TY - GEN
T1 - Function secret sharing
AU - Boyle, Elette
AU - Gilboa, Niv
AU - Ishai, Yuval
N1 - Funding Information:
Research supported by the European Union’s Tenth Framework Programme (FP10/2010-2016) under grant agreement no. 259426 ERC-CaC. The first and third authors were additionally supported by ISF grants 1361/10 and 1709/14 and BSF grant 2012378.
Publisher Copyright:
© International Association for Cryptologic Research 2015.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - Motivated by the goal of securely searching and updating distributed data, we introduce and study the notion of function secret sharing (FSS). This new notion is a natural generalization of distributed point functions (DPF), a primitive that was recently introduced by Gilboa and Ishai (Eurocrypt 2014). Given a positive integer p ≥ 2 and a class F of functions f: {0, 1}n → (image found), where (image found) is an Abelian group, a p-party FSS scheme for F allows one to split each f ∈ F into p succinctly described functions fi: {0, 1}n →(image found), 1 ≤ i ≤ p, such that: (1) ∑p i=1 fi = f, and (2) any strict subset of the fi hides f. Thus, an FSS for F can be thought of as method for succinctly performing an “additive secret sharing” of functions from F. The original definition of DPF coincides with a twoparty FSS for the class of point functions, namely the class of functions that have a nonzero output on at most one input. We present two types of results. First, we obtain efficiency improvements and extensions of the original DPF construction. Then, we initiate a systematic study of general FSS, providing some constructions and establishing relations with other cryptographic primitives. More concretely, we obtain the following main results: – Improved DPF. We present an improved (two-party) DPF construction from a pseudorandom generator (PRG), reducing the length of the key describing each fi from O(λ ・ nlog2 3) to O(λn), where λ is the PRG seed length. – Multi-party DPF. We present the first nontrivial construction of a p-party DPF for p ≥ 3, obtaining a near-quadratic improvement over a naive construction that additively shares the truth-table of f. This constrcution too can be based on any PRG. – FSS for simple functions. We present efficient PRG-based FSS constructions for natural function classes that extend point functions, including interval functions and partial matching functions. – A study of general FSS. We show several relations between general FSS and other cryptographic primitives. These include a construction of general FSS via obfuscation, an indication for the implausibility of constructing general FSS from weak cryptographic assumptions such as the existence of one-way functions, a completeness result, and a relation with pseudorandom functions.
AB - Motivated by the goal of securely searching and updating distributed data, we introduce and study the notion of function secret sharing (FSS). This new notion is a natural generalization of distributed point functions (DPF), a primitive that was recently introduced by Gilboa and Ishai (Eurocrypt 2014). Given a positive integer p ≥ 2 and a class F of functions f: {0, 1}n → (image found), where (image found) is an Abelian group, a p-party FSS scheme for F allows one to split each f ∈ F into p succinctly described functions fi: {0, 1}n →(image found), 1 ≤ i ≤ p, such that: (1) ∑p i=1 fi = f, and (2) any strict subset of the fi hides f. Thus, an FSS for F can be thought of as method for succinctly performing an “additive secret sharing” of functions from F. The original definition of DPF coincides with a twoparty FSS for the class of point functions, namely the class of functions that have a nonzero output on at most one input. We present two types of results. First, we obtain efficiency improvements and extensions of the original DPF construction. Then, we initiate a systematic study of general FSS, providing some constructions and establishing relations with other cryptographic primitives. More concretely, we obtain the following main results: – Improved DPF. We present an improved (two-party) DPF construction from a pseudorandom generator (PRG), reducing the length of the key describing each fi from O(λ ・ nlog2 3) to O(λn), where λ is the PRG seed length. – Multi-party DPF. We present the first nontrivial construction of a p-party DPF for p ≥ 3, obtaining a near-quadratic improvement over a naive construction that additively shares the truth-table of f. This constrcution too can be based on any PRG. – FSS for simple functions. We present efficient PRG-based FSS constructions for natural function classes that extend point functions, including interval functions and partial matching functions. – A study of general FSS. We show several relations between general FSS and other cryptographic primitives. These include a construction of general FSS via obfuscation, an indication for the implausibility of constructing general FSS from weak cryptographic assumptions such as the existence of one-way functions, a completeness result, and a relation with pseudorandom functions.
UR - http://www.scopus.com/inward/record.url?scp=84942617355&partnerID=8YFLogxK
U2 - 10.1007/978-3-662-46803-6_12
DO - 10.1007/978-3-662-46803-6_12
M3 - Conference contribution
AN - SCOPUS:84942617355
SN - 9783662468029
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 337
EP - 367
BT - Advances in Cryptology - 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2015, Proceedings
A2 - Fischlin, Marc
A2 - Oswald, Elisabeth
PB - Springer Verlag
T2 - 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2015
Y2 - 26 April 2015 through 30 April 2015
ER -