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- Phong Q. Nguyen, Igor E. Shparlinski
- Journal of Cryptology
- 2002

We present a polynomial-time algorithm that provably recovers the signer's secret DSA key when a few consecutive bits of the random nonces k (used at each signature generation) are known for a numberâ€¦ (More)

- Phong Q. Nguyen, Igor E. Shparlinski
- Des. Codes Cryptography
- 2003

Nguyen and Shparlinski recently presented a polynomial-time algorithm that provably recovers the signerâ€™s secret DSA key when a few bits of the random nonces k (used at each signature generation) areâ€¦ (More)

- Dan Boneh, Igor E. Shparlinski
- CRYPTO
- 2001

Let E/Fp be an elliptic curve, and G âˆˆ E/Fp. Define the Diffieâ€“Hellman function as DHE,G(aG, bG) = abG. We show that if there is an efficient algorithm for predicting the LSB of the x or y coordinateâ€¦ (More)

uniformly for any integers a, b, c with gcd(a, b, c, p) Ì„ 1. Incomplete sums are estimated as well. The question is motivated by the assumption, often made in cryptography, that the triples (gx, gy,â€¦ (More)

- John B. Friedlander, Michael Larsen, Daniel Lieman, Igor E. Shparlinski
- Des. Codes Cryptography
- 1999

A catalogue record of this book is available from the British Library Library of Congress Cataloguing in Publication data Kon iagin, S. V. (SergeË‡Ä± Vladimirovich) Character sums with exponentialâ€¦ (More)

Let p be a large prime such that pâˆ’1 has some large prime factors, and let Î¸ âˆˆ ZZp be an r-th power residue for all small factors of pâˆ’ 1. The corresponding Diffie-Hellman (DH) distribution is (Î¸x,â€¦ (More)

- San Ling, Igor E. Shparlinski, Ron Steinfeld, Huaxiong Wang
- J. Symb. Comput.
- 2012

We give a rigorous deterministic polynomial time algorithm for the modular inversion hidden number problem introduced by D. Boneh, S. Halevi and N. A. Howgrave-Graham in 2001. For our algorithm weâ€¦ (More)

- Don Coppersmith, Igor E. Shparlinski
- Journal of Cryptology
- 2000

We obtain several lower bounds, exponential in terms of lg p , on the degrees of polynomials and algebraic functions coinciding with values of the discrete logarithm modulo a prime p at sufficientlyâ€¦ (More)

- Florian Hess, Igor E. Shparlinski
- Des. Codes Cryptography
- 2005

We show that the elliptic curve analogue of the linear congruential generator produces sequences with high linear complexity and good multidimensional distribution.