TY - GEN
T1 - Efficient multiparty protocols via log-depth threshold formulae (Extended abstract)
AU - Cohen, Gil
AU - Damgård, Ivan Bjerre
AU - Ishai, Yuval
AU - Kölker, Jonas
AU - Miltersen, Peter Bro
AU - Raz, Ran
AU - Rothblum, Ron D.
PY - 2013
Y1 - 2013
N2 - We put forward a new approach for the design of efficient multiparty protocols: 1. Design a protocol π for a small number of parties (say, 3 or 4) which achieves security against a single corrupted party. Such protocols are typically easy to construct, as they may employ techniques that do not scale well with the number of corrupted parties. 2. Recursively compose π with itself to obtain an efficient n-party protocol which achieves security against a constant fraction of corrupted parties. The second step of our approach combines the "player emulation" technique of Hirt and Maurer (J. Cryptology, 2000) with constructions of logarithmic-depth formulae which compute threshold functions using only constant fan-in threshold gates. Using this approach, we simplify and improve on previous results in cryptography and distributed computing. In particular: - We provide conceptually simple constructions of efficient protocols for Secure Multiparty Computation (MPC) in the presence of an honest majority, as well as broadcast protocols from point-to-point channels and a 2-cast primitive. - We obtain new results on MPC over blackbox groups and other algebraic structures. The above results rely on the following complexity-theoretic contributions, which may be of independent interest: - We show that for every j,k ∈ ℕ such that m Delta equal to k-1/j-1 is an integer, there is an explicit (poly(n)-time) construction of a logarithmic-depth formula which computes a good approximation of an (n/m)-out-of-n threshold function using only j-out-of-k threshold gates and no constants. For the special case of n-bit majority from 3-bit majority gates, a non-explicit construction follows from the work of Valiant (J. Algorithms, 1984). - For this special case, we provide an explicit construction with a better approximation than for the general threshold case, and also an exact explicit construction based on standard complexity-theoretic or cryptographic assumptions.
AB - We put forward a new approach for the design of efficient multiparty protocols: 1. Design a protocol π for a small number of parties (say, 3 or 4) which achieves security against a single corrupted party. Such protocols are typically easy to construct, as they may employ techniques that do not scale well with the number of corrupted parties. 2. Recursively compose π with itself to obtain an efficient n-party protocol which achieves security against a constant fraction of corrupted parties. The second step of our approach combines the "player emulation" technique of Hirt and Maurer (J. Cryptology, 2000) with constructions of logarithmic-depth formulae which compute threshold functions using only constant fan-in threshold gates. Using this approach, we simplify and improve on previous results in cryptography and distributed computing. In particular: - We provide conceptually simple constructions of efficient protocols for Secure Multiparty Computation (MPC) in the presence of an honest majority, as well as broadcast protocols from point-to-point channels and a 2-cast primitive. - We obtain new results on MPC over blackbox groups and other algebraic structures. The above results rely on the following complexity-theoretic contributions, which may be of independent interest: - We show that for every j,k ∈ ℕ such that m Delta equal to k-1/j-1 is an integer, there is an explicit (poly(n)-time) construction of a logarithmic-depth formula which computes a good approximation of an (n/m)-out-of-n threshold function using only j-out-of-k threshold gates and no constants. For the special case of n-bit majority from 3-bit majority gates, a non-explicit construction follows from the work of Valiant (J. Algorithms, 1984). - For this special case, we provide an explicit construction with a better approximation than for the general threshold case, and also an exact explicit construction based on standard complexity-theoretic or cryptographic assumptions.
UR - http://www.scopus.com/inward/record.url?scp=84884479881&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-40084-1_11
DO - 10.1007/978-3-642-40084-1_11
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AN - SCOPUS:84884479881
SN - 9783642400834
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 185
EP - 202
BT - Advances in Cryptology, CRYPTO 2013 - 33rd Annual Cryptology Conference, Proceedings
T2 - 33rd Annual International Cryptology Conference, CRYPTO 2013
Y2 - 18 August 2013 through 22 August 2013
ER -