Functional Signatures and Pseudorandom Functions
Author(s)Boyle, Elette; Goldwasser, Shafi; Ivan, Ioana Elisabeta
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We introduce two new cryptographic primitives: functional digital signatures and functional pseudorandom functions. In a functional signature scheme, in addition to a master signing key that can be used to sign any message, there are signing keys for a function f, which allow one to sign any message in the range of f. As a special case, this implies the ability to generate keys for predicates P, which allow one to sign any message m for which P(m) = 1. We show applications of functional signatures to constructing succinct non-interactive arguments and delegation schemes. We give several general constructions for this primitive based on different computational hardness assumptions, and describe the trade-offs between them in terms of the assumptions they require and the size of the signatures. In a functional pseudorandom function, in addition to a master secret key that can be used to evaluate the pseudorandom function F on any point in the domain, there are additional secret keys for a function f, which allow one to evaluate F on any y for which there exists an x such that f(x) = y. As a special case, this implies pseudorandom functions with selective access, where one can delegate the ability to evaluate the pseudorandom function on inputs y for which a predicate P(y) = 1 holds. We define and provide a sample construction of a functional pseudorandom function family for prefix-fixing functions. This construction yields, in particular, punctured pseudorandom functions, which have proven an invaluable tool in recent advances in obfuscation (Sahai and Waters ePrint 2013).
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Public-Key Cryptography – PKC 2014
Springer-Verlag Berlin Heidelberg
Boyle, Elette, Shafi Goldwasser, and Ioana Ivan. “Functional Signatures and Pseudorandom Functions.” in Public-Key Cryptography – PKC 2014, edited by Hugo Krawczyk. Springer: Berlin, 2014. (Lecture Notes in Computer Science; volume 8383) (2014): 501–519.
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