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We show the following reductions from the learning with errors problem (LWE) to the learning with rounding problem (LWR): (1) Learning the secret and (2) distinguishing samples from random strings is at least as hard for LWR as it is for LWE for efficient algorithms if the number of samples is no larger than O(q/Bp), where q is the LWR modulus, p is the(More)
We consider the problem of extracting entropy by sparse transformations, namely functions with a small number of overall input-output dependencies. In contrast to previous works, we seek extractors for essentially all the entropy without any assumption on the underlying distribution beyond a min-entropy requirement. We give two simple constructions of(More)
Rational proofs, recently introduced by Azar and Micali (STOC 2012), are a variant of interactive proofs in which the prover is neither honest nor malicious, but rather rational. The advantage of rational proofs over their classical counterparts is that they allow for extremely low communication and verification time. Azar and Micali demonstrated their(More)
We revisit the security of cryptographic primitives in the random-oracle model against attackers having a bounded amount of auxiliary information about the random oracle. This situation arises most naturally when an attacker carries out offline preprocessing to generate state (namely, auxiliary information) that is later used as part of an on-line attack,(More)
BACKGROUND The increase in multiple antimicrobial-resistant bacteria seriously threatens global public health. Novel effective strategies are urgently needed. l-Serine was reported as the most effective amino acid inhibitor against bacterial growth and can sensitize Escherichia coli cells to gentamicin. It is currently unknown whether l-serine affects other(More)
Pseudorandom functions (PRFs) play a fundamental role in symmetric-key cryptography. However, they are inherently complex and cannot be implemented in the class AC<sup>0</sup> (MOD<sub>2</sub>). Weak pseudorandom functions (weak PRFs) do not suffer from this complexity limitation, yet they suffice for many cryptographic applications. We study the minimal(More)
We give an efficient structural decomposition theorem for formulas that depends on their negation complexity and demonstrate its power with the following applications. We prove that every formula that contains t negation gates can be shrunk using a random restriction to a formula of size O(t) with the shrinkage exponent of monotone formulas. As a result,(More)
Bacterial persisters, usually slow-growing, non-replicating cells highly tolerant to antibiotics, play a crucial role contributing to the recalcitrance of chronic infections and treatment failure. Understanding the molecular mechanism of persister cells formation and maintenance would obviously inspire the discovery of new antibiotics. The significant(More)
Rational proofs, introduced by Azar and Micali (STOC 2012) are a variant of interactive proofs in which the prover is neither honest nor malicious, but rather rational. The advantage of rational proofs over their classical counterparts is that they allow for extremely low communication and verification time. In recent work, Guo et al. (ITCS 2014)(More)