Skip to main content

2018 | OriginalPaper | Buchkapitel

Verifiable Delay Functions

verfasst von : Dan Boneh, Joseph Bonneau, Benedikt Bünz, Ben Fisch

Erschienen in: Advances in Cryptology – CRYPTO 2018

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We study the problem of building a verifiable delay function (VDF). A \(\text {VDF}\)requires a specified number of sequential steps to evaluate, yet produces a unique output that can be efficiently and publicly verified. \(\text {VDF}\)s have many applications in decentralized systems, including public randomness beacons, leader election in consensus protocols, and proofs of replication. We formalize the requirements for \(\text {VDF}\)s and present new candidate constructions that are the first to achieve an exponential gap between evaluation and verification time.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
1
A randomness extractor can then be applied to the output to map it to a uniform distribution.
 
2
The difficulty in proving indifferentiability arises because the distinguisher can query the VDF/RO construction and the RO itself separately, therefore the simulator must be able to simulate queries to the random oracle H given only access to the Random Delay Oracle. Indifferentiability doesn’t require the simulator to respond in exactly the same time, but it is still required to be efficient. This becomes an issue if the delay t is superpolynomial.
 
3
If square roots are iterated on a value x without an interleaved permutation then there is a shortcut to the iterated computation that first computes \(v = (\frac{p+1}{4})^\ell \mod p\) and then the single exponentiation \(x^v\).
 
5
This is reasonable if the evaluator has an NVIDIA Titan V GPU, which can compute up to \(10^{14}\) pipelined arithmetic operations per second (https://​www.​nvidia.​com/​en-us/​titan/​titan-v/​).
 
