The computational SLR: a logic for reasoning about computational indistinguishability

Computational indistinguishability is a notion in complexity-theoretic cryptography and is used to define many security criteria. However, in traditional cryptography, proving computational indistinguishability is usually informal and becomes error-prone when cryptographic constructions are complex. This paper presents a formal proof system based on an extension of Hofmann's SLR language, which can capture probabilistic polynomial-time computations through typing and is sufficient for expressing cryptographic constructions. In particular, we define rules that directly justify the computational indistinguishability between programs, and then prove that these rules are sound with respect to the set-theoretic semantics, and thus the standard definition of security. We also show that it is applicable in cryptography by verifying, in our proof system, Goldreich and Micali's construction of a pseudorandom generator, and the equivalence between next-bit unpredictability and pseudorandomness.

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The Circuit Value Problem

Limits to Parallel Computation ◽

10.1093/oso/9780195085914.003.0010 ◽

1995 ◽

Author(s):

Raymond Greenlaw ◽

H. James Hoover ◽

Walter L. Ruzzo

Keyword(s):

Turing Machine ◽

Polynomial Time ◽

Linear Time ◽

Random Access ◽

Formal Proof ◽

Problem Definition ◽

Topological Order ◽

Language L ◽

Deterministic Turing Machine ◽

Definition Of

In this chapter we return to the Circuit Value Problem, introduced in Section 4.2. First, we will give the formal proof of Theorem 4.2.2 that CVP is P-complete, which we only sketched previously. Then we will show that a number of useful variants and restricted versions of CVP are also P-complete. Recall the definition of the Circuit Value Problem (Definition 4.2.1) in which given an encoding ᾱ of a Boolean circuit α, a designated output y , and values for the inputs x1,..., xn, we ask if output y of α is TRUE. To show CVP is P-complete under ≤mNC1 reducibility requires showing CVP is in P, and that each language L in P is ≤mNC1 reducible to CVP. It is easy to see that given the encoding ᾱ of a circuit and the values of its inputs, one can compute the value of each gate in a number of steps that is polynomial in the size of α. On a random access machine this can be done in linear time by considering the gates in topological order (which also can be computed in linear time; see Gormen, Leiserson, and Rivest [70], for example). On a deterministic Turing machine the process is a bit more clumsy but can still be done in polynomial time. Pippenger shows that even time O(nlogn) suffices, where n is the length of the encoding of α [284]. Thus, we have the following lemma. Lemma 6.1.1 The Circuit Value Problem is in P. The more difficult step in proving that CVP is P-complete under ≤mNC1 reducibility is showing there is a ≤mNC1 reduction from each language in P to CVP. Ladner proved this by simulating Turing machines with circuits. The idea is as follows. First, recall that for each language L in P, there is a 1-tape Turing machine M that on input x = x1,..., xn halts in time t(n) = nO(1) with output equal to 1 if and only if x is in L. Note that, for each n, the machine M uses at most t(n) space on its tape.

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Random Linear Network Coding with Probabilistic Polynomial-Time Wiretap Adversary

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.556-562.6354 ◽

2014 ◽

Vol 556-562 ◽

pp. 6354-6357

Author(s):

Zhi Wen Hu ◽

Xian Ming Wang ◽

Tao Tao Lv ◽

Shan Shan Zhao ◽

Rui Jun Jing

Keyword(s):

Network Coding ◽

Polynomial Time ◽

Network Capacity ◽

Single Source ◽

Secret Key ◽

Linear Network ◽

Pseudorandom Generator ◽

Linear Network Coding ◽

Random Linear Network Coding ◽

Probabilistic Polynomial Time

Linear network coding can achieve the network capacity in the single source multicast case. For the single source multicast network with wiretap adversary, the paper of Cai and Yeung constructs an information-secure linear coding which tightly achieves the transmitting rate upper bound , where is the capacity of the network and is the maximum number of edges the adversary can wiretap. The current paper considers the cryptographic security for the messages in the random linear network coding setting. The indistinguishability under chosen-message-attack (or CMA-Security) from probabilistic polynomial-time (PPT) wiretap adversary is defined. With a pseudorandom generator against linear cryptanalysis, an end-to-end protocol is constructed for multicast network using random linear network coding. When the adversary wiretap less than edges, the protocol is CMA-Secure and attains transmitting rate approaching the network’s capacity from below, asymptotically in the expanding ratio (i.e., length of output string/length of input string) of the pseudorandom generator. Compared with secret-key based scheme, no secret is needed by the receiver nodes, which means the key managing issues for dynamic networks would never come up.

