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Introduction

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Cryptography in Constant Parallel Time

Part of the book series: Information Security and Cryptography ((ISC))

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Notes

  1. 1.

    An interesting feature of the case of commitment is that we can also improve the parallel complexity at the receiver’s end. Specifically, it can be implemented by an AC 0 circuit (or even by a weaker circuit family). This feature of commitment carries on to some applications of commitments such as distributed coin-flipping and ZK proofs.

References

  1. Alekhnovich, M.: More on average case vs approximation complexity. In: Proc. of 44th FOCS, pp. 298–307 (2003)

    Google Scholar 

  2. Applebaum, B.: Pseudorandom generators with long stretch and low locality from random local one-way functions. In: Proc. of 44th STOC, pp. 805–816 (2012). Full version in ECCC TR11-007

    Google Scholar 

  3. Applebaum, B., Barak, B., Wigderson, A.: Public-key cryptography from different assumptions. In: Proc. of 42nd STOC, pp. 171–180 (2010)

    Google Scholar 

  4. Applebaum, B., Bogdanov, A., Rosen, A.: A dichotomy for local small-bias generators. In: Proc. of 9th TCC, pp. 1–18 (2012)

    Google Scholar 

  5. Applebaum, B., Ishai, Y., Kushilevitz, E.: On One-Way Functions with Optimal Locality. Unpublished manuscript available at http://www.cs.technion.ac.il/~abenny (2005)

  6. Applebaum, B., Ishai, Y., Kushilevitz, E.: Computationally private randomizing polynomials and their applications. Comput. Complex. 15(2), 115–162 (2006). Preliminary version in Proc. of 20th CCC, 2005

    Article  MATH  MathSciNet  Google Scholar 

  7. Applebaum, B., Ishai, Y., Kushilevitz, E.: Cryptography in NC0. SIAM J. Comput. 36(4), 845–888 (2006). Preliminary version in Proc. of 45th FOCS, 2004

    Article  MATH  MathSciNet  Google Scholar 

  8. Applebaum, B., Ishai, Y., Kushilevitz, E.: On pseudorandom generators with linear stretch in NC0. Comput. Complex. 17(1), 38–69 (2008). Preliminary version in Proc. of 10th RANDOM, 2006

    Article  MATH  MathSciNet  Google Scholar 

  9. Applebaum, B., Ishai, Y., Kushilevitz, E.: Cryptography with constant input locality. J. Cryptol. 22(4), 429–469 (2009). Preliminary version in Proc. of 27th CRYPTO, 2007

    Article  MATH  MathSciNet  Google Scholar 

  10. Applebaum, B., Ishai, Y., Kushilevitz, E.: Cryptography by cellular automata or how fast can complexity emerge in nature? In: ICS, pp. 1–19 (2010)

    Google Scholar 

  11. Applebaum, B., Moses, Y.: Locally computable UOWHF with linear shrinkage. In: Advances in Cryptology: Proc. of EUROCRYPT ’13 (2013)

    Google Scholar 

  12. Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and hardness of approximation problems. J. ACM 45(3), 501–555 (1998). Preliminary version in Proc. of 33rd FOCS, 1992

    Article  MATH  MathSciNet  Google Scholar 

  13. Arora, S., Safra, S.: Probabilistic checking of proofs: a new characterization of NP. J. ACM 45(1), 70–122 (1998). Preliminary version in Proc. of 33rd FOCS, 1992

    Article  MATH  MathSciNet  Google Scholar 

  14. Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. Comput. 13, 850–864 (1984). Preliminary version in FOCS 82

    Article  MATH  MathSciNet  Google Scholar 

  15. Bogdanov, A., Qiao, Y.: On the security of Goldreich’s one-way function. In: Proc. of 13th RANDOM, pp. 392–405 (2009)

    Google Scholar 

  16. Bogdanov, A., Rosen, A.: Input locality and hardness amplification. In: Proc. of 8th TCC, pp. 1–18 (2011)

    Google Scholar 

  17. Cook, J., Etesami, O., Miller, R., Trevisan, L.: Goldreich’s one-way function candidate and myopic backtracking algorithms. In: Proc. of 6th TCC, pp. 521–538 (2009). Full version in ECCC TR12-175

    Google Scholar 

  18. Cook, S.A.: The complexity of theorem-proving procedures. In: Proc. of 3rd STOC, pp. 151–158. ACM, New York (1971)

    Google Scholar 

  19. Cryan, M., Miltersen, P.B.: On pseudorandom generators in NC0. In: Proc. of 26th MFCS (2001)

    Google Scholar 

  20. Feistel, H.: Cryptography and computer privacy. Sci. Am. 228(5), 15–23 (1973)

    Article  Google Scholar 

  21. Goldberg, A.V., Kharitonov, M., Yung, M.: Lower bounds for pseudorandom number generators. In: Proc. of 30th FOCS, pp. 242–247 (1989)

