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Abstract: We consider a polynomial analogue of the hidden number problem which has recently been introduced by Boneh and Venkatesan. Namely we consider the sparse polynomial approximation problem of recovering an unknown polynomial f(X) # IF p [X] with at most m non-zero terms from approximate values of f(t) at polynomially many points t # IF p selected uniformly at random. The case of a polynomial f(X) = #X corresponds to the hidden number problem. The above problem is related to the noisy... (Update)
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.... show that the distribution of the t i s is sufficiently uniform, which is usually obtained by exponential sum techniques (see [63, 111, 112, 48, 130, 129] for some examples) One may also extend the solution to the hidden number problem to the case when an oracle for CVP (in...
...problem in polynomialtime whenever 2h n k, where k = log K log p min , and p min = min 1#i#n p i . We also remark that the result of [25] is a Lee norm analogue of Hamming norm results of [2, 7, 10, 11, 16, 19, 22, 24, 25, 26, 27] on noisy polynomial reconstruction problem...
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BibTeX entry: (Update)
I. E. Shparlinski, Sparse polynomial approximation in finite fields, Preprint, 2000, 1--16. 14 http://citeseer.ist.psu.edu/shparlinski00sparse.html More
@inproceedings{ shparlinski01sparse,
author = "Igor Shparlinski",
title = "Sparse polynomial approximation in finite fields",
booktitle = "{ACM} Symposium on Theory of Computing",
pages = "209-215",
year = "2001",
url = "citeseer.ist.psu.edu/shparlinski00sparse.html" }
Citations (may not include all citations):309 Random number generation and quasi--Monte Carlo methods (context) - Niederreiter - 1992
114 Improved decoding of Reed--Solomon and algebraic geometric c.. - Guruswami, Sudan - 1999
55 Hardness of computing the most significant bits of secret ke.. (context) - Boneh, Venkatesan - 1996
49 Minkowski's convex body theorem and integer programming (context) - Kannan - 1987
46 Cambridge University Press (context) - Lidl, Niederreiter et al. - 1997
37 Basic number theory (context) - Weil - 1974
34 The insecurity of the Digital Signature Algorithm with parti.. - Nguyen, Shparlinski - 2000
32 On zero testing and interpolation of k-sparse multivariate p.. (context) - Clausen, Dress et al. - 1991
31 List decoding of algebraic-geometric codes - Shokrollahi, Wasserman - 1999
22 The XTR public key system - Lenstra, Verheul - 2000
20 Factoring polynomials with rational coe#cients (context) - Lenstra, Lenstra et al. - 1982
19 A hierarchy of polynomial time basis reduction algorithms (context) - Schnorr - 1987
19 Lattice reduction in cryptology: An update - Nguyen, Stern - 2000
17 Noisy polynomial interpolation and noisy Chinese remainderin.. - Bleichenbacher, Nguyen - 2000
15 Algorithmic geometry of numbers - Kannan - 1987
15 ective polynomial computation (context) - Zippel - 1993
15 Computational complexity of sparse rational interpolation - Grigoriev, Karpinski et al. - 1994
15 The insecurity of the elliptic curve Digital Signature Algor.. - Nguyen, Shparlinski - 2000
14 Security of the most significant bits of the Shamir message .. (context) - Vasco, Shparlinski
14 the statistical properties of Di#e--Hellman distributions (context) - Canetti, Friedlander et al.
12 Rounding in lattices and its cryptographic applications - Boneh, Venkatesan - 1997
11 Lattice attacks on digital signature schemes (context) - Howgrave-Graham, Smart
9 The complexity of sparse polynomials interpolation over fini.. (context) - Werther - 1994
8 Sparse polynomial interpolation in non-standard bases - Lakshman, Saunders - 1995
7 Reconstructing randomly sampled multivariate polynomials fro.. - Wasserman - 1998
5 the generalized hidden number problem and bit security of XT.. - Shparlinski - 2000
5 the hardness of the shortest vector problem - Micciancio - 1998
4 The insecurity of some DSA-like signature schemes with parti.. (context) - Mahassni, Shparlinski - 2000
4 Security of polynomial transformations of the Di#e--Hellman .. (context) - Shparlinski - 2000
3 Security of most significant bits of g x - Shparlinski - 2000
2 Codes and Cryptography (context) - Friedlander, Larsen et al. - 1999
The graph only includes citing articles where the year of publication is known.
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