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Fast batch verification for modular exponentiation and digital signatures
, 1998
"... Abstract Many tasks in cryptography (e.g., digital signature verification) call for verification of a basicoperation like modular exponentiation in some group: given ( g, x, y) check that gx = y. Thisis typically done by recomputing gx and checking we get y. We would like to do it differently,and f ..."
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Cited by 129 (2 self)
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Abstract Many tasks in cryptography (e.g., digital signature verification) call for verification of a basicoperation like modular exponentiation in some group: given ( g, x, y) check that gx = y. Thisis typically done by recomputing gx and checking we get y. We would like to do it differently,and faster. The approach we use is batching. Focusing first on the basic modular exponentiation operation, we provide some probabilistic batch verifiers, or tests, that verify a sequence of modular exponentiations significantly faster than the naive recomputation method. This yields speedupsfor several verification tasks that involve modular exponentiations.
The complexity of decision versus search
 SIAM Journal on Computing
, 1994
"... A basic question about NP is whether or not search reduces in polynomial time to decision. We indicate that the answer is negative: under a complexity assumption (that deterministic and nondeterministic doubleexponential time are unequal) we construct a language in NP for which search does not red ..."
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Cited by 32 (1 self)
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A basic question about NP is whether or not search reduces in polynomial time to decision. We indicate that the answer is negative: under a complexity assumption (that deterministic and nondeterministic doubleexponential time are unequal) we construct a language in NP for which search does not reduce to decision. These ideas extend in a natural way to interactive proofs and program checking. Under similar assumptions we present languages in NP for which it is harder to prove membership interactively than it is to decide this membership, and languages in NP which are not checkable. Keywords: NPcompleteness, selfreducibility, interactive proofs, program checking, sparse sets,
SelfTesting/Correcting Protocols
"... ) Matthew Franklin ? Juan A. Garay ?? Moti Yung ? ? ? Abstract. In this paper we suggest the notion of selftesting/correcting protocols. The work initiates the merge of distributed computing and the area of "program checking" introduced by Blum, and specifically employs extended notions f ..."
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Cited by 1 (0 self)
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) Matthew Franklin ? Juan A. Garay ?? Moti Yung ? ? ? Abstract. In this paper we suggest the notion of selftesting/correcting protocols. The work initiates the merge of distributed computing and the area of "program checking" introduced by Blum, and specifically employs extended notions from the work of Blum, Luby and Rubinfeld. In this setting, given a protocol P (a collection of programs on a network of n processors) which allegedly implements a distributed function f , a selftester for f is a (simpler) protocol which makes calls to P to estimate the probability that P when executed in a given environment is faulty (i.e., P and f differ in some of the outputs). A selfcorrecting protocol is another protocol which allows for the computation of f correctly on every input (with high probability) as long as P in the same type of environment is not too faulty. We first consider selftesting/correcting under a basic form of environmental malfunction, that of crash fai...