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A practical metric for melanopic metrology

Lighting Research and Technology ◽

10.1177/1477153518824147 ◽

2019 ◽

Vol 51 (8) ◽

pp. 1178-1191 ◽

Cited By ~ 4

Author(s):

SM Berman ◽

RD Clear

Keyword(s):

Ganglion Cell ◽

Retinal Ganglion Cell ◽

Vision Research ◽

Spectral Response ◽

Retinal Ganglion ◽

Standard Definition ◽

Standard Unit ◽

Vision Science ◽

The Past ◽

Definition Of

Over the past decade, there has been a growing interest in lighting research on the effects of the recently discovered melanopsin receptor (also referred to as the intrinsically photosensitive retinal ganglion cell) and its impacts on health and vision. Presently, there is not a generally accepted metrology for dealing with the spectral response of the melanopsin receptor as applied to both lighting and vision research. A proposition to handle this issue from a vision science perspective has been presented in 2014 in the journal Trends in Neurosciences and from a more lighting perspective in 2017 in Lighting Research and Technology. These propositions are complex, and do not retain the CIE standard definition of a lumen. In this paper, we propose an approach based on effective watts and melanopic/photopic ratios that is both simpler and more closely aligned with CIE standard unit definitions. In addition, we include some practical examples of how such ratios are accessible now, and can be used for both lighting and vision research as well as applications.

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ON THE NOTION OF CANONICAL DERIVATIONS FROM OPEN ASSUMPTIONS AND ITS ROLE IN PROOF-THEORETIC SEMANTICS

The Review of Symbolic Logic ◽

10.1017/s1755020315000027 ◽

2015 ◽

Vol 8 (2) ◽

pp. 296-305 ◽

Cited By ~ 7

Author(s):

NISSIM FRANCEZ

Keyword(s):

Natural Deduction ◽

Proof System ◽

Logical Constants ◽

Local Completeness ◽

Definition Of ◽

The Impact

AbstractThe paper proposes an extension of the definition of a canonical proof, central to proof-theoretic semantics, to a definition of a canonical derivation from open assumptions. The impact of the extension on the definition of (reified) proof-theoretic meaning of logical constants is discussed. The extended definition also sheds light on a puzzle regarding the definition of local-completeness of a natural-deduction proof-system, underlying its harmony.

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The Humdrum Use of Ultimate Authority: Defining and Analysing Chapter VII Resolutions

Nordic Journal of International Law ◽

10.1163/090273509x12448190941129 ◽

2009 ◽

Vol 78 (3) ◽

pp. 309-342 ◽

Cited By ~ 6

Author(s):

Patrik Johansson

Keyword(s):

Cold War ◽

United Nations ◽

Security Council ◽

Security Council Resolution ◽

Post Cold War ◽

Standard Definition ◽

The Status ◽

Definition Of ◽

The Cold War ◽

Business As Usual

AbstractUnder Chapter VII of the Charter of the United Nations, the Security Council has the unique authority to make decisions that are binding on member states. However, the lack of a standard definition of what makes a Security Council resolution "a Chapter VII resolution" has caused disagreement regarding the status of several resolutions. This is unfortunate as the international community should never have to doubt whether a Security Council resolution is in fact adopted under Chapter VII or not. It is also unnecessary. This article addresses this problem by proposing a definition of Chapter VII resolutions, based on two criteria referred to as "Article 39 determinations" and "Chapter VII decisions". On the basis of the proposed definition, the article describes and analyses a dramatic increase in the use of Chapter VII during the post-Cold War era. It concludes that as Chapter VII has come to constitute the majority of Security Council resolutions in recent years, the resort to Chapter VII no longer signifies exceptional determination and resolve, which it did during the Cold War; instead Chapter VII today implies business as usual. An appendix lists all Chapter VII resolutions from 1946–2008.

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The Standard Definition of Magic Matrix

Advances in Applied Mathematics ◽

10.12677/aam.2021.108282 ◽

2021 ◽

Vol 10 (08) ◽

pp. 2714-2724

Author(s):

兴祥刘

Keyword(s):

Standard Definition ◽

Definition Of

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Comment on a Standard Definition of Response Rates

Journal of Marketing Research ◽

10.2307/3151610 ◽

1984 ◽

Vol 21 (3) ◽

pp. 336 ◽

Cited By ~ 54

Author(s):

Frederick Wiseman ◽

Maryann Billington

Keyword(s):

Response Rates ◽

Standard Definition ◽

Definition Of

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Tongue Thrust: A Point of View

Journal of Speech and Hearing Disorders ◽

10.1044/jshd.4102.172 ◽

1976 ◽

Vol 41 (2) ◽

pp. 172-184 ◽

Cited By ~ 2

Author(s):

Marvin L. Hanson

Keyword(s):

Orthodontic Treatment ◽

Point Of View ◽

Patient Age ◽

Present Evidence ◽

Standard Definition ◽

Myofunctional Therapy ◽

Developmental Factors ◽

Patient Âgé ◽

Definition Of ◽

Tongue Thrust

The purpose of the present paper is to present evidence to support the following hypotheses: (1) there is a relationship between tongue thrust and malocclusion, and it is probably a reciprocal one; (2) tongue thrust may yield spontaneously to nonthrusting patterns; (3) if tongue thrust does not yield spontaneously to nonthrusting patterns, some form of treatment should be considered; (4) if myofunctional therapy is the treatment of choice, its timing with respect to patient age, developmental factors, and orthodontic treatment should be an individual matter. The need for more definitive research is described. In order for such research to be meaningful, a standard definition of tongue thrust is required. Such a definition is proposed.

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