Zero-knowledge proofs allow to encode a computation so that it can be verified without revealing any additional information beyond its correctness. In this work we focus on proofs that are statistically sound meaning that even an unbounded prover cannot make the verifier accept a false statement, except with negligible probability, ... more >>>

We show that every NP relation that can be verified by a bounded-depth polynomial-sized circuit, or a bounded-space polynomial-time algorithm, has a computational zero-knowledge proof (with statistical soundness) with communication that is only additively larger than the witness length. Our construction relies only on the minimal assumption that one-way functions ... more >>>

A classical challenge in complexity theory and cryptography is to simulate interactive proof systems by non-interactive proof systems. In this work we leverage approaches from recent works in derandomization to address this challenge, focusing on non-interactive simulations that are sound against uniform adversarial algorithms.

Our results concern fundamental questions in ... more >>>

A dot-product proof (DPP) is a simple probabilistic proof system in which the input statement $x$ and the proof ${\pi}$ are vectors over a finite field $\mathbb{F}$, and the proof is verified by making a single dot-product query $\langle {q},({x} \| {\pi})\rangle$ jointly to ${x}$ and ${\pi}$. A DPP can ... more >>>

The celebrated $\mathbf{IP}=\mathbf{PSPACE}$ Theorem gives an efficient interactive proof for any bounded-space algorithm. In this work we study interactive proofs for non-deterministic bounded space computations. While Savitch's Theorem shows that nondeterministic bounded-space algorithms can be simulated by deterministic bounded-space algorithms, this simulation has a quadratic overhead. We give interactive protocols ... more >>>

The leading technical approach in uniform hardness-to-randomness in the last two decades faced several well-known barriers that caused results to rely on overly strong hardness assumptions, and yet still yield suboptimal conclusions.

In this work we show uniform hardness-to-randomness results that *simultaneously break through all of the known barriers*. Specifically, ... more >>>

Collision-resistant hash functions (CRH) are a fundamental and ubiquitous cryptographic primitive. Several recent works have studied a relaxation of CRH called t-way multi-collision-resistant hash functions (t-MCRH). These are families of functions for which it is computationally hard to find a t-way collision, even though such collisions are abundant (and even ... more >>>

The inner product function $\langle x,y \rangle = \sum_i x_i y_i \bmod 2$ can be easily computed by a (linear-size) ${AC}^0(\oplus)$ circuit: that is, a constant depth circuit with AND, OR and parity (XOR) gates. But what if we impose the restriction that the parity gates can only be on ... more >>>

The polarization lemma for statistical distance ($\mathrm{SD}$), due to Sahai and Vadhan (JACM, 2003), is an efficient transformation taking as input a pair of circuits $(C_0,C_1)$ and an integer $k$ and outputting a new pair of circuits $(D_0,D_1)$ such that if $\mathrm{SD}(C_0,C_1)\geq\alpha$ then $\mathrm{SD}(D_0,D_1) \geq 1-2^{-k}$ and if $\mathrm{SD}(C_0,C_1) \leq ... more >>>