A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Lattice Reduction in Cryptology: An Update
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
On the hardness of the shortest vector problem
On the hardness of the shortest vector problem
Sparse polynomial approximation in finite fields
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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
The Hidden Number Problem in Extension Fields and Its Applications
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
On the Unpredictability of Bits of the Elliptic Curve Diffie--Hellman Scheme
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Hidden Number Problem with the Trace and Bit Security of XTR and LUC
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
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
Hidden number problem with hidden multipliers, timed-release crypto, and noisy exponentiation
Mathematics of Computation
The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces
Designs, Codes and Cryptography
On the hardness of approximating the permanent of structured matrices
Computational Complexity
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
On the bit security of the weak Diffie-Hellman problem
Information Processing Letters
Security of polynomial transformations of the Diffie-Hellman key
Finite Fields and Their Applications
| Hi-index | 0.01 |
Boneh and Venkatesan have recently proposed a polynomial time algorithm for recovering a "hidden" element α of a finite field Fp of p elements from rather short strings of the most significant bits of the remainder modulo p of αt for several values of t selected uniformly at random from Fp*. Unfortunately the applications to the computational security of most significant bits of private keys of some finite field exponentiation based cryptosystems given by Boneh and Venkatesan are not quite correct. For the Diffie-Hellman cryptosystem the result of Boneh and Venkatesan has been corrected and generalized in our recent paper. Here a similar analysis is given for the Shamir message passing scheme. The results depend on some bounds of exponential sums.