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The modular inversion hidden number problem
 In ASIACRYPT 2001, volume 2248 of LNCS
, 2001
"... Abstract. We study a class of problems called Modular Inverse Hidden Number Problems (MIHNPs). The basic problem in this class is the following: Given many pairs � � � � −1 xi, msbk (α + xi) mod p for random xi ∈ Zp the problem is to find α ∈ Zp (here msbk(x) refers to the k most significant bits o ..."
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Cited by 16 (1 self)
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Abstract. We study a class of problems called Modular Inverse Hidden Number Problems (MIHNPs). The basic problem in this class is the following: Given many pairs � � � � −1 xi, msbk (α + xi) mod p for random xi ∈ Zp the problem is to find α ∈ Zp (here msbk(x) refers to the k most significant bits of x). We describe an algorithm for this problem when k> (log 2 p)/3 and conjecture that the problem is hard whenever k < (log 2 p)/3. We show that assuming hardness of some variants of this MIHNP problem leads to very efficient algebraic PRNGs and MACs.
Twin Signatures: An Alternative to the HashandSign Paradigm
, 2001
"... This paper introduces a simple alternative to the hashandsign paradigm called twinning. A twin signature is obtained by signing twice the same short message by a probabilistic signature scheme. Analysis of the concept in di#erent settings yields the following results:  We prove that no generi ..."
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Cited by 13 (2 self)
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This paper introduces a simple alternative to the hashandsign paradigm called twinning. A twin signature is obtained by signing twice the same short message by a probabilistic signature scheme. Analysis of the concept in di#erent settings yields the following results:  We prove that no generic algorithm can e#ciently forge a twin DSA signature. Although generic algorithms o#er a less stringent form of security than computational reductions in the standard model, such successful proofs still produce positive evidence in favor of the correctness of the new paradigm.
Use of Sparse and/or Complex Exponents in Batch Verification of Exponentiations
, 2005
"... Modular exponentiation in an abelian group is one of the most frequently used mathematical primitives in modern cryptography. ..."
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Modular exponentiation in an abelian group is one of the most frequently used mathematical primitives in modern cryptography.