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REPORTS > KEYWORD > EXPONENTIAL SUMS:
Reports tagged with exponential sums:
TR99-021 | 8th April 1999
Igor E. Shparlinski

#### ON THE UNIFORMITY OF DISTRIBUTION OF A CERTAIN PSEUDO-RANDOM FUNCTION

We show that a pseudo-random number generator,
introduced recently by M. Naor and O. Reingold,
possess one more attractive and useful property.
Namely, it is proved that for almost all values of parameters it
produces a uniformly distributed sequence.
The proof is based on some recent bounds of exponential
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TR00-040 | 19th May 2000
Maria Isabel Gonzalez Vasco, Igor E. Shparlinski

#### Security of the Most Significant Bits of the Shamir Message Passing Scheme

Boneh and Venkatesan have recently proposed a polynomial time
algorithm for recovering a hidden'' element $\alpha$ of a
finite field $\F_p$ of $p$ elements from rather short
strings of the most significant bits of the remainder
mo\-du\-lo $p$ of $\alpha t$ for several values of $t$ selected uniformly
at random ... more >>>

TR00-045 | 23rd June 2000
Maria Isabel Gonzalez Vasco, Igor E. Shparlinski

#### On the Security of Diffie--Hellman Bits

Boneh and Venkatesan have recently proposed a polynomial time
algorithm for recovering a hidden'' element $\alpha$ of a
finite field $\F_p$ of $p$ elements from rather short
strings of the most significant bits of the remainder
mo\-du\-lo $p$ of $\alpha t$ for several values of $t$ selected
uniformly at ... more >>>

TR02-071 | 6th June 2002
Bruno Codenotti, Igor E. Shparlinski

#### Non-approximability of the Permanent of Structured Matrices over Finite Fields

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 ... more >>>

TR06-107 | 26th August 2006

#### An improved bound on correlation between polynomials over Z_m and MOD_q

Revisions: 1

Let m,q > 1 be two integers that are co-prime and A be any subset of Z_m. Let P be any multi-linear polynomial of degree d in n variables over Z_m. We show that the MOD_q boolean function on n variables has correlation at most exp(-\Omega(n/(m2^{m-1})^d)) with the boolean function ... more >>>

TR09-084 | 24th September 2009

#### Linear systems over composite moduli

We study solution sets to systems of generalized linear equations of the following form:
$\ell_i (x_1, x_2, \cdots , x_n)\, \in \,A_i \,\, (\text{mod } m)$,
where $\ell_1, \ldots ,\ell_t$ are linear forms in $n$ Boolean variables, each $A_i$ is an arbitrary subset of $\mathbb{Z}_m$, and $m$ is a composite ... more >>>

TR14-010 | 23rd January 2014
Jean Bourgain, Zeev Dvir, Ethan Leeman

#### Affine extractors over large fields with exponential error

We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length. Our construction relies on a deep theorem of Deligne giving tight estimates for exponential sums over smooth varieties in high dimensions.

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