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Cryptography in Constant Parallel Time Summary:by Benny Applebaum Research Thesis Submitted to the Senate of the Technion Israel Institute of Technology Tamuz 5767 Haifa June 2007 We study the parallel time-complexity of basic cryptographic primitives. Specically, we consider the possibility of computing instances of these primitives by NC0 circuits, in which each output bit depends on a constant number of input bits. Despite previous eorts in this direction, there has been no convincing theoretical evidence supporting this possibility, which was posed as an open question in several previous works (e.g., [Has87, Gol00, CM01, KL01, MST03]). We essentially settle this question by providing strong evidence for the possibility of cryptography in NC0. In particular, we derive the following results: Cryptographic primitives in NC0. We show that many cryptographic primitives can be real- ized in NC0 under standard intractability assumptions used in cryptography, such as ones related to factoring, discrete logarithm, or lattice problems. This includes one-way functions, pseudorandom generators, symmetric and public key encryption schemes, digital signatures, message authentica- tion schemes (MACs), commitment schemes, collision resistant hash functions and zero-knowledge proofs. Moreover, we provide a compiler that transforms an implementation of a cryptographic primitive in a relatively high" complexity class into an NC0 implementation. This compiler is also used to derive new (unconditional) NC0 reductions between dierent cryptographic primitives. In some cases, no parallel reductions of this type were previously known, even in NC. Interestingly, we get non-black-box reductions. ... password: MDBjMGEK Please select one mirror to download
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OLDER EBOOKSSponsored LinksCryptography in Constant Parallel Time Keywordsnc0 cryptographic primitives cryptography parallel possibility schemes reductions constant implementation previous compiler evidence functions derive digital thesis encryption signatures message cryptographic primitives constant parallel previous eorts computing instances convincing theoretical theoretical evidence results cryptographic has87 gol00 previous works evidence supportingCryptography in Constant Parallel Time download copyrightThis site does not store Cryptography in Constant Parallel Time on its server. We only index and link to Cryptography in Constant Parallel Time provided by other sites. Please contact the content providers to delete Cryptography in Constant Parallel Time if any and email us, we'll remove relevant links or contents immediately. |
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