Abstract
We explore the minimal assumptions that are necessary for non-trivial argument systems, such as Kilian’s argument system for NP with poly-logarithmic communication complexity [K92]. We exhibit an oracle relative to which there is a 2-round argument system with poly-logarithmic communication complexity for some language in NP, but no one-way functions. The language lies outside BPTime(2o(n)), so the relaxation to computational soundness is essential for achieving sublinear communication complexity. We obtain as a corollary that under black-box reductions, non-trivial argument systems do not imply one-way functions.
Work supported by US-Israel BSF Grant 2002246. Presently visiting Tsinghua University, Beijing, China.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-540-32732-5_32
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Wee, H. (2006). Finding Pessiland. In: Halevi, S., Rabin, T. (eds) Theory of Cryptography. TCC 2006. Lecture Notes in Computer Science, vol 3876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11681878_22
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DOI: https://doi.org/10.1007/11681878_22
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