Chapter 4 A Status Report on the P Versus NP Question

Allender, Eric

doi:10.1016/s0065-2458(09)01204-2

Cited by 3 publications

(1 citation statement)

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“…The computational security relies on unproven assumptions, but the information-theoretic security does not require such assumptions. Any unconditional proof for computationally secure cryptographic schemes requires proving that P = N P , which is still an unsolved problem in computer science [120][121][122], but may be proved in the future. However, the information-theoretic security enforces some requirements which affects the practicability of a cryptographic scheme.…”

Section: Information-theoretic Vs Computational Securitymentioning

confidence: 99%

Security Protocols in a Nutshell

Toorani¹

2016

Preprint

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Security protocols are building blocks in secure communications. They deploy some security mechanisms to provide certain security services. Security protocols are considered abstract when analyzed, but they can have extra vulnerabilities when implemented. This manuscript provides a holistic study on security protocols. It reviews foundations of security protocols, taxonomy of attacks on security protocols and their implementations, and different methods and models for security analysis of protocols. Specifically, it clarifies differences between information-theoretic and computational security, and computational and symbolic models. Furthermore, a survey on computational security models for authenticated key exchange (AKE) and password-authenticated key exchange (PAKE) protocols, as the most important and well-studied type of security protocols, is provided.

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Section: Information-theoretic Vs Computational Securitymentioning

confidence: 99%

Security Protocols in a Nutshell

Toorani¹

2016

Preprint

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$$P\mathop{ =}\limits^{?}NP$$

Aaronson

2016

Open Problems in Mathematics

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A non-canonical example to support P is not equal to NP

Yang

2011

Trans. Tianjin Univ.

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Abstract：The more unambiguous statement of the P versus NP problem and the judgement of its hardness, are the key ways to find the full proof of the P versus NP problem. There are two sub-problems in the P versus NP problem. The first is the classifications of different mathematical problems (languages), and the second is the distinction between a non-deterministic Turing machine (NTM) and a deterministic Turing machine (DTM). The process of an NTM can be a power set of the corresponding DTM, which proves that the states of an NTM can be a power set of the corresponding DTM. If combining this viewpoint with Cantor's theorem, it is shown that an NTM is not equipotent to a DTM. This means that "generating the power set P(A) of a set A" is a non-canonical example to support that P is not equal to NP.

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Chapter 4 A Status Report on the P Versus NP Question

Cited by 3 publications

References 93 publications

Security Protocols in a Nutshell

Security Protocols in a Nutshell

$$P\mathop{ =}\limits^{?}NP$$

A non-canonical example to support P is not equal to NP

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