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A natural encoding scheme proved probabilistic polynomial complete

1983
*
Theoretical Computer Science
*

We

doi:10.1016/0304-3975(83)90004-x
fatcat:y4fzxxpfmnao5bqs5qcfmevmgu
*prove**a**natural**encoding**scheme*to be intractable (by showing it UR-*complete*,*a*technique which may be used when 21 problem does not yield to*a*proof of NP-*completeness*). ... Our result suggests that PR-*completeness*may be*a*more widely applicable technique than WC'S previously believed.*A*natual*encoding**scheme*29.7 ... Manuel Blum. who very adroitly steered us out of*a*dull line of research, and also taught us*a*simple and elegant method of exposition that should be*a*guiding principle in all our future ...##
###
A natural encoding scheme proved probabilistic polynomial complete

1982
*
23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)
*

We

doi:10.1109/sfcs.1982.54
dblp:conf/focs/VaziraniV82
fatcat:dwnaogim2bax7nd6lrfkz4moi4
*prove**a**natural**encoding**scheme*to be intractable (by showing it UR-*complete*,*a*technique which may be used when 21 problem does not yield to*a*proof of NP-*completeness*). ... Our result suggests that PR-*completeness*may be*a*more widely applicable technique than WC'S previously believed.*A*natual*encoding**scheme*29.7 ... Manuel Blum. who very adroitly steered us out of*a*dull line of research, and also taught us*a*simple and elegant method of exposition that should be*a*guiding principle in all our future ...##
###
A Complete Public-Key Cryptosystem

2009
*
Groups - Complexity - Cryptology
*

We present

doi:10.1515/gcc.2009.1
fatcat:xhqruesu6ba63oxpimdqjtemti
*a*cryptosystem which is*complete*for the class of*probabilistic*public-key cryptosystems with bounded error. ... Besides traditional encryption*schemes*such as RSA and El Gamal, this class contains*probabilistic*encryption of Goldwasser-Micali as well as Ajtai-Dwork and NTRU cryptosystems. ... As*complete*cryptographic primitives are the*natural*bridges from cryptography to complexity theory, our successful attempt to construct*a**complete*cryptosystem suggests that*probabilistic*encryption*schemes*...##
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Adapting the Weaknesses of the Random Oracle Model to the Generic Group Model
[chapter]

2002
*
Lecture Notes in Computer Science
*

*encoding*function (or one drawn from

*a*specific set of

*encoding*functions). ... This paper presents results that show that there exist problems in that are provably hard in the generic group model but easy to solve whenever the random

*encoding*function is replaced with

*a*specific ...

*A*generic algorithm is

*a*

*probabilistic*,

*polynomial*-time Turing machine M that takes representations of group elements σ(x 1 ), . . . , σ(x m ) as inputs. ...

##
###
Cryptography and Algorithmic Randomness
[article]

2013
*
arXiv
*
pre-print

In the random oracle model, the cryptographic hash function used in

arXiv:1305.2391v1
fatcat:etmw4pbhwnaivivd4yntzqgi6u
*a*cryptographic*scheme*is formulated as*a*random variable uniformly distributed over all possibility of the function, called the random ... In modern cryptography, the random oracle model is widely used as an imaginary framework in which the security of*a*cryptographic*scheme*is discussed. ... Normally,*a**probabilistic*(uniform)*polynomial*-time Turing machine is called*a**probabilistic**polynomial*-time adversary when it is used as an adversary against*a*cryptographic*scheme*. ...##
###
Time-Lock Puzzles from Randomized Encodings

2016
*
Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16
*

Finally, generalizing the above, we construct other types of puzzles such as proofs of work from randomized

doi:10.1145/2840728.2840745
dblp:conf/innovations/BitanskyG0PVW16
fatcat:fu7hh7gjkrhkpc3rv5ajyon2we
*encodings*and*a*suitable worst-case hardness assumption (that is necessary for such puzzles to ...*A*sender can quickly generate*a*puzzle with*a*solution s that remains hidden until*a*moderately large amount of time t has elapsed. ...*A*.4.1 Proof of Theorem*A*.4 The*completeness*and efficiency properties of the puzzle follow directly from the*completeness*and efficiency properties of the message-hiding*encoding**scheme*. ...##
###
Author index volume 24 (1983)

1983
*
Theoretical Computer Science
*

Vazirani,

doi:10.1016/0304-3975(83)90011-7
fatcat:uxvhuif7dzayjmstxo3vsfnady
*A**natural**encoding**scheme**proved**probabilistic**polynomial**complete*Vazirani, V.V., see U.V. ... ., The time-precision tradeoff problem on on-line*probabilistic*Turing machines Wedde, H., An iterative and starvation-free solution for*a*general class of distributed control problems based on ...##
###
The Usefulness of Sparsifiable Inputs: How to Avoid Subexponential iO
[article]

