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Electronic Colloquium on Computational Complexity

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All reports by Author Ron Rothblum:

TR24-088 | 29th April 2024
Tamer Mour, Alon Rosen, Ron Rothblum

Locally Testable Tree Codes

Tree codes, introduced in the seminal works of Schulman (STOC 93', IEEE Transactions on Information Theory 96') are codes designed for interactive communication. Encoding in a tree code is done in an online manner: the $i$-th codeword symbol depends only on the first $i$ message symbols. Codewords should have good ... more >>>

TR23-118 | 17th August 2023
Hugo Aaronson, Tom Gur, Ninad Rajgopal, Ron Rothblum

Distribution-Free Proofs of Proximity

Revisions: 2

Motivated by the fact that input distributions are often unknown in advance, distribution-free property testing considers a setting in which the algorithmic task is to accept functions $f : [n] \to \{0,1\}$ having a certain property $\Pi$ and reject functions that are $\varepsilon$-far from $\Pi$, where the distance is measured ... more >>>

TR15-024 | 16th February 2015
Oded Goldreich, Tom Gur, Ron Rothblum

Proofs of Proximity for Context-Free Languages and Read-Once Branching Programs

Proofs of proximity are probabilistic proof systems in which the verifier only queries a sub-linear number of input bits, and soundness only means that, with high probability, the input is close to an accepting input. In their minimal form, called Merlin-Arthur proofs of proximity (MAP), the verifier receives, in addition ... more >>>

TR13-183 | 22nd December 2013
Yael Tauman Kalai, Ran Raz, Ron Rothblum

How to Delegate Computations: The Power of No-Signaling Proofs

Revisions: 1

We construct a 1-round delegation scheme (i.e., argument-system) for every language computable in time t=t(n), where the running time of the prover is poly(t) and the running time of the verifier is n*polylog(t). In particular, for every language in P we obtain a delegation scheme with almost linear time verification. ... more >>>

TR13-107 | 7th August 2013
Gil Cohen, Ivan Bjerre Damgard, Yuval Ishai, Jonas Kolker, Peter Bro Miltersen, Ran Raz, Ron Rothblum

Efficient Multiparty Protocols via Log-Depth Threshold Formulae

We put forward a new approach for the design of efficient multiparty protocols:

1. Design a protocol for a small number of parties (say, 3 or 4) which achieves
security against a single corrupted party. Such protocols are typically easy
to construct as they may employ techniques that do not ... more >>>

TR13-078 | 28th May 2013
Tom Gur, Ron Rothblum

Non-Interactive Proofs of Proximity

Revisions: 1

We initiate a study of non-interactive proofs of proximity. These proof-systems consist of a verifier that wishes to ascertain the validity of a given statement, using a short (sublinear length) explicitly given proof, and a sublinear number of queries to its input. Since the verifier cannot even read the entire ... more >>>

TR11-159 | 27th November 2011
Oded Goldreich, Ron Rothblum

Enhancements of Trapdoor Permutations

Revisions: 1 , Comments: 1

We take a closer look at several enhancements of the notion of trapdoor permutations. Specifically, we consider the notions of enhanced trapdoor permutation (Goldreich 2004) and doubly enhanced trapdoor permutation (Goldreich 2008) as well as intermediate notions (Rothblum 2010). These enhancements arose in the study of Oblivious Transfer and NIZK, ... more >>>

TR10-146 | 21st September 2010
Ron Rothblum

Homomorphic Encryption: from Private-Key to Public-Key

We show that any private-key encryption scheme that is weakly
homomorphic with respect to addition modulo 2, can be transformed
into a public-key encryption scheme. The homomorphic feature
referred to is a minimalistic one; that is, the length of a
homomorphically generated encryption should be independent of the
number of ... more >>>

TR10-145 | 21st September 2010
Ron Rothblum

A Taxonomy of Enhanced Trapdoor Permutations

Trapdoor permutations (TDPs) are among the most widely studied
building blocks of cryptography. Despite the extensive body of
work that has been dedicated to their study, in many setting and
applications (enhanced) trapdoor permutations behave
unexpectedly. In particular, a TDP may become easy to invert when
the inverter is given ... more >>>

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