scholarly journals Query complexity of approximate equilibria in anonymous games

2017 ◽  
Vol 90 ◽  
pp. 80-98 ◽  
Author(s):  
Paul W. Goldberg ◽  
Stefano Turchetta
Keyword(s):  
Query Complexity ◽  
Anonymous Games

scholarly journals Constant Rate PCPs for Circuit-SAT with Sublinear Query Complexity

2016 ◽  
Vol 63 (4) ◽  
pp. 1-57 ◽  
Author(s):  
Eli Ben-Sasson ◽  
Yohay Kaplan ◽  
Swastik Kopparty ◽  
Or Meir ◽  
Henning Stichtenoth
Keyword(s):  
Query Complexity ◽  
Constant Rate

scholarly journals An Exponential Separation Between MA and AM Proofs of Proximity

2021 ◽  
Vol 30 (2) ◽  
Author(s):  
Tom Gur ◽  
Yang P. Liu ◽  
Ron D. Rothblum
Keyword(s):  
Quantum Information ◽  
Lower Bound ◽  
Recent Result ◽  
Query Complexity ◽  
Random String ◽  
Natural Property ◽  
Public And Private ◽  
Alternate Proof ◽  
Interactive Proofs ◽  
Exponential Separation

AbstractInteractive proofs of proximity allow a sublinear-time verifier to check that a given input is close to the language, using a small amount of communication with a powerful (but untrusted) prover. In this work, we consider two natural minimally interactive variants of such proofs systems, in which the prover only sends a single message, referred to as the proof. The first variant, known as -proofs of Proximity (), is fully non-interactive, meaning that the proof is a function of the input only. The second variant, known as -proofs of Proximity (), allows the proof to additionally depend on the verifier's (entire) random string. The complexity of both s and s is the total number of bits that the verifier observes—namely, the sum of the proof length and query complexity. Our main result is an exponential separation between the power of s and s. Specifically, we exhibit an explicit and natural property $$\Pi$$ Π that admits an with complexity $$O(\log n)$$ O ( log n ) , whereas any for $$\Pi$$ Π has complexity $$\tilde{\Omega}(n^{1/4})$$ Ω ~ ( n 1 / 4 ) , where n denotes the length of the input in bits. Our lower bound also yields an alternate proof, which is more general and arguably much simpler, for a recent result of Fischer et al. (ITCS, 2014). Also, Aaronson (Quantum Information & Computation 2012) has shown a $$\Omega(n^{1/6})$$ Ω ( n 1 / 6 ) lower bound for the same property $$\Pi$$ Π .Lastly, we also consider the notion of oblivious proofs of proximity, in which the verifier's queries are oblivious to the proof. In this setting, we show that s can only be quadratically stronger than s. As an application of this result, we show an exponential separation between the power of public and private coin for oblivious interactive proofs of proximity.

scholarly journals Exact quantum algorithms have advantage for almost all Boolean functions

2015 ◽  
pp. 435-452
Author(s):  
Andris Ambainis ◽  
Jozef Gruska ◽  
Shenggen Zheng
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Query Complexity ◽  
Exact Quantum ◽  
Quantum Query Complexity ◽  
Almost All ◽  
Quantum Query

It has been proved that almost all n-bit Boolean functions have exact classical query complexity n. However, the situation seemed to be very different when we deal with exact quantum query complexity. In this paper, we prove that almost all n-bit Boolean functions can be computed by an exact quantum algorithm with less than n queries. More exactly, we prove that ANDn is the only n-bit Boolean function, up to isomorphism, that requires n queries.

scholarly journals Cryptanalysis of PMACx, PMAC2x, and SIVx

2017 ◽  
pp. 162-176
Author(s):  
Kazuhiko Minematsu ◽  
Tetsu Iwata
Keyword(s):  
Provable Security ◽  
Block Cipher ◽  
Query Complexity ◽  
Block Length ◽  
Encryption Scheme ◽  
Authenticated Encryption ◽  
Pseudorandom Functions ◽  
Tweakable Block Cipher ◽  
Deterministic Authenticated Encryption ◽  
Provably Secure

At CT-RSA 2017, List and Nandi proposed two variable input length pseudorandom functions (VI-PRFs) called PMACx and PMAC2x, and a deterministic authenticated encryption scheme called SIVx. These schemes use a tweakable block cipher (TBC) as the underlying primitive, and are provably secure up to the query complexity of 2n, where n denotes the block length of the TBC. In this paper, we falsify the provable security claims by presenting concrete attacks. We show that with the query complexity of O(2n/2), i.e., with the birthday complexity, PMACx, PMAC2x, and SIVx are all insecure.

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