All reports by Author Dan Carmon:

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TR22-110
| 1st August 2022
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Eli Ben-Sasson, Dan Carmon, Swastik Kopparty, David Levit#### Scalable and Transparent Proofs over All Large Fields, via Elliptic Curves

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TR21-103
| 18th July 2021
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Eli Ben-Sasson, Dan Carmon, Swastik Kopparty, David Levit#### Elliptic Curve Fast Fourier Transform (ECFFT) Part I: Fast Polynomial Algorithms over all Finite Fields

Revisions: 1

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TR20-083
| 30th May 2020
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Eli Ben-Sasson, Dan Carmon, Yuval Ishai, Swastik Kopparty, Shubhangi Saraf#### Proximity Gaps for Reed-Solomon Codes

Revisions: 3

Eli Ben-Sasson, Dan Carmon, Swastik Kopparty, David Levit

Concretely efficient interactive oracle proofs (IOPs) are of interest due to their applications to scaling blockchains, their minimal security assumptions, and their potential future-proof resistance to quantum attacks.

Scalable IOPs, in which prover time scales quasilinearly with the computation size and verifier time scales poly-logarithmically with it, have been known ... more >>>

Eli Ben-Sasson, Dan Carmon, Swastik Kopparty, David Levit

Over finite fields $F_q$ containing a root of unity of smooth order $n$ (smoothness means $n$ is the product of small primes), the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division, interpolation and multi-point evaluation. These operations can ... more >>>

Eli Ben-Sasson, Dan Carmon, Yuval Ishai, Swastik Kopparty, Shubhangi Saraf

A collection of sets displays a proximity gap with respect to some property if for every set in the collection, either (i) all members are $\delta$-close to the property in relative Hamming distance or (ii) only a tiny fraction of members are $\delta$-close to the property. In particular, no set ... more >>>