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Abstract: We give a survey of recent results on the hidden number problem introduced by Boneh and Venkatesan in 1996 and its numerous generalizations. (Update)
Active bibliography (related documents): More All
1.5: Non-approximability of the Permanent of Structured.. - Codenotti, Shparlinski (2002) (Correct)
1.4: Noisy Chinese Remaindering in the Lee Norm - Shparlinski, Steinfeld (2002) (Correct)
1.1: Sparse Polynomial Approximation in Finite Fields - Shparlinski (2000) (Correct)
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0.5: Exponential Sums and Lattice Reduction: - Cryptography (Correct)
0.4: The Hidden Number Problem in Extension Fields and Its.. - Vasco, Näslund.. (Correct)
0.4: On the Generalized Hidden Number Problem and Bit Security of XTR - Shparlinski (2000) (Correct)
BibTeX entry: (Update)
@misc{ shparlinski-playing,
author = "Igor E. Shparlinski",
title = "Playing "Hide-and-Seek" in Finite Fields: The Hidden Number Problem and
Its Applications",
url = "citeseer.ist.psu.edu/shparlinski02playing.html" }
Citations (may not include all citations):1065 Handbook of Applied Cryptography (context) - Menezes, van Oorschot et al. - 1996
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
103 Factoring polynomials with rational coe#cients (context) - Lenstra, Lenstra et al. - 1982
82 Improved low-degree testing and its applications - Arora, Sudan - 1997
65 Learning polynomials with queries: the highly noisy case - Goldreich, Rubinfeld et al.
55 Hardness of computing the most significant bits of secret ke.. (context) - Boneh, Venkatesan - 1996
46 Cambridge University Press (context) - Lidl, Niederreiter et al. - 1997
42 Time-lock puzzles and timed-release crypto - Rivest, Shamir et al. - 1996
34 The insecurity of the Digital Signature Algorithm with parti.. - Nguyen, Shparlinski
32 On zero testing and interpolation of k-sparse multivariate p.. (context) - Clausen, Dress et al. - 1991
31 List decoding of algebraicgeometric codes - Shokrollahi, Wasserman - 1999
27 Character sums with exponential functions and their applicat.. (context) - Konyagin, Shparlinski - 1999
22 Elementary and analytic theory of algebraic numbers (context) - Narkiewicz - 1990
22 The XTR public key system - Lenstra, Verheul - 2000
20 Finding smooth integers in shorts intervals using CRT decodi.. - Boneh - 2000
19 Lattice reduction in cryptology: An update - Nguyen, Stern - 2000
19 A hierarchy of polynomial time basis reduction algorithms (context) - Schnorr - 1987
18 Chinese remaindering with errors - Goldreich, Ron et al. - 2000
17 Noisy polynomial interpolation and noisy Chinese remainderin.. - Bleichenbacher, Nguyen - 2000
16 and monodromy groups (context) - Katz, sums et al. - 1988
16 A public-key cryptosystem and a digital signature system bas.. (context) - Smith, Skinner - 1995
16 Lattice attacks on digital signature schemes (context) - Howgrave-Graham, Smart - 2001
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
14 Security of the most significant bits of the Shamir message .. (context) - Vasco, Shparlinski - 2002
12 Rounding in lattices and its cryptographic applications - Boneh, Venkatesan - 1997
12 A sieve algorithm for the shortest lattice vector problem - Ajtai, Kumar et al. - 2001
11 The dark side of the hidden number problem: Lattice attacks .. (context) - Nguyen
10 The two faces of lattices in cryptology - Nguyen, Stern - 2001
9 Certificates of recoverability with scalable recovery agent .. (context) - Verheul - 2000
9 The complexity of sparse polynomial interpolation over finit.. (context) - Werther - 1994
9 Sparse polynomial approximation in finite fields - Shparlinski - 2001
8 the statistical properties of Di#e--Hellman distributions (context) - Canetti, Friedlander et al. - 2000
8 The insecurity of Nyberg--Rueppel and other DSA-like signatu.. (context) - Mahassni, Nguyen et al. - 2001
8 Sparse polynomial interpolation in non-standard bases - Lakshman, Saunders - 1995
8 Reconstructing algebraic functions from erroneous data (context) - Ar, Lipton et al. - 1999
7 the security of Di#e-- Hellman bits (context) - Vasco, Shparlinski
7 Reconstructing randomly sampled multivariate polynomials fro.. - Wasserman - 1998
6 The modular inversion hidden number problem - Boneh, Halevi et al. - 2001
6 The hidden number problem with the trace and bit security of.. (context) - Li, Naslund et al. - 2002
6 Key improvements to XTR (context) - Lenstra, Verheul
5 the unpredictability of bits of the elliptic curve Di#e--Hel.. (context) - Boneh, Shparlinski - 2001
5 the generalised hidden number problem and bit security of XT.. (context) - Shparlinski - 2001
5 Character sums and abelian Ramanujan graphs (context) - Li - 1992
4 Exponential sums and group generators for elliptic curves ov.. - Kohel, Shparlinski - 2000
4 Cohomologie 'etale (context) - Deligne - 1977
4 Number theory with applications (context) - Li - 1996
3 Soft-decision (context) - Guruswami, Sahai et al. - 2000
3 Hidden number problem with hidden multipliers, timed-release.. (context) - Howgrave-Graham, Nguyen et al.
3 Exact and approximate testing /correcting of algebraic funct.. - Kiwi, Magniez et al.
2 Security of most significant bits of g (context) - Shparlinski
2 A small subgroup attack on a key agreement protocol of Arazi - Brown, Menezes
1 The hidden number problem in extension fields and its applic.. (context) - Vasco, Naslund et al. - 2002
1 Security of polynomial transformations of the Di#e-- Hellman.. (context) - Shparlinski - 2000
1 Noisy Chinese remaindering in the Lee norm - Shparlinski, Steinfeld - 2001
1 Some remarks on Lucas-based Cryptograph (context) - Bleichenbacher, Bosma et al. - 1995
1 Chinese remaindering for algebraic numbers in a hidden field (context) - Shparlinski, Steinfeld - 2001
1 Non-approximability of the permanent of structured matrices .. - Codenotti, Shparlinski - 2002
1 A primitive for proving the security of every bit and about .. - Kiltz - 2001
Documents on the same site (http://www.cs.mq.edu.au/~igor/Publ.html): More
A Public Key Cryptosystem Based On Sparse Polynomials - Grant, Krastev, Lieman.. (1998) (Correct)
Security of Most Significant Bits of g^x^2 - Shparlinski (2000) (Correct)
On the Uniformity of Distribution of Congruential.. - Mahassni, Shparlinski (2000) (Correct)
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