I. Shparlinski

Publications836
h-index41
Citations8,915
Highly Influential Citations485
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The Insecurity of the Digital Signature Algorithm with Partially Known Nonces
TLDR
A polynomial-time algorithm that provably recovers the signer's secret DSA key when a few consecutive bits of the random nonces k 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.
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The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces
TLDR
All previously known results for the elliptic curve variant of DSA (ECDSA) were only heuristic, including those of Howgrave-Graham and Smart who introduced the topic.
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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…
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On the Unpredictability of Bits of the Elliptic Curve Diffie--Hellman Scheme
TLDR
If there is an efficient algorithm for predicting the LSB of the x or y coordinate of abG given 〈E, G, aG, bG〉 for a certain family of elliptic curves, then there is a algorithm for computing the Diffie-Hellman function on all curves in this family.
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On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields
TLDR
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, and this estimate is applied to obtain a deterministic O(q 1/2 + e) algorithm for finding generators of the group in echelon form.
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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…
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Recurrence Sequences
TLDR
This work surveys a selection of number-theoretic properties of linear recurrence sequences together with their direct generalizations and describes applications of these properties which are important for a variety of applications.
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Character Sums with Exponential Functions and their Applications: Bounds of Short Character Sums
TLDR
An enumeration problem in finite fields with applications to Algebraic Number Fields and Pseudo-random Number Generators and Multiplicative Translations of Sets.
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Curves with many points and multiplication in finite fileds
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On the cycle structure of repeated exponentiation modulo a prime
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