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Abstract: We show that for several natural classes of "structured" matrices, including symmetric, circulant, Hankel and Toeplitz matrices, approximating the permanent modulo a prime p is as hard as computing the exact value. Results of this kind are well known for the class of arbitrary matrices; however the techniques used do not seem to apply to "structured" matrices. Our approach is based on recent advances in the hidden number problem introduced by Boneh and Venkatesan in 1996 combined with... (Update)
Context of citations to this paper: More
.... Pairing: Approx HNP, see [25] Noisy Chinese Remaindering: CR HNP, see [58] Non approximability of Permanents: HNP, see [14]. Sprase Determinants: HNP, see [14] Hard Polynomials: HNP, see [14] 13 Conclusion There are certainly several possible directions...
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BibTeX entry: (Update)
B. Codenotti and I. E. Shparlinski, `Non-approximability of the permanent of structured matrices over finite fields', Preprint , 2002, 1--11. http://citeseer.ist.psu.edu/codenotti02nonapproximability.html More
@misc{ codenotti02nonapproximability,
author = "B. Codenotti and I. Shparlinski",
title = "Non-approximability of the permanent of structured matrices over finite
fields",
text = "B. Codenotti and I. E. Shparlinski, `Non-approximability of the permanent
of structured matrices over finite fields', Preprint , 2002, 1--11.",
year = "2002",
url = "citeseer.ist.psu.edu/codenotti02nonapproximability.html" }
Citations (may not include all citations):309 Random number generation and quasi--Monte Carlo methods (context) - Niederreiter - 1992
116 Algorithmic number theory (context) - Bach, Shallit - 1996
55 Hardness of computing the most significant bits of secret ke.. (context) - Boneh, Venkatesan - 1996
34 The insecurity of the Digital Signature Algorithm with parti.. - Nguyen, Shparlinski - 2002
30 the hardness of computing the permanent of random matrices (context) - Feige, Lund - 1997
29 Completeness classes in algebra (context) - Valiant - 1979
27 Character sums with exponential functions and their applicat.. (context) - Konyagin, Shparlinski - 1999
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
11 A deterministic strongly polynomial algorithm for matrix sca.. - Linial, Samorodinski et al. - 1998
9 Sparse polynomial approximation in finite fields - Shparlinski - 2001
8 The insecurity of Nyberg--Rueppel and other DSA-like signatu.. (context) - Mahassni, Nguyen et al. - 2001
7 the security of Di#e-- Hellman bits (context) - Vasco, Shparlinski - 1999
7 Completeness and reduction in algebraic complexity theory (context) - Burgisser - 2000
6 The hidden number problem with the trace and bit security of.. (context) - Li, Naslund et al. - 2002
5 the generalised hidden number problem and bit security of XT.. (context) - Shparlinski - 2001
4 the hardness of permanent - Cai, Pavan et al. - 1999
4 How fast can one compute the permanent of circulant matrices - Bernasconi, Codenotti et al. - 1999
2 the permanent of certain circulant matrices - Codenotti, Resta - 2001
2 A polynomial-time algorithm for the permanent of a matrix wi.. (context) - Jerrum, Sinclair et al. - 2000
2 Security of most significant bits of g (context) - Shparlinski - 2002
2 Computation of sparse circulant permanents via determinants - Codenotti, Resta - 2002
1 The computational complexity of immanants - Burgisser - 2000
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