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Abstract: We consider a certain generalization of the hidden number problem which has recently been introduced by Boneh and Venkatesan. We apply our results to study the bit security of the XTR cryptosystem and obtain some analogues of the results which have been known for the bit security of the Di#e-Hellman scheme. 1 1 Introduction Let p be a prime. We denote by IF = IF p and IK = IF q the fields of p and q = p m elements, respectively, where m # 1 is integer. As usual we assume that IF is... (Update)
Context of citations to this paper: More
...the trivial estimate N F (r, h) # h deg F . The bound of Lemma 3 on the number of zeros of sparse polynomials from [4, 7] has been used in [30] to derive some results about analogues of the hidden number problem for the trace of elements of multiplicative subgroups in finite...
.... with the exponential sum technique lead to a series of new results about the bits security of some cryptographic constructions [11, 14, 22, 23] as well as to attacks on some of them [6, 13, 17, 18] However the case where G is the point group of an elliptic curve has turned...
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BibTeX entry: (Update)
I. E. Shparlinski, On the generalized hidden number problem and bit security of XTR, Preprint, 2000, 1--14. http://citeseer.ist.psu.edu/shparlinski00generalized.html More
@misc{ shparlinski00generalized,
author = "I. Shparlinski",
title = "the generalized hidden number problem and bit security of XTR",
text = "I. E. Shparlinski, On the generalized hidden number problem and bit security
of XTR, Preprint, 2000, 1--14.",
year = "2000",
url = "citeseer.ist.psu.edu/shparlinski00generalized.html" }
Citations (may not include all citations):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
34 The insecurity of the Digital Signature Algorithm with parti.. - Nguyen, Shparlinski - 2000
27 Character sums with exponential functions and their applicat.. (context) - Konyagin, Shparlinski - 1999
22 The XTR public key system - Lenstra, Verheul - 2000
20 Factoring polynomials with rational coe#cients (context) - Lenstra, Lenstra et al. - 1982
19 Lattice reduction in cryptology: An update - Nguyen, Stern - 2000
19 A hierarchy of polynomial time basis reduction algorithms (context) - Schnorr - 1987
15 The insecurity of the elliptic curve Digital Signature Algor.. - Nguyen, Shparlinski - 2000
15 Algorithmic geometry of numbers - Kannan - 1987
14 the statistical properties of Di#e--Hellman distributions (context) - Canetti, Friedlander et al.
14 Security of the most significant bits of the Shamir message .. (context) - Vasco, Shparlinski
12 Rounding in lattices and its cryptographic applications - Boneh, Venkatesan - 1997
11 Lattice attacks on digital signature schemes (context) - Howgrave-Graham, Smart
9 Sparse polynomial approximation in finite fields - Shparlinski - 2000
9 Certificates of recoverability with scalable recovery agent .. (context) - Verheul - 2000
7 Doing more with fewer bits - Brouwer, Pellikaan et al. - 1999
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
2 Codes and Cryptography (context) - Friedlander, Larsen et al. - 1999
Documents on the same site (http://www.comp.mq.edu.au/~igor/Publ.html): More
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