O. Goldreich and V. Rosen. On the Security of Modular Exponentiation with Application to the Construction of Pseudorandom Generators. J. of Cryptology, 16:71--93, 2003. Home/Search Document Details and Download
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An Improved Pseudorandom Generator Based on Hardness of.. - Dedic, Reyzin, Vadhan (2002) (1 citation) (Correct)
....factoring assumption. It outputs more than pn 2 pseudorandom bits per p exponentiations, each with the same base and an exponent shorter than n 2 bits. Our generator is based on results by Hastad, Schrift and Shamir [HSS93] but unlike their generator and its improvement by Goldreich and Rosen [GR00], it does not use hashing or extractors, and is thus simpler and somewhat more e#cient. In addition, we present a general technique that can be used to speed up pseudorandom generators based on iterating one way permutations. We construct our generator by applying this technique to results of ....
....giving a generator that output n 2 #(log n) pseudorandom bits per fixed base modular exponentiation and one hashing. Note that having the same base for each modular exponentiation is important, because it allows for precomputation (as further described in Section 4) Goldreich and Rosen [GR00] further improved this generator by demonstrating, in particular, that one can use exponents of length n 2 instead of full length exponents. However, families of hash functions (or, rather, extractors) were still necessary, thus resulting in a loss of e#ciency of each iteration, and the number of ....
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Oded Goldreich and Vered Rosen. On the security of modular exponentiation with application to the construction of pseudorandom generators. Technical Report 2000/064, Cryptology e-print archive, http://eprint.iacr.org, 2000. Prior version appears in [Ros01].
An Efficient Pseudo-Random Generator with Applications to.. - Damgård, Nielsen (Correct)
....logarithm problem. Later Luby et al. ILL89] used the Goldreich Levin hard core bit theorem[GL89] to show that existence of pseudo random generators follow from existence of any one way functions. Also, more e#cient generators have been proposed, based on specific assumptions, see for instance [GR00,HSS93,Gen00]. In this paper, we propose a new generator based on Paillier s composite degree residuosity assumption (DCRA) This generator expands a uniformly chosen bit string r of length k 2 bits, where k is the security parameter, into a pseudo random bit string of length 2k log 2 (k) using one ....
....This generator expands a uniformly chosen bit string r of length k 2 bits, where k is the security parameter, into a pseudo random bit string of length 2k log 2 (k) using one modular exponentiation. Compared to earlier high expansion rate generators based on assumptions related to factoring [GR00,HSS93], we note the following di#erences: our generator is based on a stronger assumption (DCRA implies that factoring is hard) In return, we get a simpler generator where no hashing is necessary to extract the output (in contrast to [GR00,HSS93] where the computing time spent per output bit is the ....
[Article contains additional citation context not shown here]
Oded Goldreich and Vered Rosen. On the security of modular exponentiation with application to the construction of pseudorandom generators. Cryptology ePrint Archive, record 2000/064, http://eprint.iacr.org/, December 2000.
On the Provable Security of an Efficient RSA-Based.. - Steinfeld, Pieprzyk.. (2006) (Correct)
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O. Goldreich and V. Rosen. On the Security of Modular Exponentiation with Application to the Construction of Pseudorandom Generators. J. of Cryptology, 16:71--93, 2003.
Unknown - Able Secret Shu (Correct)
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O. Goldreich and V. Rosen. On the Security of Modular Exponentiation with Application to the Construction of Pseudorandom Generators. Cryptology ePrint Archive, record 2000.
Shue for Paillier's Encryption Scheme - Takao Onodera Keisuke (Correct)
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O. Goldreich and V. Rosen. On the Security of Modular Exponentiation with Application to the Construction of Pseudorandom Generators. Cryptology ePrint Archive, record 2000.
Efficient Primitives from Exponentiation in Z_p - Jiang (2006) (Correct)
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O. Goldreich, V. Rosen, On the Security of Modular Exponentiation with Application to the Construction of Pseudorandom Generators, J. Cryptology, 16(2): 71-93 (2003).
Group Signatures: Better Efficiency and New Theoretical Aspects - Camenisch, Groth (2005) (2 citations) (Correct)
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Oded Goldreich and Vered Rosen. On the security of modular exponentiation with application to the construction of pseudorandom generators. Journal of Cryptology, 16(2):71--93, 2003. 14
An Improved Pseudorandom Generator Based on Hardness of.. - Dedic, Reyzin, Vadhan (2002) (1 citation) (Correct)
No context found.
Vered Rosen. On the security of modular exponentiation with application to the construction of pseudorandom generators. Technical Report TR01-007, ECCC (Electronic Colloquium on Computational Complexity, http://www.eccc.uni-trier.de/eccc), 2001.
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