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  • 1.
    Goldmann, Mikael
    et al.
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Naslund, M.
    Russell, A.
    Complexity bounds on general hard-core predicates2001In: Journal of Cryptology, ISSN 0933-2790, E-ISSN 1432-1378, Vol. 14, no 3, p. 177-195Article in journal (Refereed)
    Abstract [en]

    A Boolean function b is a hard-core predicate for a one-way function S if b is polynomial-time computable but b(x) is difficult to predict from lf(x). A general one-way function. A seminal result of Goldreich and Levin asserts that the family of parity functions is a general family of hard-core predicates. We show that no general family of hard-core predicates can consist of functions with O(n(1-epsilon)) average sensitivity for any epsilon > 0. As a result, such families cannot consist of functions in AC(0), monotone functions, functions computed by generalized threshold gates, or symmetric d-threshold functions, for d = O(n(1/2-epsilon)) and epsilon > 0.

  • 2.
    Hast, Gustav
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Nearly one-sided tests and the Goldreich-Levin predicate2004In: Journal of Cryptology, ISSN 0933-2790, E-ISSN 1432-1378, Vol. 17, no 3, p. 209-229Article in journal (Refereed)
    Abstract [en]

    We study statistical tests with binary output that rarely outputs one, which we call nearly one-sided statistical tests. We provide an efficient reduction establishing improved security for the Goldreich-Levin hard-core bit against nearly one-sided tests. The analysis is extended to prove the security of the Blum-Micali pseudo-random generator combined with the Goldreich-Levin bit. Finally, some applications where nearly one-sided tests occur naturally are discussed.

  • 3.
    Håstad, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    The security of the IAPM and IACBC modes2007In: Journal of Cryptology, ISSN 0933-2790, E-ISSN 1432-1378, Vol. 20, no 2, p. 153-163Article in journal (Refereed)
    Abstract [en]

    We give new and shorter proofs for message integrity and confidentiality of the IAPM mode and of the IACBC mode proposed by Jutla [6].

  • 4.
    Håstad, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Näslund, Mats
    Practical construction and analysis of pseudo-randomness primitives2008In: Journal of Cryptology, ISSN 0933-2790, E-ISSN 1432-1378, Vol. 21, no 1, p. 1-26Article in journal (Refereed)
    Abstract [en]

    We give a careful, fixed-size parameter analysis of a standard (Blum and Micali in SIAM J. Comput. 13( 4): 850-864, 1984; Goldreich and Levin in Proceedings of 21st ACM Symposium on Theory of Computing, pp. 25-32, 1989) way to form a pseudo-random generator from a one-way function and then pseudo-random functions from said generator (Goldreich et al. in J. Assoc. Comput. Mach. 33( 4): 792-807, 1986) While the analysis is done in the model of exact security, we improve known bounds also asymptotically when many bits are output each round and we find all auxiliary parameters efficiently, giving a uniform result. These optimizations makes the analysis effective even for security parameters/key-sizes supported by typical block ciphers and hash functions. This enables us to construct very practical pseudo-random generators with strong properties based on plausible assumptions.

  • 5. Pietrzak, Krzysztof
    et al.
    Wikström, Douglas
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    Parallel Repetition of Computationally Sound Protocols Revisited2012In: Journal of Cryptology, ISSN 0933-2790, E-ISSN 1432-1378, Vol. 25, no 1, p. 116-135Article in journal (Refereed)
    Abstract [en]

    We prove a negative result concerning error reduction by parallel repetition for computationally sound protocols, e.g., interactive arguments. Our main result is a complete and computationally sound eight round interactive argument for which k-fold parallel repetition does not reduce the error below a constant for any polynomial k. The starting point for our construction is the work of Bellare, Impagliazzo and Naor (FOCS'97). For any fixed k, they construct a four round protocol for which k-fold parallel repetition does not lower the soundness error. The communication complexity of this protocol is linear in k. By using universal arguments due to Barak and Goldreich (CCC 2002), we turn this protocol into an eight-round protocol whose complexity is basically independent of k.

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