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This essay’s content is rendered by the titles of the successive sections. 1. Effective solvability versus intuitive solvability. — 2. Decidability, i.e. effective solvability, in predicate logic. The speedup phenomenon — 3. Contributions of the second-order logic to the problems of solvability — 4. The infinite progress of science in the light of Turing’s idea of the oracle. The term “oracle” is a technical counterpart of the notion of mathematical intuition.
A more detailed summary can be obtained through juxtaposing the textboxes labelled with letters A...F. Conclusion: in the progress of science an essential role is played by the feedback between intellectual intuitions (intuitive solvability) and algorithmic procedures (effective solvability).
Nested symmetric encryption is a well-known technique for low-latency communication privacy. But just what problem does this technique aim to solve? In answer, we provide a provable-security treatment for onion authenticated-encryption (onion-AE). Extending the conventional notion for authenticated-encryption, we demand indistinguishability from random bits and time-of-exit authenticity verification. We show that the encryption technique presently used in Tor does not satisfy our definition of onion-AE security, but that a construction by , based on a strong, tweakable, wideblock PRP, does do the job. We go on to discuss three extensions of onion-AE, giving definitions to handle inbound flows, immediate detection of authenticity errors, and corrupt ORs.
REFERENCES  COURTOIS, N. T.: : Cryptanalysis of GOST , (a very long extended set of slides about the cryptanalysis of GOST, 2010–2014), http://www.nicolascourtois.com/papers/GOST.pdf ; (An earlier and shorter version was presented at 29C3 Conference at 29th Chaos Communication Congress (29C3), December 27–30, 2012, in Hamburg, Germany).  _____ Decryption oracle slide attacks on T-310 , Cryptologia, 42 (2018), no. 3, 191–204; http://www.tandfonline.com/doi/full/10.1080/01611194.2017.1362062  _____ Data Encryption Standard (DES) (slides used in GA
In order to keep the confidential data in the cloud against unauthorized parties, a cryptographic access control solution based on Attribute-Based Encryption (ABE) and Identity-Based Signature (IBS) is introduced in this paper. Under the premise that cloud service provider is untrustful, the proposed scheme can ensure the data security of the cloud storage system in an open environment, as well as reduce the complexity of management. Analysis and experimental results show that the scheme can be semantically secure against adaptive chosen ciphertext attacks under the random oracle model. Our concrete access control scheme can enhance the efficiency of the cloud to a certain extent.