2018
*
IACR Cryptology ePrint Archive
*

As

dblp:journals/iacr/AgrikolaCH18
fatcat:rkoddbxhqba5dnkpidjdnrczcy
*a*result, we obtain*a*variant of piO which allows to obfuscate*a*large class of*probabilistic*programs, from*polynomially*secure indistinguishability obfuscation and extremely lossy functions. ... with threshold decryption, an encryption*scheme*secure under arbitrary key-dependent messages,*a*spooky encryption*scheme*for all circuits,*a*function secret sharing*scheme*with additive reconstruction ... We outline*a**natural*approach to achieve this. ...##
###
Other Complexity Classes and Measures
[chapter]

1998
*
Algorithms and Theory of Computation Handbook
*

Some

doi:10.1201/9781420049503-c30
fatcat:gwoukqhjy5gsjlwxfoxcdojwzm
*natural*problems seem not to be*complete*for any of the complexity classes we have seen so far. ... Also inside the*polynomial*hierarchy is the important class BPP of problems that can be solved efficiently and reliably by*probabilistic*algorithms, to which we now turn. ... It is*natural*to ask whether all NP-*complete*optimization problems have polynomialtime approximation*schemes*. ...##
###
Other Complexity Classes and Measures
[chapter]

2009
*
Algorithms and Theory of Computation Handbook, Second Edition, Volume 1
*

Some

doi:10.1201/9781584888239-c24
fatcat:hztj575iznhqdpdwcnjx5j5fdq
*natural*problems seem not to be*complete*for any of the complexity classes we have seen so far. ... Also inside the*polynomial*hierarchy is the important class BPP of problems that can be solved efficiently and reliably by*probabilistic*algorithms, to which we now turn. ... It is*natural*to ask whether all NP-*complete*optimization problems have polynomialtime approximation*schemes*. ...##
###
Computationally Private Randomizing Polynomials and Their Applications
[chapter]

2014
*
Information Security and Cryptography
*

Randomizing

doi:10.1007/978-3-642-17367-7_5
fatcat:vatwybrubzcxzmhr5xy67lu2n4
*polynomials*allow representing*a*function f (x) by*a*low-degree randomized mappingf (x, r) whose output distribution on an input x is*a*randomized*encoding*of f (x). ...*encoding*of f (x). ... More formally,*a*NIZK (with an efficient prover) for an NP relation R(x, w) is*a*pair of*probabilistic**polynomial*-time algorithms (P, V ) with the following properties: • (*Completeness*) for every (x, w ...##
###
Graded Encoding Schemes from Obfuscation
[chapter]

2018
*
Lecture Notes in Computer Science
*

To introduce

doi:10.1007/978-3-319-76581-5_13
fatcat:bz4uctwmh5cb5lehkhvw7if63a
*a*graded structure, we develop*a*new view of*encodings*at different levels as*polynomials*of different degrees. ... We construct*a*graded*encoding**scheme*(GES), an approximate form of graded multilinear maps. ... The*encodings*of AFHLP can be viewed as level-1*encodings*in our*scheme*(with linear*polynomials*P ). Adding*encodings*. ...##
###
Probabilistic Recursion Theory and Implicit Computational Complexity
[chapter]

2014
*
Lecture Notes in Computer Science
*

We show that

doi:10.1007/978-3-319-10882-7_7
fatcat:wi2zcjjutjeexfe7cwy3e56ygq
*probabilistic*computable functions, i.e., those functions outputting distributions and computed by*probabilistic*Turing machines, can be characterized by*a**natural*generalization of Church ... The obtained algebra, following Leivant, can be restricted so as to capture the notion of*a*polytime sampleable distribution,*a*key concept in average-case complexity and cryptography. ... Immediate from Theorem 4 and Proposition 11. 2*A*more direct way to*prove*polytime*completeness*consists in showing how single-tape PTMs can be*encoded*into predicative recurrence. ...##
###
Probabilistic Recursion Theory and Implicit Computational Complexity

2014
*
Scientific Annals of Computer Science
*

We show that

doi:10.7561/sacs.2014.2.177
fatcat:whd4wlyi7jcdpljt6ekodurize
*probabilistic*computable functions, i.e., those functions outputting distributions and computed by*probabilistic*Turing machines, can be characterized by*a**natural*generalization of Church ... The obtained algebra, following Leivant, can be restricted so as to capture the notion of*a*polytime sampleable distribution,*a*key concept in average-case complexity and cryptography. ... Immediate from Theorem 4 and Proposition 11. 2*A*more direct way to*prove*polytime*completeness*consists in showing how single-tape PTMs can be*encoded*into predicative recurrence. ...##
###
Computational Complexity of Problems on Probabilistic Grammars and Transducers
[chapter]

2000
*
Lecture Notes in Computer Science
*

In this paper we

doi:10.1007/978-3-540-45257-7_2
fatcat:errugei3c5c5loz3edfdu2e3km
*prove*that the problem is NP-hard and does not allow for*a**Polynomial*Time Approximation*Scheme*. The result extends to Stochastic Regular Syntax-Directed Translation*Schemes*. ... Computing the probability of parsing*a*given string or its most probable parse with Stochastic Regular Grammars can be performed in linear time. ... optimization problems do not admit*polynomial*approximation*schemes*. ...
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