Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding

Ben–Sasson, Eli; Goldreich, Oded; Harsha, Prahladh; Sudan, Madhu; Vadhan, Salil

doi:10.1137/s0097539705446810

Cited by 188 publications

(275 citation statements)

References 51 publications

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“…In the exact pattern matching setting, the algorithm of Freedman, Ishai, Pinkas and Reingold [13] achieves polylogarithmic overhead in m and n and polynomial overhead in security parameters in the honest-but-curious setting. Using efficient arguments [17,18] with the modern probabilistically checkable proofs (PCPs) of proximity [19], one can extend (at least asymptotically) their results to the malicious (static corruption) model. However, the protocol in [13] works only for exact matching and does not address more general problems, including singlecharacter wildcards and substring matching, which are the main focus of our work.…”

Section: Comparison To Previous Workmentioning

confidence: 99%

5PM: Secure Pattern Matching

Baron

Defrawy

Minkovich

et al. 2012

Lecture Notes in Computer Science

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Abstract. In this paper we consider the problem of secure pattern matching that allows singlecharacter wildcards and substring matching in the malicious (stand-alone) setting. Our protocol, called 5PM, is executed between two parties: Server, holding a text of length n, and Client, holding a pattern of length m to be matched against the text, where our notion of matching is more general and includes non-binary alphabets, non-binary Hamming distance and non-binary substring matching.5PM is the first secure expressive pattern matching protocol designed to optimize round complexity by carefully specifying the entire protocol round by round. In the malicious model, 5PM requires O((m + n)k 2 ) bandwidth and O(m + n) encryptions, where m is the pattern length and n is the text length. Further, 5PM can hide pattern size with no asymptotic additional costs in either computation or bandwidth. Finally, 5PM requires only two rounds of communication in the honest-but-curious model and eight rounds in the malicious model. Our techniques reduce pattern matching and generalized Hamming distance problems to a novel linear algebra formulation that allows for generic solutions based on any additively homomorphic encryption. We believe our efficient algebraic techniques are of independent interest.

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Section: Comparison To Previous Workmentioning

confidence: 99%

5PM: Secure Pattern Matching

Baron

Defrawy

Minkovich

et al. 2012

Lecture Notes in Computer Science

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show abstract

“…More specifically, we would like to construct a "robust" verifier in N C 0 for the computation of the original circuit, such that if an error is detected in the computation, then most of the circuit's output are set to 0. Fortunately, the PCPP (PCP of Proximity) Theorem [4] provides us with exactly such a verifier. Informally, in a PCPP for an NP language L, the verifier is given oracle access to a PCP π and is also given oracle access to an instance z.…”

Section: Our Techniquesmentioning

confidence: 99%

“…In this section, we present necessary preliminaries on PCP of proximities (denoted by PCPP), and state the efficient PCPP theorem of [4]. A PCP of proximity is a relaxation of a standard PCP, that only verifies that the input is close to an element of the language.…”

Section: Pcp Of Proximitymentioning

confidence: 99%

“…We call r the randomness complexity, q the query complexity, and d the decision complexity of V . Definition 4 (PCPP verifier for a pair language [4]). For functions s, δ : N → [0, 1], a verifier V is a probabilistically checkable proof of proximity (PCPP) system for a pair language L with proximity parameter δ and soundness error s, if the following two conditions hold for every pair of strings (a, z):…”

Section: Definition 3 (Pcp Verifiers)mentioning

confidence: 99%

“…We mention that [4] does not discuss the complexity of constructing the PCPP proof, but the efficiency follows by a close inspection of their construction.…”

Section: Definition 3 (Pcp Verifiers)mentioning

confidence: 99%

See 2 more Smart Citations

Securing Circuits against Constant-Rate Tampering

Dachman-Soled

Kalai

2012

Lecture Notes in Computer Science

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Abstract. We present a compiler that converts any circuit into one that remains secure even if a constant fraction of its wires are tampered with. Following the seminal work of Ishai et al. (Eurocrypt 2006), we consider adversaries who may choose an arbitrary set of wires to corrupt, and may set each such wire to 0 or to 1, or may toggle with the wire. We prove that such adversaries, who continuously tamper with the circuit, can learn at most logarithmically many bits of secret information (in addition to black-box access to the circuit). Our results are information theoretic.

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Robust locally testable codes and products of codes

Ben–Sasson¹,

Sudan²

2006

Random Struct Algorithms

Self Cite

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We continue the investigation of locally testable codes, i.e., error-correcting codes for whom membership of a given word in the code can be tested probabilistically by examining it in very few locations. We give two general results on local testability: First, motivated by the recently proposed notion of robust probabilistically checkable proofs, we introduce the notion of robust local testability of codes. We relate this notion to a product of codes introduced by Tanner, and show a very simple composition lemma for this notion. Next, we show that codes built by tensor products can be tested robustly and somewhat locally, by applying a variant of a test and proof technique introduced by Raz and Safra in the context of testing low-degree multivariate polynomials (which are a special case of tensor codes).Combining these two results gives us a generic construction of codes of inverse polynomial rate, that are testable with poly-logarithmically many queries. We note these locally testable tensor codes can be obtained from any linear error correcting code with good distance. Previous results on local testability, albeit much stronger quantitatively, rely heavily on algebraic properties of the underlying codes.

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Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding

Cited by 188 publications

References 51 publications

5PM: Secure Pattern Matching

5PM: Secure Pattern Matching

Securing Circuits against Constant-Rate Tampering

Robust locally testable codes and products of codes

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