Skip to main content
Top
Published in: Journal of Cryptology 4/2016

01-10-2016

Toward a Game Theoretic View of Secure Computation

Authors: Gilad Asharov, Ran Canetti, Carmit Hazay

Published in: Journal of Cryptology | Issue 4/2016

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We demonstrate how Game Theoretic concepts and formalism can be used to capture cryptographic notions of security. In the restricted but indicative case of two-party protocols in the face of malicious fail-stop faults, we first show how the traditional notions of secrecy and correctness of protocols can be captured as properties of Nash equilibria in games for rational players. Next, we concentrate on fairness. Here we demonstrate a Game Theoretic notion and two different cryptographic notions that turn out to all be equivalent. In addition, we provide a simulation-based notion that implies the previous three. All four notions are weaker than existing cryptographic notions of fairness. In particular, we show that they can be met in some natural setting where existing notions of fairness are provably impossible to achieve.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

Appendix
Available only for authorised users
Footnotes
1
An alternative and more general formalism might measure the runtime of a strategy as a function of the length of its inputs. However, the present formalism is considerably simpler.
 
2
At first glance, it might look as if the utilities from Definition 4.2 do not incentivize the parties to participate in the interaction to begin with. However, this concern can be dealt with by giving each party some fixed high payoff in case it participates.
 
