A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
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Information Processing Letters
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Security of the most significant bits of the Shamir message passing scheme
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Time-lock Puzzles and Timed-release Crypto
Time-lock Puzzles and Timed-release Crypto
On the hardness of the shortest vector problem
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The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces
Designs, Codes and Cryptography
On the Bit Security of NTRUEncrypt
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Quantum period reconstruction of approximate sequences
Information Processing Letters
Bits Security of the Elliptic Curve Diffie---Hellman Secret Keys
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
On the bits of elliptic curve Diffie-Hellman Keys
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
Security of polynomial transformations of the Diffie-Hellman key
Finite Fields and Their Applications
Limits of a conjecture on a leakage-resilient cryptosystem
Information Processing Letters
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We consider a generalisation of the hidden number problem recently introduced by Boneh and Venkatesan. The initial problem can be stated as follows: recover a number a ∈ Fp such that for many known random t ∈ Fp approximations to the values of ⌊at⌋p are known. Here we study a version of the problem where the "multipliers" t are not known but rather certain approximations to them are given. We present a probabilistic polynomial time solution when the error is small enough, and we show that the problem cannot be solved if the error is sufficiently large. We apply the result to the bit security of "timed-release crypto" introduced by Rivest, Shamir and Wagner, to noisy exponentiation black-boxes and to the bit security of the "inverse" exponentiation. We also show that it implies a certain bit security result for Weil pairing on elliptic curves.