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A natural encoding scheme proved probabilistic polynomial complete

Umesh V. Vazirani, Vijay V. Vazirani
1983 Theoretical Computer Science  
We 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  ... 
doi:10.1016/0304-3975(83)90004-x fatcat:y4fzxxpfmnao5bqs5qcfmevmgu

A natural encoding scheme proved probabilistic polynomial complete

Umesh V. Vazirani, Vijay V. Vazirani
1982 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)  
We 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  ... 
doi:10.1109/sfcs.1982.54 dblp:conf/focs/VaziraniV82 fatcat:dwnaogim2bax7nd6lrfkz4moi4

A Complete Public-Key Cryptosystem

Dima Grigoriev, Edward A. Hirsch, Konstantin Pervyshev
2009 Groups - Complexity - Cryptology  
We present 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  ... 
doi:10.1515/gcc.2009.1 fatcat:xhqruesu6ba63oxpimdqjtemti

Adapting the Weaknesses of the Random Oracle Model to the Generic Group Model [chapter]

Alexander W. Dent
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.  ... 
doi:10.1007/3-540-36178-2_6 fatcat:qjvslo3syve2hotym2qlak4xru

Cryptography and Algorithmic Randomness [article]

Kohtaro Tadaki, Norihisa Doi
2013 arXiv   pre-print
In the random oracle model, the cryptographic hash function used in 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.  ... 
arXiv:1305.2391v1 fatcat:etmw4pbhwnaivivd4yntzqgi6u

Time-Lock Puzzles from Randomized Encodings

Nir Bitansky, Shafi Goldwasser, Abhishek Jain, Omer Paneth, Vinod Vaikuntanathan, Brent Waters
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 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.  ... 
doi:10.1145/2840728.2840745 dblp:conf/innovations/BitanskyG0PVW16 fatcat:fu7hh7gjkrhkpc3rv5ajyon2we

Author index volume 24 (1983)

1983 Theoretical Computer Science  
Vazirani, 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  ... 
doi:10.1016/0304-3975(83)90011-7 fatcat:uxvhuif7dzayjmstxo3vsfnady

The Usefulness of Sparsifiable Inputs: How to Avoid Subexponential iO [article]

Thomas Agrikola, Geoffroy Couteau, Dennis Hofheinz
2018 IACR Cryptology ePrint Archive  
As 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.  ... 
dblp:journals/iacr/AgrikolaCH18 fatcat:rkoddbxhqba5dnkpidjdnrczcy

Other Complexity Classes and Measures [chapter]

Eric Allender, Michael Loui, Kenneth Regan
1998 Algorithms and Theory of Computation Handbook  
Some 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.  ... 
doi:10.1201/9781420049503-c30 fatcat:gwoukqhjy5gsjlwxfoxcdojwzm

Other Complexity Classes and Measures [chapter]

Eric Allender, Michael Loui, Kenneth Regan
2009 Algorithms and Theory of Computation Handbook, Second Edition, Volume 1  
Some 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.  ... 
doi:10.1201/9781584888239-c24 fatcat:hztj575iznhqdpdwcnjx5j5fdq

Computationally Private Randomizing Polynomials and Their Applications [chapter]

Benny Applebaum
2014 Information Security and Cryptography  
Randomizing 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  ... 
doi:10.1007/978-3-642-17367-7_5 fatcat:vatwybrubzcxzmhr5xy67lu2n4

Graded Encoding Schemes from Obfuscation [chapter]

Pooya Farshim, Julia Hesse, Dennis Hofheinz, Enrique Larraia
2018 Lecture Notes in Computer Science  
To introduce 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.  ... 
doi:10.1007/978-3-319-76581-5_13 fatcat:bz4uctwmh5cb5lehkhvw7if63a

Probabilistic Recursion Theory and Implicit Computational Complexity [chapter]

Ugo Dal Lago, Sara Zuppiroli
2014 Lecture Notes in Computer Science  
We show that 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.  ... 
doi:10.1007/978-3-319-10882-7_7 fatcat:wi2zcjjutjeexfe7cwy3e56ygq

Probabilistic Recursion Theory and Implicit Computational Complexity

Ugo Dal Lago, Sara Zuppiroli, Maurizio Gabbrielli
2014 Scientific Annals of Computer Science  
We show that 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.  ... 
doi:10.7561/sacs.2014.2.177 fatcat:whd4wlyi7jcdpljt6ekodurize

Computational Complexity of Problems on Probabilistic Grammars and Transducers [chapter]

Francisco Casacuberta, Colin de la Higuera
2000 Lecture Notes in Computer Science  
In this paper we 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.  ... 
doi:10.1007/978-3-540-45257-7_2 fatcat:errugei3c5c5loz3edfdu2e3km
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