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REPORTS > KEYWORD > EPSILON-BIASED GENERATOR:
Reports tagged with epsilon-biased generator:
TR05-087 | 9th August 2005
Alexander Healy, Emanuele Viola

#### Constant-Depth Circuits for Arithmetic in Finite Fields of Characteristic Two

We study the complexity of arithmetic in finite fields of characteristic two, $\F_{2^n}$.
We concentrate on the following two problems:

Iterated Multiplication: Given $\alpha_1, \alpha_2,..., \alpha_t \in \F_{2^n}$, compute $\alpha_1 \cdot \alpha_2 \cdots \alpha_t \in \F_{2^n}$.

Exponentiation: Given $\alpha \in \F_{2^n}$ and a $t$-bit integer $k$, compute $\alpha^k \in \F_{2^n}$.

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TR18-112 | 5th June 2018
Raghu Meka, Omer Reingold, Avishay Tal

#### Pseudorandom Generators for Width-3 Branching Programs

Revisions: 1

We construct pseudorandom generators of seed length $\tilde{O}(\log(n)\cdot \log(1/\epsilon))$ that $\epsilon$-fool ordered read-once branching programs (ROBPs) of width $3$ and length $n$. For unordered ROBPs, we construct pseudorandom generators with seed length $\tilde{O}(\log(n) \cdot \mathrm{poly}(1/\epsilon))$. This is the first improvement for pseudorandom generators fooling width $3$ ROBPs since the work ... more >>>

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