Still Wrong Use of Pairings in Cryptography

Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable technologies. There have been however a wide range of incorrect use of these primitives. The paper of Galbraith, Paterson, and Smart (2006) pointed out most of the issues related to the incorrect use of pairing-based cryptography. However, we noticed that some recently proposed applications still do not use these primitives correctly. This leads to unrealizable, insecure or too inefficient designs of pairing-based protocols. We observed that one reason is not being aware of the recent advancements on solving the discrete logarithm problems in some groups. The main purpose of this article is to give an understandable, informative, and the most up-to-date criteria for the correct use of pairing-based cryptography. We thereby deliberately avoid most of the technical details and rather give special emphasis on the importance of the correct use of bilinear maps by realizing secure cryptographic protocols. We list a collection of some recent papers having wrong security assumptions or realizability/efficiency issues. Finally, we give a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page

A New Cryptosystem Based On Hidden Order Groups

Let $G_1$ be a cyclic multiplicative group of order $n$. It is known that the Diffie-Hellman problem is random self-reducible in $G_1$ with respect to a fixed generator $g$ if $\phi(n)$ is known. That is, given $g, g^x\in G_1$ and having oracle access to a `Diffie-Hellman Problem' solver with fixed generator $g$, it is possible to compute $g^{1/x} \in G_1$ in polynomial time (see theorem 3.2). On the other hand, it is not known if such a reduction exists when $\phi(n)$ is unknown (see conjuncture 3.1). We exploit this ``gap'' to construct a cryptosystem based on hidden order groups and present a practical implementation of a novel cryptographic primitive called an \emph{Oracle Strong Associative One-Way Function} (O-SAOWF). O-SAOWFs have applications in multiparty protocols. We demonstrate this by presenting a key agreement protocol for dynamic ad-hoc groups.Comment: removed examples for multiparty key agreement and join protocols, since they are redundan

A Machine-Checked Formalization of the Generic Model and the Random Oracle Model

Most approaches to the formal analyses of cryptographic protocols make the perfect cryptography assumption, i.e. the hypothese that there is no way to obtain knowledge about the plaintext pertaining to a ciphertext without knowing the key. Ideally, one would prefer to rely on a weaker hypothesis on the computational cost of gaining information about the plaintext pertaining to a ciphertext without knowing the key. Such a view is permitted by the Generic Model and the Random Oracle Model which provide non-standard computational models in which one may reason about the computational cost of breaking a cryptographic scheme. Using the proof assistant Coq, we provide a machine-checked account of the Generic Model and the Random Oracle Mode

An Optimizing Protocol Transformation for Constructor Finite Variant Theories in Maude-NPA

