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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 140 (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 33 (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,
M.: SelfTesting/Correcting Protocols
 7th International IS&N Conference on Intelligence in Services and Networks (ISNâ€™00). SpringerVerlag LNCS 1693
, 1999
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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 basic operation like modular exponentiation in some group: given (g; x; y) check that gx = y. This is typically done by recomputing gx and checking we get y. We would like to do it differently, and ..."
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Abstract Many tasks in cryptography (e.g., digital signature verification) call for verification of a basic operation like modular exponentiation in some group: given (g; x; y) check that gx = y. This is 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 speedups for several verification tasks that involve modular exponentiations. Focusing specifically on digital signatures, we then suggest a weaker notion of (batch) verification which we call &quot;screening. &quot; It seems useful for many usages of signatures, and has the advantage that it can be done very fast; in particular, we show how to screen a sequence of RSA signatures at the cost of one RSA verification plus hashing.