    Google Scholar 

  22. Goldreich, O.: Candidate one-way functions based on expander graphs. Electron. Colloq. Comput. Complex. 7, 090 (2000)

    Google Scholar 

  23. Haitner, I., Reingold, O., Vadhan, S.P.: Efficiency improvements in constructing pseudorandom generators from one-way functions. In: Proc. of 42nd STOC, pp. 437–446 (2010)

    Google Scholar 

  24. Håstad, J.: One-way permutations in NC0. Inf. Process. Lett. 26, 153–155 (1987)

    Article  MATH  Google Scholar 

  25. Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  26. Impagliazzo, R., Naor, M.: Efficient cryptographic schemes provably as secure as subset sum. J. Cryptol. 9, 199–216 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  27. Ishai, Y., Kushilevitz, E.: Randomizing polynomials: a new representation with applications to round-efficient secure computation. In: Proc. of 41st FOCS, pp. 294–304 (2000)

    Google Scholar 

  28. Ishai, Y., Kushilevitz, E.: Perfect constant-round secure computation via perfect randomizing polynomials. In: Proc. of 29th ICALP, pp. 244–256 (2002)

    Google Scholar 

  29. Ishai, Y., Kushilevitz, E., Li, X., Ostrovsky, R., Prabhakaran, M., Sahai, A., Zuckerman, D.: Robust Pseudorandom Generators. Personal communication (2012)

    Google Scholar 

  30. Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Cryptography with constant computational overhead. In: Proc. of 40th STOC, pp. 433–442 (2008)

    Google Scholar 

  31. Kam, J.B., Davida, G.I.: Structured design of substitution-permutation encryption networks. IEEE Trans. Comput. 28(10), 747–753 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  32. Krause, M., Lucks, S.: On the minimal hardware complexity of pseudorandom function generators (extended abstract). In: Proc. of 18th STACS. LNCS, vol. 2010, pp. 419–430 (2001)

    Google Scholar 

  33. Levin, L.A.: Universal sequential search problems. PINFTRANS: Problems of Information Transmission (translated from Problemy Peredachi Informatsii (Russian)) 9 (1973)

    Google Scholar 

  34. Linial, N., Mansour, Y., Nisan, N.: Constant depth circuits, Fourier transform, and learnability. J. ACM 40(3), 607–620 (1993). Preliminary version in Proc. of 30th FOCS, 1989

    MATH  MathSciNet  Google Scholar 

  35. McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. Technical Report DSN PR 42-44, Jet Prop. Lab. (1978)

    Google Scholar 

  36. Mossel, E., Shpilka, A., Trevisan, L.: On ε-biased generators in NC0. In: Proc. of 44th FOCS, pp. 136–145 (2003)

    Google Scholar 

  37. Naor, M., Reingold, O.: Synthesizers and their application to the parallel construction of pseudo-random functions. J. Comput. Syst. Sci. Int. 58(2), 336–375 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  38. Naor, M., Reingold, O.: Number-theoretic constructions of efficient pseudo-random functions. J. ACM 51(2), 231–262 (2004). Preliminary version in Proc. of 38th FOCS, 1997

    MATH  MathSciNet  Google Scholar 

  39. Shannon, C.E.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28(4), 656–715 (1949)

    Article  MATH  MathSciNet  Google Scholar 

  40. Viola, E.: On constructing parallel pseudorandom generators from one-way functions. In: Proc. of 20th Conference on Computational Complexity (CCC), pp. 183–197 (2005)

    Google Scholar 

  41. Webster, A.F., Tavares, S.E.: On the design of s-boxes. In: Advances in Cryptology: Proc. of CRYPTO ’85, pp. 523–534. Springer, Berlin (1986)

    Chapter  Google Scholar 

  42. Yao, A.C.: Theory and application of trapdoor functions. In: Proc. of 23rd FOCS, pp. 80–91 (1982)

    Google Scholar 

  43. Yu, X., Yung, M.: Space lower-bounds for pseudorandom-generators. In: Proc. of 9th Structure in Complexity Theory Conference, pp. 186–197 (1994)

    Google Scholar 

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  1. School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel

    Benny Applebaum

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  1. Benny Applebaum
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Applebaum, B. (2014). Introduction. In: Cryptography in Constant Parallel Time. Information Security and Cryptography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17367-7_1

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  • DOI: https://doi.org/10.1007/978-3-642-17367-7_1

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  • Print ISBN: 978-3-642-17366-0

  • Online ISBN: 978-3-642-17367-7

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