voters and the authorities. An interesting property of the scheme is that the time and communication complexity for the voter is independent of the number of authorities. A voter simply posts a single encrypted message accompanied by a compact proof that it contains a valid vote. Our result is complementary to the result by Cramer, Franklin, Schoenmakers, and Yung in the sense that in their scheme the work for voters is linear in the number of authorities but can be instantiated to yield information-theoretic privacy, while in our scheme the voter's effort is independent of the number of authorities but always provides computational privacy-protection. We will also point out that the majority of proposed voting schemes provide computational privacy only (often without even considering the lack of information-theoretic privacy), and that our new scheme is by far superior to those schemes.

Quantum protocols for anonymous voting and surveying

“…These [6,10,11,12,13,14] involve the use of a homomorphic, probabilistic encryption scheme consisting of a plaintext space V, a ciphertext space C (each of which form group structures (V, •) and (C, • ′ ) under appropriate binary operations • and • ′ ) together with a family of homomorphic encryption schemes…”

“…Homomorphic election schemes are important since they allow one to derive tallies without the need to decrypt individual votes. Such schemes lead to resilient election schemes [6,13].…”

Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems

“…By virtue of the Pohlig-Hellman algorithm [17], the DDH problem in C a,p 2 can be reduced to the DDH problem in the subgroups of order t and v. As one can easily solve the discrete logarithm related to the first subgroup, one can efficiently the Decision Diffie-Hellman problem for this subgroup too. Now, let P be a generator of the subgroup C a,p 2 [v] and suppose that points X = x * P, Y = y * P, Z = z * P in C a,p 2 [v] are given. To solve the Decision DiffieHellman problem in C a,p 2 [v], we need to determine whether z = x * y mod v. By the Identity property of the Weil pairing, its bilinearity and Corollary 5, the Weil pairing e v (P, D(P )) is a v-th root of unity of GF(p 6 ).…”

“…Now, let P be a generator of the subgroup C a,p 2 [v] and suppose that points X = x * P, Y = y * P, Z = z * P in C a,p 2 [v] are given. To solve the Decision DiffieHellman problem in C a,p 2 [v], we need to determine whether z = x * y mod v. By the Identity property of the Weil pairing, its bilinearity and Corollary 5, the Weil pairing e v (P, D(P )) is a v-th root of unity of GF(p 6 ). So on the one hand, e v (X, D(Y )) = e v (P, D(P )) xy and on the other hand e v (P,…”

Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems

“…There are several cryptographic protocols whose security depends on the difficulty of the Decision Diffie-Hellman problem, like the publicly verifiable voting system in [2] and the Cramer-Shoup [3] public key cryptosystem that is provable secure against adaptive chosen ciphertext attacks. Theorem 6 shows that these protocols should not be based on (CTP) supersingular elliptic curves, even with the "appropriate" key sizes.…”