[EN] Maude-NPA is an analysis tool for cryptographic security protocols that takes into account the algebraic properties of the cryptosystem. Maude-NPA can reason about a wide range of cryptographic properties. However, some algebraic properties, and protocols using them, have been beyond Maude-NPA capabilities, either because the cryptographic properties cannot be expressed using its equational unification features or because the state space is unmanageable. In this paper, we provide a protocol transformation that can safely get rid of cryptographic properties under some conditions. The time and space difference between verifying the protocol with all the crypto properties and verifying the protocol with a minimal set of the crypto properties is remarkable. We also provide, for the first time, an encoding of the theory of bilinear pairing into Maude-NPA that goes beyond the encoding of bilinear pairing available in the Tamarin toolPartially supported by the EU (FEDER) and the Spanish MCIU under grant RTI2018-094403-B-C32, by the Spanish Generalitat Valenciana under grant PROMETEO/2019/098, and by the US Air Force Office of Scientific Research under award number FA9550-17-1-0286. Julia Sapiña has been supported by the Generalitat Valenciana APOSTD/2019/127 grantAparicio-Sánchez, D.; Escobar Román, S.; Gutiérrez Gil, R.; Sapiña-Sanchis, J. (2020). An Optimizing Protocol Transformation for Constructor Finite Variant Theories in Maude-NPA. Springer Nature. 230-250. https://doi.org/10.1007/978-3-030-59013-0_12S230250Maude-NPA manual v3.1. http://maude.cs.illinois.edu/w/index.php/Maude_Tools:_Maude-NPAThe Tamarin-Prover Manual, 4 June 2019. https://tamarin-prover.github.io/manual/tex/tamarin-manual.pdfAl-Riyami, S.S., Paterson, K.G.: Tripartite authenticated key agreement protocols from pairings. In: Paterson, K.G. (ed.) Cryptography and Coding 2003. LNCS, vol. 2898, pp. 332–359. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-40974-8_27Baader, F., Snyder, W.: Unification theory. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 1, pp. 447–533. Elsevier Science (2001)Baelde, D., Delaune, S., Gazeau, I., Kremer, S.: Symbolic verification of privacy-type properties for security protocols with XOR. In: 30th IEEE Computer Security Foundations Symposium, CSF 2017, pp. 234–248. IEEE Computer Society (2017)Blanchet, B.: Modeling and verifying security protocols with the applied pi calculus and ProVerif. Found. Trends Privacy Secur. 1(1–2), 1–135 (2016)Clavel, M., et al.: Maude manual (version 3.0). Technical report, SRI International, Computer Science Laboratory (2020). http://maude.cs.uiuc.eduComon-Lundh, H., Delaune, S.: The finite variant property: how to get rid of some algebraic properties. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 294–307. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-32033-3_22Cremers, C.J.F.: The scyther tool: verification, falsification, and analysis of security protocols. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 414–418. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70545-1_38Dreier, J., Duménil, C., Kremer, S., Sasse, R.: Beyond subterm-convergent equational theories in automated verification of stateful protocols. In: Maffei, M., Ryan, M. (eds.) POST 2017. LNCS, vol. 10204, pp. 117–140. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54455-6_6Escobar, S., Hendrix, J., Meadows, C., Meseguer, J.: Diffie-Hellman cryptographic reasoning in the Maude-NRL protocol analyzer. In: Proceedings of 2nd International Workshop on Security and Rewriting Techniques (SecReT 2007) (2007)Escobar, S., Meadows, C., Meseguer, J.: A rewriting-based inference system for the NRL protocol analyzer and its meta-logical properties. Theor. Comput. Sci. 367(1–2), 162–202 (2006)Escobar, S., Meadows, C., Meseguer, J.: Maude-NPA: cryptographic protocol analysis modulo equational properties. In: Aldini, A., Barthe, G., Gorrieri, R. (eds.) FOSAD 2007-2009. LNCS, vol. 5705, pp. 1–50. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03829-7_1Escobar, S., et al.: Protocol analysis in Maude-NPA using unification modulo homomorphic encryption. In: Proceedings of PPDP 2011, pp. 65–76. ACM (2011)Escobar, S., Meadows, C.A., Meseguer, J., Santiago, S.: State space reduction in the Maude-NRL protocol analyzer. Inf. Comput. 238, 157–186 (2014)Escobar, S., Sasse, R., Meseguer, J.: Folding variant narrowing and optimal variant termination. J. Log. Algebr. Program. 81(7–8), 898–928 (2012)Fabrega, F.J.T., Herzog, J.C., Guttman, J.D.: Strand spaces: why is a security protocol correct? In: Proceedings of IEEE Symposium on Security and Privacy, pp. 160–171 (1998)Guttman, J.D.: Security goals and protocol transformations. In: Mödersheim, S., Palamidessi, C. (eds.) TOSCA 2011. LNCS, vol. 6993, pp. 130–147. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-27375-9_8Joux, A.: A one round protocol for tripartite Diffie-Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385–393. Springer, Heidelberg (2000). https://doi.org/10.1007/10722028_23Kim, Y., Perrig, A., Tsudik, G.: Communication-efficient group key agreement. In: Dupuy, M., Paradinas, P. (eds.) SEC 2001. IIFIP, vol. 65, pp. 229–244. Springer, Boston, MA (2002). https://doi.org/10.1007/0-306-46998-7_16Küsters, R., Truderung, T.: Using ProVerif to analyze protocols with Diffie-Hellman exponentiation. In: IEEE Computer Security Foundations, pp. 157–171 (2009)Küsters, R., Truderung, T.: Reducing protocol analysis with XOR to the XOR-free case in the horn theory based approach. J. Autom. Reason. 46(3–4), 325–352 (2011)Meadows, C.: The NRL protocol analyzer: an overview. J. Logic Program. 26(2), 113–131 (1996)Meier, S., Cremers, C., Basin, D.: Strong invariants for the efficient construction of machine-checked protocol security proofs. In: 2010 23rd IEEE Computer Security Foundations Symposium, pp. 231–245 (2010)Meseguer, J.: Conditional rewriting logic as a united model of concurrency. Theoret. Comput. Sci. 96(1), 73–155 (1992)Meseguer, J.: Variant-based satisfiability in initial algebras. Sci. Comput. Program. 154, 3–41 (2018)Meseguer, J.: Generalized rewrite theories, coherence completion, and symbolic methods. J. Log. Algebr. Meth. Program. 110, 100483 (2020)Mödersheim, S., Viganò, L.: The open-source fixed-point model checker for symbolic analysis of security protocols. In: Aldini, A., Barthe, G., Gorrieri, R. (eds.) FOSAD 2007-2009. LNCS, vol. 5705, pp. 166–194. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03829-7_6Sasse, R., Escobar, S., Meadows, C., Meseguer, J.: Protocol analysis modulo combination of theories: a case study in Maude-NPA. In: Cuellar, J., Lopez, J., Barthe, G., Pretschner, A. (eds.) STM 2010. LNCS, vol. 6710, pp. 163–178. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22444-7_11Schmidt, B., Sasse, R., Cremers, C., Basin, D.A.: Automated verification of group key agreement protocols. In: 2014 IEEE Symposium on Security and Privacy, SP 2014, pp. 179–194. IEEE Computer Society (2014)Skeirik, S., Meseguer, J.: Metalevel algorithms for variant satisfiability. J. Log. Algebraic Methods Program. 96, 81–110 (2018)TeReSe: Term Rewriting Systems. Cambridge University Press, Cambridge (2003)Yang, F., Escobar, S., Meadows, C.A., Meseguer, J., Narendran, P.: Theories of homomorphic encryption, unification, and the finite variant property. In: Proceedings of PPDP 2014, pp. 123–133. ACM (2014