Peter Manohar
Email: pmanohar [at] cs [dot] cmu [dot] edu
Office: 9007 Gates Hillman Center
About Me
I am a first year PhD student at Carnegie Mellon University, advised by Venkat Guruswami. I am broadly interested in Complexity Theory and Cryptography, specifically in topics such as probabilistically checkable proofs, property testing, and coding theory.
Prior to CMU, I completed a B.S. in EECS at UC Berkeley, where I was advised by Alessandro Chiesa and Ren Ng.
My research is supported by an NSF fellowship and an ARCS scholarship.


Papers
 On Local Testability in the NonSignaling Setting
Alessandro Chiesa, Peter Manohar, Igor Shinkar
ITCS 2020
Abstract:
Nonsignaling strategies are a generalization of quantum strategies that have been studied in physics for decades, and have recently found applications in theoretical computer science. These applications motivate the study of localtoglobal phenomena for nonsignaling functions.
We prove that lowdegree testing in the nonsignaling setting is possible, assuming that the locality of the nonsignaling function exceeds a threshold. We additionally show that if the locality is below the threshold then the test fails spectacularly, in that there exists a nonsignaling function which passes the test with probability 1 and yet is maximally far from being lowdegree.
Along the way, we present general results about the local testability of linear codes in the nonsignaling setting. These include formulating natural definitions that capture the condition that a nonsignaling function "belongs" to a given code, and characterizing the sets of local constraints that imply membership in the code. We prove these results by formulating a logical inference system for linear constraints on nonsignaling functions that is complete and sound.
Preprint available at [ ECCC].
 Succinct Arguments in the Quantum Random Oracle Model
Alessandro Chiesa, Peter Manohar, Nicholas Spooner
TCC 2019 and QIP 2020
Abstract:
Succinct noninteractive arguments (SNARGs) are highly efficient certificates of membership in nondeterministic languages. Constructions of SNARGs in the random oracle model are widely believed to be postquantum secure, provided the oracle is instantiated with a suitable postquantum hash function. No formal evidence, however, supports this belief.
In this work we provide the first such evidence by proving that the SNARG construction of Micali is unconditionally secure in the quantum random oracle model. We also prove that, analogously to the classical case, the SNARG inherits the zero knowledge and proof of knowledge properties of the PCP underlying the Micali construction. We thus obtain the first zero knowledge SNARG of knowledge (zkSNARK) that is secure in the quantum random oracle model.
Our main tool is a new lifting lemma that shows how, for a rich class of oracle games, we can generically deduce security against quantum attackers by bounding a natural classical property of these games. This means that in order to prove our theorem we only need to establish classical properties about the Micali construction. This approach not only lets us prove postquantum security but also enables us to prove explicit bounds that are tight up to small factors.
Finally, we use our techniques to prove that SNARGs based on interactive oracle proofs (IOPs) with roundbyround soundness are unconditionally secure in the quantum random oracle model. This result establishes the postquantum security of many SNARGs of practical interest.
Full version available at [ ePrint].
 Probabilistic Checking against NonSignaling Strategies from Linearity Testing
Alessandro Chiesa, Peter Manohar, Igor Shinkar
ITCS 2019
Abstract:
Nonsignaling strategies are a generalization of quantum strategies that have been studied in physics over the past three decades. Recently, they have found applications in theoretical computer science, including to proving inapproximability results for linear programming and to constructing protocols for delegating computation. A central tool for these applications is probabilistically checkable proofs (PCPs) that are sound against nonsignaling strategies.
In this paper we prove that the exponentiallength constantquery PCP construction due to Arora et al. (JACM 1998) is sound against nonsignaling strategies.
Our result offers a new lengthvsquery tradeoff when compared to the nonsignaling PCP of Kalai, Raz, and Rothblum (STOC 2013 and 2014) and, moreover, may serve as an intermediate step to a proof of a nonsignaling analogue of the PCP Theorem.
Full version available at [ ECCC].
 Testing Linearity against NonSignaling Strategies
Alessandro Chiesa, Peter Manohar, Igor Shinkar
CCC 2018
Abstract:
Nonsignaling strategies are collections of distributions with certain nonlocal correlations. They have been studied in Physics as a strict generalization of quantum strategies to understand the power and limitations of Nature's apparent nonlocality. Recently, they have received attention in Theoretical Computer Science due to connections to Complexity and Cryptography.
We initiate the study of Property Testing against nonsignaling strategies, focusing first on the classical problem of linearity testing (Blum, Luby, and Rubinfeld; JCSS 1993). We prove that any nonsignaling strategy that passes the linearity test with high probability must be close to a quasidistribution over linear functions.
Quasidistributions generalize the notion of probability distributions over global objects (such as functions) by allowing negative probabilities, while at the same time requiring that local views follow standard distributions (with nonnegative probabilities). Quasidistributions arise naturally in the study of Quantum Mechanics as a tool to describe various nonlocal phenomena.
Our analysis of the linearity test relies on Fourier analytic techniques applied to quasidistributions. Along the way, we also establish general equivalences between nonsignaling strategies and quasidistributions, which we believe will provide a useful perspective on the study of Property Testing against nonsignaling strategies beyond linearity testing.
Full version available at [ ECCC].
 On AxisParallel Tests for Tensor Product Codes
Alessandro Chiesa, Peter Manohar, Igor Shinkar
RANDOM 2017
Abstract:
Many lowdegree tests examine the input function via its restrictions to random hyperplanes of a certain dimension. Examples include the linevsline (Arora, Sudan 2003), planevsplane (Raz, Safra 1997), and cubevscube (Bhangale, Dinur, Navon 2017) tests.
In this paper we study tests that only consider restrictions along axisparallel hyperplanes, which have been studied by Polishchuk and Spielman (1994) and BenSasson and Sudan (2006).
While such tests are necessarily "weaker", they work for a more general class of codes, namely tensor product codes.
Moreover, axisparallel tests play a key role in constructing LTCs with inverse polylogarithmic rate and short PCPs (Polishchuk, Spielman 1994; BenSasson, Sudan 2008; Meir 2010). We present two results on axisparallel tests.
(1) Bivariate lowdegree testing with lowagreement.
We prove an analogue of the Bivariate LowDegree Testing Theorem of Polishchuk and Spielman in the lowagreement regime, albeit with much larger field size. Namely, for the 2wise tensor product of the ReedSolomon code, we prove that for sufficiently large fields, the 2query variant of the axisparallel line test (rowvscolumn test) works for arbitrarily small agreement. Prior analyses of axisparallel tests assumed high agreement, and no results for such tests in the lowagreement regime were known.
Our proof technique deviates significantly from that of Polishchuk and Spielman, which relies on algebraic methods such as Bézout's Theorem, and instead leverages a fundamental result in extremal graph theory by Kövári, Sós, and Turán. To our knowledge, this is the first time this result is used in the context of lowdegree testing.
(2) Improved robustness for tensor product codes.
Robustness is a strengthening of local testability that underlies many applications. We prove that the axisparallel hyperplane test for the mwise tensor product of a linear code with block length n and distance d is Omega(d^m/n^m)robust. This improves on a theorem of Viderman (2012) by a factor of 1/poly(m). While the improvement is not large, we believe that our proof is a notable simplification compared to prior work.
Full version available at [ ECCC].
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