How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Simultaneous security of bits in the discrete log
Proc. of a workshop on the theory and application of cryptographic techniques on Advances in cryptology---EUROCRYPT '85
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
The discrete logarithm hides O(log n) bits
SIAM Journal on Computing - Special issue on cryptography
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Finite fields
Rounding in lattices and its cryptographic applications
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Sparse polynomial approximation in finite fields
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Lattice Attacks on Digital Signature Schemes
Designs, Codes and Cryptography
On The Correlation Of Binary M-sequences
Designs, Codes and Cryptography
On the Generalised Hidden Number Problem and Bit Security of XTR
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Adi Shamir: On the Universality of the Next Bit Test
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Some Remarks on Lucas-Based Cryptosystems
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Hardness of Computing the Most Significant Bits of Secret Keys in Diffie-Hellman and Related Schemes
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Unbelievable Security. Matching AES Security Using Public Key Systems
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Certificates of Recoverability with Scale Recovery Agent Security
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Lattice Reduction in Cryptology: An Update
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
The Two Faces of Lattices in Cryptology
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
The Insecurity of Nyberg-Rueppel and Other DSA-Like Signature Schemes with Partially Known Nonces
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Security of the most significant bits of the Shamir message passing scheme
Mathematics of Computation
On the hardness of the shortest vector problem
On the hardness of the shortest vector problem
The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces
Designs, Codes and Cryptography
The security of all RSA and discrete log bits
Journal of the ACM (JACM)
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
The security of all RSA and discrete log bits
Journal of the ACM (JACM)
On the hardness of approximating the permanent of structured matrices
Computational Complexity
Fast irreducibility testing for XTR using a gaussian normal basis of low complexity
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Security of polynomial transformations of the Diffie-Hellman key
Finite Fields and Their Applications
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We consider a certain generalization of the hidden number problem introduced by Boneh and Venkatesan in 1996. Considering the XTR variation of Diffie-Hellman, we apply our results to show security of the log1/2p most significant bits of the secret, in analogy to the results known for the classical Diffie-Hellman scheme. Our method is based on bounds of exponential sums which were introduced by Deligne in 1977. We proceed to show that the results are also applicable to the LUC scheme. Here, assuming the LUC function is one-way, we can in addition show that each single bit of the argument is a hard-core bit.