Literatur
1.
Zurück zum Zitat RANDAO: A DAO working as RNG of Ethereum. Technical report (2016) RANDAO: A DAO working as RNG of Ethereum. Technical report (2016)
5.
6.
Zurück zum Zitat Armknecht, F., Barman, L., Bohli, J.-M., Karame, G.O.: Mirror: enabling proofs of data replication and retrievability in the cloud. In: USENIX Security Symposium, pp. 1051–1068 (2016) Armknecht, F., Barman, L., Bohli, J.-M., Karame, G.O.: Mirror: enabling proofs of data replication and retrievability in the cloud. In: USENIX Security Symposium, pp. 1051–1068 (2016)
9.
Zurück zum Zitat Ben-Sasson, E., et al. Zerocash: decentralized anonymous payments from Bitcoin. In: IEEE Symposium on Security and Privacy (2014) Ben-Sasson, E., et al. Zerocash: decentralized anonymous payments from Bitcoin. In: IEEE Symposium on Security and Privacy (2014)
11.
Zurück zum Zitat Ben-Sasson, E., Chiesa, A., Tromer, E., Virza, M.: Scalable zero knowledge via cycles of elliptic curves. Algorithmica 79, 1102–1160 (2014)MathSciNetCrossRef Ben-Sasson, E., Chiesa, A., Tromer, E., Virza, M.: Scalable zero knowledge via cycles of elliptic curves. Algorithmica 79, 1102–1160 (2014)MathSciNetCrossRef
13.
Zurück zum Zitat Bentov, I., Pass, R., Shi, E.: Snow white: provably secure proofs of stake. IACR Cryptology ePrint Archive, 2016 (2016) Bentov, I., Pass, R., Shi, E.: Snow white: provably secure proofs of stake. IACR Cryptology ePrint Archive, 2016 (2016)
14.
Zurück zum Zitat Bitansky, N., Canetti, R., Chiesa, A., Tromer, E.: Recursive composition and bootstrapping for SNARKs and proof-carrying data. In: Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, pp. 111–120. ACM (2013) Bitansky, N., Canetti, R., Chiesa, A., Tromer, E.: Recursive composition and bootstrapping for SNARKs and proof-carrying data. In: Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, pp. 111–120. ACM (2013)
15.
Zurück zum Zitat Bitansky, N., Goldwasser, S., Jain, A., Paneth, O., Vaikuntanathan, V., Waters, B.: Time-lock puzzles from randomized encodings. In: ACM Conference on Innovations in Theoretical Computer Science (2016) Bitansky, N., Goldwasser, S., Jain, A., Paneth, O., Vaikuntanathan, V., Waters, B.: Time-lock puzzles from randomized encodings. In: ACM Conference on Innovations in Theoretical Computer Science (2016)
20.
Zurück zum Zitat Buchmann, J., Williams, H.C.: A key-exchange system based on imaginary quadratic fields. J. Cryptol. 1(2), 107–118 (1988)MathSciNetCrossRef Buchmann, J., Williams, H.C.: A key-exchange system based on imaginary quadratic fields. J. Cryptol. 1(2), 107–118 (1988)MathSciNetCrossRef
21.
Zurück zum Zitat Cai, J., Lipton, R.J., Sedgewick, R., Yao, A.C.: Towards uncheatable benchmarks. In: Structure in Complexity Theory (1993) Cai, J., Lipton, R.J., Sedgewick, R., Yao, A.C.: Towards uncheatable benchmarks. In: Structure in Complexity Theory (1993)
22.
Zurück zum Zitat Cai, J.-Y., Nerurkar, A., Wu, M.-Y.: The design of uncheatable benchmarks using complexity theory (1997) Cai, J.-Y., Nerurkar, A., Wu, M.-Y.: The design of uncheatable benchmarks using complexity theory (1997)
24.
Zurück zum Zitat Clark, J., Hengartner, U.: On the use of financial data as a random beacon. In: Usenix EVT/WOTE (2010) Clark, J., Hengartner, U.: On the use of financial data as a random beacon. In: Usenix EVT/WOTE (2010)
25.
Zurück zum Zitat Codenottia, B., Datta, B.N., Datta, K., Leoncini, M.: Parallel algorithms for certain matrix computations. Theor. Comput. Sci. 180, 287–308 (1997)MathSciNetCrossRef Codenottia, B., Datta, B.N., Datta, K., Leoncini, M.: Parallel algorithms for certain matrix computations. Theor. Comput. Sci. 180, 287–308 (1997)MathSciNetCrossRef
27.
Zurück zum Zitat Dai, W.: B-money. Consulted 1, 2012 (1998) Dai, W.: B-money. Consulted 1, 2012 (1998)
29.
Zurück zum Zitat Dean, D., Stubblefield, A.: Using client puzzles to protect TLS. In: USENIX Security Symposium, vol. 42 (2001) Dean, D., Stubblefield, A.: Using client puzzles to protect TLS. In: USENIX Security Symposium, vol. 42 (2001)
33.
Zurück zum Zitat Mathieu, É.: Mémoire sur l’étude des fonctions de plusieurs quantités sur la manière de les former et sur les substitutions qui les laissent invariables. J. Math. Pures Appl. 6(2), 241–323 (1861)MathSciNet Mathieu, É.: Mémoire sur l’étude des fonctions de plusieurs quantités sur la manière de les former et sur les substitutions qui les laissent invariables. J. Math. Pures Appl. 6(2), 241–323 (1861)MathSciNet
34.
Zurück zum Zitat Garay, J., Kiayias, A., Leonardos, N.: The Bitcoin backbone protocol: analysis and applications. Cryptology ePrint Archive # 2014/765 (2014) Garay, J., Kiayias, A., Leonardos, N.: The Bitcoin backbone protocol: analysis and applications. Cryptology ePrint Archive # 2014/765 (2014)
37.
38.
Zurück zum Zitat Hou, X.-d.: Permutation polynomials over finite fieldsa survey of recent advances. Finite Fields Appl. 32, 82–119 (2015) Hou, X.-d.: Permutation polynomials over finite fieldsa survey of recent advances. Finite Fields Appl. 32, 82–119 (2015)
39.