Literature
1.
go back to reference I. Abraham, D. Dolev, R. Gonen, J.Y. Halpern, Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation, in PODC (2006), pp. 53–62 I. Abraham, D. Dolev, R. Gonen, J.Y. Halpern, Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation, in PODC (2006), pp. 53–62
2.
go back to reference S. Agrawal, M. Prabhakaran, On fair exchange, fair coins and fair sampling, in CRYPTO’13 (2013), pp. 259–276 S. Agrawal, M. Prabhakaran, On fair exchange, fair coins and fair sampling, in CRYPTO’13 (2013), pp. 259–276
3.
go back to reference G. Asharov, Y. Lindell. Utility dependence in correct and fair rational secret sharing. J. Cryptol. 24(1), 157–202 (2011) G. Asharov, Y. Lindell. Utility dependence in correct and fair rational secret sharing. J. Cryptol. 24(1), 157–202 (2011)
4.
go back to reference D. Beaver, S. Goldwasser, Multiparty computation with faulty majority, in 30th FOCS (1989), pp. 468–473 D. Beaver, S. Goldwasser, Multiparty computation with faulty majority, in 30th FOCS (1989), pp. 468–473
5.
go back to reference M. Blum. How to exchange (secret) keys. ACM Trans. Comput. Syst. 1(2), 175–193 (1983) M. Blum. How to exchange (secret) keys. ACM Trans. Comput. Syst. 1(2), 175–193 (1983)
6.
go back to reference R. Cleve, Limits on the security of coin flips when half the processors are faulty, in 18th STOC (1986), pp. 364–369 R. Cleve, Limits on the security of coin flips when half the processors are faulty, in 18th STOC (1986), pp. 364–369
7.
go back to reference R. Cleve, Controlled gradual disclosure schemes for random bits and their applications, in CRYPTO’89 (1989), pp. 573–588 R. Cleve, Controlled gradual disclosure schemes for random bits and their applications, in CRYPTO’89 (1989), pp. 573–588
8.
go back to reference Y. Dodis, S. Halevi, T. Rabin, A cryptographic solution to a game theoretic problem, in CRYPTO’00. LNCS, vol. 1880 (Springer, 2000), pp. 112–130 Y. Dodis, S. Halevi, T. Rabin, A cryptographic solution to a game theoretic problem, in CRYPTO’00. LNCS, vol. 1880 (Springer, 2000), pp. 112–130
10.
go back to reference G. Fuchsbauer, J. Katz, D. Naccache, Efficient rational secret sharing in standard communication networks, in 7th TCC. LNCS, vol. 5978 (Springer, 2010), pp. 419–436 G. Fuchsbauer, J. Katz, D. Naccache, Efficient rational secret sharing in standard communication networks, in 7th TCC. LNCS, vol. 5978 (Springer, 2010), pp. 419–436
11.
go back to reference J.A. Garay, P.D. MacKenzie, M. Prabhakaran, K. Yang, Resource fairness and composability of cryptographic protocols, in 3rd Theory of Cryptography Conference TCC 2006. LNCS, vol. 3876 (Springer, 2006), pp. 404–428 J.A. Garay, P.D. MacKenzie, M. Prabhakaran, K. Yang, Resource fairness and composability of cryptographic protocols, in 3rd Theory of Cryptography Conference TCC 2006. LNCS, vol. 3876 (Springer, 2006), pp. 404–428
12.
go back to reference O. Goldreich, Foundations of Cryptography: Volume 2—Basic Applications. Cambridge University Press, Cambridge (2004) O. Goldreich, Foundations of Cryptography: Volume 2—Basic Applications. Cambridge University Press, Cambridge (2004)
13.
go back to reference S. Goldwasser, L.A. Levin, Fair computation of general functions in presence of immoral majority, in CRYPTO 1990. LCNS, vol. 537 (Springer, 1991), pp. 77–93 S. Goldwasser, L.A. Levin, Fair computation of general functions in presence of immoral majority, in CRYPTO 1990. LCNS, vol. 537 (Springer, 1991), pp. 77–93
14.
go back to reference S. Goldwasser, S. Micali, Probabilistic encryption and how to play mental poker keeping secret all partial information. J. Comput. Syst. Sci. 28(2), 270–299 (1984) S. Goldwasser, S. Micali, Probabilistic encryption and how to play mental poker keeping secret all partial information. J. Comput. Syst. Sci. 28(2), 270–299 (1984)
15.
go back to reference S. Goldwasser, S. Micali, C. Rachoff, The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989) S. Goldwasser, S. Micali, C. Rachoff, The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989)
16.
go back to reference S.D. Gordon, C. Hazay, J. Katz, Y. Lindell, Complete fairness in secure two-party computation. J. SIGACT News 43(1), 21–23 (2012) S.D. Gordon, C. Hazay, J. Katz, Y. Lindell, Complete fairness in secure two-party computation. J. SIGACT News 43(1), 21–23 (2012)
17.
go back to reference S.D. Gordon, J. Katz, Rational secret sharing, in Security and cryptography for networks (SCN). LNCS, vol. 4116 (Springer, 2006), pp. 229–241 S.D. Gordon, J. Katz, Rational secret sharing, in Security and cryptography for networks (SCN). LNCS, vol. 4116 (Springer, 2006), pp. 229–241
18.
go back to reference S.D. Gordon, J. Katz, Partial fairness in secure two-party computation. J. Cryptol. 25(1), 14–40 (2012) S.D. Gordon, J. Katz, Partial fairness in secure two-party computation. J. Cryptol. 25(1), 14–40 (2012)
19.
go back to reference R. Gradwohl, N. Livne, A. Rosen, Sequential rationality in cryptographic protocols, in FOCS (2010), pp. 623–632 R. Gradwohl, N. Livne, A. Rosen, Sequential rationality in cryptographic protocols, in FOCS (2010), pp. 623–632
20.
go back to reference A. Groce, J. Katz, Fair computation with rational players, in Eurocrypt (2012), pp. 81–98 A. Groce, J. Katz, Fair computation with rational players, in Eurocrypt (2012), pp. 81–98
21.
go back to reference J. Halpern, V. Teague, Efficient rational secret sharing in standard communication networks, in 36th STOC (2004), pp. 623–632 J. Halpern, V. Teague, Efficient rational secret sharing in standard communication networks, in 36th STOC (2004), pp. 623–632
22.
go back to reference J. Halpern, R. Pass, Game theory with costly computation, in ICS (2010), pp. 120-142 J. Halpern, R. Pass, Game theory with costly computation, in ICS (2010), pp. 120-142
23.
go back to reference S. Izmalkov, M. Lepinski, S. Micali, Verifiably secure devices, in 5th TCC. LNCS, vol. 4948 (Springer, 2008), pp. 273–301 S. Izmalkov, M. Lepinski, S. Micali, Verifiably secure devices, in 5th TCC. LNCS, vol. 4948 (Springer, 2008), pp. 273–301
24.
go back to reference S. Izmalkov, S. Micali, M. Lepinski, Rational secure computation and ideal mechanism design, in 46th FOCS (2005), pp. 585–595 S. Izmalkov, S. Micali, M. Lepinski, Rational secure computation and ideal mechanism design, in 46th FOCS (2005), pp. 585–595
25.
go back to reference J. Katz, Bridging game theory and cryptography: recent results and future directions, in 5th TCC. LNCS, vol. 4948 (Springer, 2008), pp. 251–272 J. Katz, Bridging game theory and cryptography: recent results and future directions, in 5th TCC. LNCS, vol. 4948 (Springer, 2008), pp. 251–272
26.
go back to reference G. Kol, M. Naor, Games for exchanging information, in 40th STOC (2008), pp. 423–432 G. Kol, M. Naor, Games for exchanging information, in 40th STOC (2008), pp. 423–432
27.
go back to reference G. Kol, M. Naor, Cryptography and game theory: designing protocols for exchanging information, in 5th TCC. LNCS, vol. 4948 (Springer, 2008), pp. 320–339 G. Kol, M. Naor, Cryptography and game theory: designing protocols for exchanging information, in 5th TCC. LNCS, vol. 4948 (Springer, 2008), pp. 320–339
28.
go back to reference A. Lysyanskaya, N. Triandopoulos, Rationality and adversarial behavior in multi-party computation, in CRYPTO’06. LNCS, vol. 4117 (Springer, 2006), pp. 180–197 A. Lysyanskaya, N. Triandopoulos, Rationality and adversarial behavior in multi-party computation, in CRYPTO’06. LNCS, vol. 4117 (Springer, 2006), pp. 180–197
29.
go back to reference S. Micali, Certified email with invisible post offices, 1997. Technical report; an invited presentation at the RSA 1997 conference S. Micali, Certified email with invisible post offices, 1997. Technical report; an invited presentation at the RSA 1997 conference
30.
go back to reference S.J. Ong, D.C. Parkes, A. Rosen, S.P. Vadhan, Fairness with an honest minority and a rational majority, in 6th TCC. LNCS, vol. 5444 (Springer, 2009), pp. 36–53 S.J. Ong, D.C. Parkes, A. Rosen, S.P. Vadhan, Fairness with an honest minority and a rational majority, in 6th TCC. LNCS, vol. 5444 (Springer, 2009), pp. 36–53
31.
go back to reference R. Pass, A. Shelat, Renegotiation-safe protocols, in Innovations in Computer Science (ICS, 2011) R. Pass, A. Shelat, Renegotiation-safe protocols, in Innovations in Computer Science (ICS, 2011)
Metadata
Title
Toward a Game Theoretic View of Secure Computation
Authors
Gilad Asharov
Ran Canetti
Carmit Hazay
Publication date
01-10-2016
Publisher
Springer US
Published in
Journal of Cryptology / Issue 4/2016
Print ISSN: 0933-2790
Electronic ISSN: 1432-1378
DOI
https://doi.org/10.1007/s00145-015-9212-6

Other articles of this Issue 4/2016

Journal of Cryptology 4/2016 Go to the issue

OriginalPaper

Bug Attacks

Premium Partner