All reports by Author Tal Malkin:

__
TR21-050
| 2nd April 2021
__

Marshall Ball, Alper Cakan, Tal Malkin#### Linear Threshold Secret-Sharing with Binary Reconstruction

__
TR20-054
| 22nd April 2020
__

Marshall Ball, Oded Goldreich, Tal Malkin#### Communication Complexity with Defective Randomness

Revisions: 3

__
TR20-023
| 10th February 2020
__

Marshall Ball, Eshan Chattopadhyay, Jyun-Jie Liao, Tal Malkin, Li-Yang Tan#### Non-Malleability against Polynomial Tampering

Revisions: 1

__
TR19-183
| 21st December 2019
__

Marshall Ball, Oded Goldreich, Tal Malkin#### Randomness Extraction from Somewhat Dependent Sources

Revisions: 1

__
TR19-055
| 9th April 2019
__

Kasper Green Larsen, Tal Malkin, Omri Weinstein, Kevin Yeo#### Lower Bounds for Oblivious Near-Neighbor Search

__
TR18-040
| 21st February 2018
__

Marshall Ball, Dana Dachman-Soled, Siyao Guo, Tal Malkin, Li-Yang Tan#### Non-Malleable Codes for Small-Depth Circuits

__
TR15-008
| 14th January 2015
__

Igor Carboni Oliveira, Siyao Guo, Tal Malkin, Alon Rosen#### The Power of Negations in Cryptography

Revisions: 1

__
TR03-086
| 1st December 2003
__

Amos Beimel, Tal Malkin#### A Quantitative Approach to Reductions in Secure Computation

Marshall Ball, Alper Cakan, Tal Malkin

Motivated in part by applications in lattice-based cryptography, we initiate the study of the size of linear threshold (`$t$-out-of-$n$') secret-sharing where the linear reconstruction function is restricted to coefficients in $\{0,1\}$. We prove upper and lower bounds on the share size of such schemes. One ramification of our results is ... more >>>

Marshall Ball, Oded Goldreich, Tal Malkin

Starting with the two standard model of randomized communication complexity, we study the communication complexity of functions when the protocol has access to a defective source of randomness.

Specifically, we consider both the public-randomness and private-randomness cases, while replacing the commonly postulated perfect randomness with distributions over $\ell$ bit ...
more >>>

Marshall Ball, Eshan Chattopadhyay, Jyun-Jie Liao, Tal Malkin, Li-Yang Tan

We present the first explicit construction of a non-malleable code that can handle tampering functions that are bounded-degree polynomials.

Prior to our work, this was only known for degree-1 polynomials (affine tampering functions), due to Chattopadhyay and Li (STOC 2017). As a direct corollary, we obtain an explicit non-malleable ... more >>>

Marshall Ball, Oded Goldreich, Tal Malkin

We initiate a comprehensive study of the question of randomness extractions from two somewhat dependent sources of defective randomness.

Specifically, we present three natural models, which are based on different natural perspectives on the notion of bounded dependency between a pair of distributions.

Going from the more restricted model ...
more >>>

Kasper Green Larsen, Tal Malkin, Omri Weinstein, Kevin Yeo

We prove an $\Omega(d \lg n/ (\lg\lg n)^2)$ lower bound on the dynamic cell-probe complexity of statistically $\mathit{oblivious}$ approximate-near-neighbor search (ANN) over the $d$-dimensional Hamming cube. For the natural setting of $d = \Theta(\log n)$, our result implies an $\tilde{\Omega}(\lg^2 n)$ lower bound, which is a quadratic improvement over the ... more >>>

Marshall Ball, Dana Dachman-Soled, Siyao Guo, Tal Malkin, Li-Yang Tan

We construct efficient, unconditional non-malleable codes that are secure against tampering functions computed by small-depth circuits. For constant-depth circuits of polynomial size (i.e.~$\mathsf{AC^0}$ tampering functions), our codes have codeword length $n = k^{1+o(1)}$ for a $k$-bit message. This is an exponential improvement of the previous best construction due to Chattopadhyay ... more >>>

Igor Carboni Oliveira, Siyao Guo, Tal Malkin, Alon Rosen

The study of monotonicity and negation complexity for Boolean functions has been prevalent in complexity theory as well as in computational learning theory, but little attention has been given to it in the cryptographic context. Recently, Goldreich and Izsak (2012) have initiated a study of whether cryptographic primitives can be ... more >>>

Amos Beimel, Tal Malkin

Secure computation is one of the most fundamental cryptographic tasks.

It is known that all functions can be computed securely in the

information theoretic setting, given access to a black box for some

complete function such as AND. However, without such a black box, not

all functions can be securely ...
more >>>