Zurück zum Zitat Jerschow, Y.I., Mauve, M.: Non-parallelizable and non-interactive client puzzles from modular square roots. In: Availability, Reliability and Security (ARES) (2011) Jerschow, Y.I., Mauve, M.: Non-parallelizable and non-interactive client puzzles from modular square roots. In: Availability, Reliability and Security (ARES) (2011)
41.
Zurück zum Zitat Juels, A., Kaliski Jr., B.S.: PORs: proofs of retrievability for large files. In: Proceedings of the 14th ACM Conference on Computer and Communications Security, pp. 584–597. ACM (2007) Juels, A., Kaliski Jr., B.S.: PORs: proofs of retrievability for large files. In: Proceedings of the 14th ACM Conference on Computer and Communications Security, pp. 584–597. ACM (2007)
42.
Zurück zum Zitat Jules, A., Brainard, J.: Client-puzzles: a cryptographic defense against connection depletion. In: Proceedings of Network and Distributed System Security Symposium (NDSS 1999), pp. 151–165 (1999) Jules, A., Brainard, J.: Client-puzzles: a cryptographic defense against connection depletion. In: Proceedings of Network and Distributed System Security Symposium (NDSS 1999), pp. 151–165 (1999)
45.
Zurück zum Zitat Kogan, D., Manohar, N., Boneh, D.: T/key: second-factor authentication from secure hash chains. In: ACM Conference on Computer and Communications Security (2017) Kogan, D., Manohar, N., Boneh, D.: T/key: second-factor authentication from secure hash chains. In: ACM Conference on Computer and Communications Security (2017)
46.
Zurück zum Zitat Lenstra, A.K., Wesolowski, B.: A random zoo: sloth, unicorn, and trx. IACR Cryptology ePrint Archive, 2015 (2015) Lenstra, A.K., Wesolowski, B.: A random zoo: sloth, unicorn, and trx. IACR Cryptology ePrint Archive, 2015 (2015)
47.
Zurück zum Zitat Lidl, R., Mullen, G.L., Turnwald, G.: Dickson Polynomials, vol. 65. Chapman & Hall/CRC, Boca Raton (1993)MATH Lidl, R., Mullen, G.L., Turnwald, G.: Dickson Polynomials, vol. 65. Chapman & Hall/CRC, Boca Raton (1993)MATH
49.
Zurück zum Zitat Mahmoody, M., Moran, T., Vadhan, S.: Publicly verifiable proofs of sequential work. In: Proceedings of the 4th Conference on Innovations in Theoretical Computer Science. ACM (2013) Mahmoody, M., Moran, T., Vadhan, S.: Publicly verifiable proofs of sequential work. In: Proceedings of the 4th Conference on Innovations in Theoretical Computer Science. ACM (2013)
51.
Zurück zum Zitat Micali, S.: CS proofs. In: 1994 Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 436–453. IEEE (1994) Micali, S.: CS proofs. In: 1994 Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 436–453. IEEE (1994)
53.
Zurück zum Zitat Miller, A., Juels, A., Shi, E., Parno, B., Katz, J.: Permacoin: repurposing bitcoin work for data preservation. In: 2014 IEEE Symposium on Security and Privacy (SP), pp. 475–490. IEEE (2014) Miller, A., Juels, A., Shi, E., Parno, B., Katz, J.: Permacoin: repurposing bitcoin work for data preservation. In: 2014 IEEE Symposium on Security and Privacy (SP), pp. 475–490. IEEE (2014)
55.
Zurück zum Zitat Morris, R., Thompson, K.: Password security: a case history. Commun. ACM 22(11), 594–597 (1979)CrossRef Morris, R., Thompson, K.: Password security: a case history. Commun. ACM 22(11), 594–597 (1979)CrossRef
56.
57.
Zurück zum Zitat Nakamoto, S.: Bitcoin: a peer-to-peer electronic cash system (2008) Nakamoto, S.: Bitcoin: a peer-to-peer electronic cash system (2008)
59.
Zurück zum Zitat Parno, B., Howell, J., Gentry, C., Raykova, M.: Pinocchio: nearly practical verifiable computation. In: IEEE Security and Privacy (2013) Parno, B., Howell, J., Gentry, C., Raykova, M.: Pinocchio: nearly practical verifiable computation. In: IEEE Security and Privacy (2013)
60.
61.
Zurück zum Zitat Pietrzak, K.: Unique proofs of sequential work from time-lock puzzles (2018). Manuscript Pietrzak, K.: Unique proofs of sequential work from time-lock puzzles (2018). Manuscript
64.
Zurück zum Zitat Rivest, R.L., Shamir, A., Wagner, D.A.: Time-lock puzzles and timed-release crypto (1996) Rivest, R.L., Shamir, A., Wagner, D.A.: Time-lock puzzles and timed-release crypto (1996)
65.
Zurück zum Zitat Syta, E., et al.: Scalable bias-resistant distributed randomness. In: 2017 IEEE Symposium on Security and Privacy (SP), pp. 444–460. IEEE (2017) Syta, E., et al.: Scalable bias-resistant distributed randomness. In: 2017 IEEE Symposium on Security and Privacy (SP), pp. 444–460. IEEE (2017)
67.
Zurück zum Zitat Van Oorschot,P.C., Wiener, M.J.: Parallel collision search with application to hash functions and discrete logarithms. In: ACM Conference on Computer and Communications Security (1994) Van Oorschot,P.C., Wiener, M.J.: Parallel collision search with application to hash functions and discrete logarithms. In: ACM Conference on Computer and Communications Security (1994)
68.
Zurück zum Zitat Wahby, R.S., Setty, S.T., Ren, Z., Blumberg, A.J., Walfish, M.: Efficient RAM and control flow in verifiable outsourced computation. In: NDSS (2015) Wahby, R.S., Setty, S.T., Ren, Z., Blumberg, A.J., Walfish, M.: Efficient RAM and control flow in verifiable outsourced computation. In: NDSS (2015)
Metadaten
Titel
Verifiable Delay Functions
verfasst von
Dan Boneh
Joseph Bonneau
Benedikt Bünz
Ben Fisch
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-96884-1_25