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Public-key cryptography from different assumptions

Public-key cryptography from different assumptions,10.1145/1806689.1806714,Benny Applebaum,Boaz Barak,Avi Wigderson

Public-key cryptography from different assumptions   (Citations: 5)
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Conference: ACM Symposium on Theory of Computing - STOC , pp. 171-180, 2010
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    • ...Applebaum, Barak, and Wigderson [2] prove that, when based on dparity blowup predicates, the output of Goldreich’s function is pseudorandom against linear functions, low-degree polynomials, and constant-depth circuits...
    • ...Applebaum, Barak, and Wigderson [2] showed that the output of Goldreich’s function based on such predicates is pseudorandom against linear functions, low-degree polynomials, and constant-depth circuits...

    Andrej Bogdanovet al. Input Locality and Hardness Amplification

    • ...In particular, generalizing our proposal to functions with m = O(n) output bits (rather than n output bits), Bogdanov and Qiao showed [6] that a necessary requirement for security is using a balanaced predicate P (i.e., P such that |{z ∈{ 0, 1} � : P (z )=1 }| =2 � −1 ). The use of balanaced predicates is also advocated in [1,7]...

    Oded Goldreich. Candidate One-Way Functions Based on Expander Graphs

    • ...This was proposed by Applebaum, Barak and Wigderson [5] as a suitable choice of f following some earlier attacks on Goldreich’s generator for “structured” f ’s (Bogdanov and Qiao [9])...
    • ...Applebaum et al. [5] proposed the“DSF assumption” and showed how to use it (with other assumptions) to build public-key cryptosystems...
    • ...When m = n this is conjectured by Goldreich [12], but in [5] m is required to be super-linear...

    Sanjeev Aroraet al. New Algorithms for Learning in Presence of Errors

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