Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
ATZ-Fachkongress

Chassis.tech plus 2024


4 Kongresse in einer Veranstaltung

Treffen Sie in München die Fachleute von Chassis, Lenkung, Bremsen sowie Reifen/Räder.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Understanding Cross-Channel Abuse with SMS-Spam Support Infrastructure Attribution Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Privately Outsourcing Exponentiation to a Single Server: Cryptanalysis and Optimal Constructions

verfasst von : Céline Chevalier, Fabien Laguillaumie, Damien Vergnaud

Erschienen in: Computer Security – ESORICS 2016

Verlag: Springer International Publishing

Einloggen

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

search-config
loading …

Abstract

We address the problem of speeding up group computations in cryptography using a single untrusted computational resource. We analyze the security of an efficient protocol for securely outsourcing multi-exponentiations proposed at ESORICS 2014. We show that this scheme does not achieve the claimed security guarantees and we present practical polynomial-time attacks on the delegation protocol which allow the untrusted helper to recover part (or the whole) of the device secret inputs. We then provide simple constructions for outsourcing group exponentiations in different settings (e.g. public/secret, fixed/variable bases and public/secret exponents). Finally, we prove that our attacks on the ESORICS 2014 protocol are unavoidable if one wants to use a single untrusted computational resource and to limit the computational cost of the limited device to a constant number of (generic) group operations. In particular, we show that our constructions are actually optimal in terms of operations in the underlying group.

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!

Jetzt informieren

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!

Jetzt informieren

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!

Jetzt informieren
Vorheriges Kapitel A Machine Learning Approach for Detecting Third-Party Trackers on the Web
Nächstes Kapitel Attribute-Based Signatures for Supporting Anonymous Certification
Fußnoten
1
In this paper, following prior works, we consider only prime order groups, but most of our results can be generalized to composite order groups.
 
2
Note that the protocol from [27] can also be described without inversion in the group \(\mathbb {G}\) but to help the reader familiar with this paper, we use the same description.
 
Literatur
1.
2.
Avanzi, R.M.: The complexity of certain multi-exponentiation techniques in cryptography. J. Cryptology 18(4), 357–373 (2005)MathSciNetCrossRefMATH
3.
4.
5.
Boyko, V., Peinado, M., Venkatesan, R.: Speeding up discrete log and factoring based schemes via precomputations. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 221–235. Springer, Heidelberg (1998)CrossRef
6.
Canard, S., Devigne, J., Sanders, O.: Delegating a pairing can be both secure and efficient. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 549–565. Springer, Heidelberg (2014)
7.
Cavallo, B., Crescenzo, G.D., Kahrobaei, D., Shpilrain, V.: Efficient and secure delegation of group exponentiation to a single server. In: Mangard, S., Schaumont, P. (eds.) Radio Frequency Identification. LNCS, vol. 9440, pp. 156–173. Springer, Heidelberg (2015)
8.
Chen, X., Li, J., Ma, J., Tang, Q., Lou, W.: New algorithms for secure outsourcing of modular exponentiations. In: Foresti, S., Yung, M., Martinelli, F. (eds.) ESORICS 2012. LNCS, vol. 7459, pp. 541–556. Springer, Heidelberg (2012)CrossRef
9.
Chevalier, C., Laguillaumie, F., Vergnaud, D.: Privately outsourcing exponentiation to a single server: Cryptanalysis and optimal constructions. Cryptology ePrint Archive, Report 2016/309 (2016). http://​eprint.​iacr.​org/​
10.
Chevallier-Mames, B., Coron, J.-S., McCullagh, N., Naccache, D., Scott, M.: Secure delegation of elliptic-curve pairing. In: Gollmann, D., Lanet, J.-L., Iguchi-Cartigny, J. (eds.) CARDIS 2010. LNCS, vol. 6035, pp. 24–35. Springer, Heidelberg (2010)CrossRef
11.
Coppersmith, D.: Finding a small root of a univariate modular equation. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 155–165. Springer, Heidelberg (1996)CrossRef
12.
Dent, A.W.: Adapting the weaknesses of the random oracle model to the generic group model. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 100–109. Springer, Heidelberg (2002)CrossRef
13.
Gallant, R.P., Lambert, R.J., Vanstone, S.A.: Faster point multiplication on elliptic curves with efficient endomorphisms. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 190–200. Springer, Heidelberg (2001)CrossRef
14.
Hohenberger, S., Lysyanskaya, A.: How to securely outsource cryptographic computations. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 264–282. Springer, Heidelberg (2005)CrossRef
15.
Howgrave-Graham, N.: Finding small roots of univariate modular equations revisited. In: Darnell, M. (ed.) Crytography and Coding. LNCS, vol. 1355, pp. 131–142. Springer, Heidelberg (1997)CrossRef
16.
17.
Jutla, C.S.: On finding small solutions of modular multivariate polynomial equations. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 158–170. Springer, Heidelberg (1998)CrossRef
18.
Kiraz, M.S., Uzunkol, O.: Efficient and verifiable algorithms for secure outsourcing of cryptographic computations. Int. J. Inf. Secur, 1–19 (2015, to appear). doi:10.​1007/​s10207-015-0308-7
19.
Lenstra, A.K., Lenstra, H.W.J., Lovász, L.: Factoring polynomials with rational coefficients. Math. Ann. 261, 515–534 (1982)MathSciNetCrossRefMATH
20.
Nguyen, P., Shparlinski, I., Stern, J.: Distribution of modular sums and the security of server aided exponentiation. Workshop Comp. Number Theor. Crypt. 20, 1–16 (1999)MathSciNet
21.
Nguyen, P.Q., Stehlé, D.: Floating-point LLL revisited. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 215–233. Springer, Heidelberg (2005)CrossRef
22.
Ning, P., di Vimercati, S.D.C., Syverson, P.F. (eds.): Proceedings of the 2007 ACM Conference on Computer and Communications Security, CCS 2007, Alexandria, Virginia, USA, October 28–31, 2007. ACM (2007)
23.
Shacham, H., Waters, B.: Compact proofs of retrievability. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 90–107. Springer, Heidelberg (2008)CrossRef
24.
Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997)CrossRef
25.
Smith, B.: Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians. Contemp. Math. Ser. 637, 15 (2015)MathSciNetMATH
26.
Straus, E.G.: Problems and solutions: Addition chains of vectors. Am. Math. Mon. 71, 806–808 (1964)MathSciNet
27.
Wang, Y., Wu, Q., Wong, D.S., Qin, B., Chow, S.S.M., Liu, Z., Tan, X.: Securely outsourcing exponentiations with single untrusted program for cloud storage. In: Kutyłowski, M., Vaidya, J. (eds.) ESORICS 2014, Part I. LNCS, vol. 8712, pp. 326–343. Springer, Heidelberg (2014)
Metadaten
Titel
Privately Outsourcing Exponentiation to a Single Server: Cryptanalysis and Optimal Constructions
verfasst von
Céline Chevalier
Fabien Laguillaumie
Damien Vergnaud
Copyright-Jahr
2016
Buch
Computer Security – ESORICS 2016

Print ISBN: 978-3-319-45743-7

Electronic ISBN: 978-3-319-45744-4

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-45744-4_13

Premium Partner

    Bildnachweise