I. Shparlinski

Publications784
h-index39
Citations8,050
Highly Influential Citations447
Claim Author Page
Author pages are created from data sourced from our academic publisher partnerships and public sources.

Recommended Authors

  • J. Bourgain
  • 492 Publications, 23,533 Citations
  • F. Luca
  • 626 Publications, 3,453 Citations
  • C. Pomerance
  • 266 Publications, 6,720 Citations
  • W. Banks
  • 130 Publications, 984 Citations
  • Publications
  • Influence
The Insecurity of the Digital Signature Algorithm with Partially Known Nonces
TLDR
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 number of DSA signatures at most linear in log q, under a reasonable assumption on the hash function used in DSA. Expand
  • 223
  • 18
  • PDF
The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces
TLDR
Nguyen and Shparlinski have recently presented 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 number of DSA signatures at most linear in log q. Expand
  • 176
  • 16
  • PDF
Parameters of Integral Circulant Graphs and Periodic Quantum Dynamics
The means for simultaneous scouring of metal surfaces contains a waste product in manufacture of fodder yeast, citric acid, ammonium citrate, aqueous solution of sodium gluconate, sulphonated ricinic… Expand
  • 83
  • 9
  • PDF
Prime numbers with Beatty sequences
A study of certain Hamiltonian systems has lead Y. Long to conjecture the existence of infinitely many primes of the form $p=2[\alpha n]+1$, where $1 0$ depends only on $\alpha$. We also prove a… Expand
  • 32
  • 8
  • PDF
On the Unpredictability of Bits of the Elliptic Curve Diffie--Hellman Scheme
TLDR
We show that just predicting one bit of the Elliptic Curve Diffie-Hellman secret in a family of curves is as hard as computing the entire secret. Expand
  • 56
  • 7
  • PDF
On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields
TLDR
In the paper an upper bound is established for certain exponential sums, analogous to Gaussian sums, defined on the points of an elliptic curve over a prime finite field. Expand
  • 74
  • 7
  • PDF
Character Sums with Exponential Functions and their Applications: Introduction
  • 65
  • 7
Curves with many points and multiplication in finite fileds
  • 63
  • 6
On the Security of Diffie-Hellman Bits
TLDR
A polynomial time algorithm for recovering a “hidden” element α of a finite field of p elements from rather short strings of the most significant bits of the remainder modulo p of αt for several values of t selected uniformly at random. Expand
  • 54
  • 5
On the Linear Complexity and Multidimensional Distribution of Congruential Generators over Elliptic Curves
TLDR
We show that the elliptic curve analogue of the linear congruential generator of pseudorandom numbers produces sequences with high linear complexity and good multidimensional distribution. Expand
  • 37
  • 5
  • PDF