Position-Based Cryptography

In this paper, we initiate the theoretical study of cryptographic protocols where the identity, or other credentials and inputs, of a party are derived from its geographic location. We start by considering the central task in this setting, i.e., securely verifying the position of a device. Despite much work in this area, we show that in the vanilla (or standard) model, the above task (i.e., of secure positioning) is impossible to achieve, even if we assume that the adversary is computationally bounded. In light of the above impossibility result, we then turn to Dziembowski's bounded retrieval model (a variant of Maurer's bounded storage model) and formalize and construct information theoretically secure protocols for two fundamental tasks: secure positioning and position-based key exchange. We then show that these tasks are in fact universal in this setting---we show how we can use them to realize secure multiparty computation. Our main contribution in this paper is threefold: to place the problem of secu...

[1]  Rafail Ostrovsky,et al.  Position Based Cryptography , 2009, CRYPTO.

[2]  Yonatan Aumann,et al.  Everlasting security in the bounded storage model , 2002, IEEE Trans. Inf. Theory.

[3]  Mikhail Nesterenko,et al.  Secure Location Verification Using Radio Broadcast , 2004, IEEE Transactions on Dependable and Secure Computing.

[4]  Amnon Ta-Shma,et al.  Non-interactive Timestamping in the Bounded Storage Model , 2004, CRYPTO.

[5]  Leonid A. Levin,et al.  A Pseudorandom Generator from any One-way Function , 1999, SIAM J. Comput..

[6]  Daniel R. Simon,et al.  Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack , 1991, CRYPTO.

[7]  Jonathan Katz,et al.  Universally Composable Multi-party Computation Using Tamper-Proof Hardware , 2007, EUROCRYPT.

[8]  Avi Wigderson,et al.  Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation (Extended Abstract) , 1988, STOC.

[9]  Noam Nisan,et al.  Randomness is Linear in Space , 1996, J. Comput. Syst. Sci..

[10]  Luca Trevisan,et al.  Extractors and pseudorandom generators , 2001, JACM.

[11]  Salil P. Vadhan,et al.  Constructing Locally Computable Extractors and Cryptosystems in the Bounded-Storage Model , 2003, Journal of Cryptology.

[12]  Ueli Maurer,et al.  Optimal Randomizer Efficiency in the Bounded-Storage Model , 2003, Journal of Cryptology.

[13]  Ronen Shaltiel,et al.  Constant-Round Oblivious Transfer in the Bounded Storage Model , 2004, Journal of Cryptology.

[14]  David A. Wagner,et al.  Secure verification of location claims , 2003, WiSe '03.

[15]  Srdjan Capkun,et al.  Secure Localization with Hidden and Mobile Base Stations , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[16]  Ueli Maurer,et al.  Unconditional Security Against Memory-Bounded Adversaries , 1997, CRYPTO.

[17]  Giovanni Di Crescenzo,et al.  Perfectly Secure Password Protocols in the Bounded Retrieval Model , 2006, TCC.

[18]  Yan Zong Ding,et al.  Error Correction in the Bounded Storage Model , 2005, TCC.

[19]  Ueli Maurer.  Conditionally-perfect secrecy and a provably-secure randomized cipher , 2004, Journal of Cryptology.

[20]  Gilles Brassard,et al.  Privacy Amplification by Public Discussion , 1988, SIAM J. Comput..

[21]  Yih-Chun Hu,et al.  Secure and precise location verification using distance bounding and simultaneous multilateration , 2009, WiSec '09.

[22]  David Zuckerman.  Randomness-optimal oblivious sampling , 1997, Random Struct. Algorithms.

[23]  Srdjan Capkun,et al.  Secure positioning of wireless devices with application to sensor networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[24]  Yan Zong Ding,et al.  Oblivious Transfer in the Bounded Storage Model , 2001, CRYPTO.

[25]  Stefan Dziembowski,et al.  Intrusion-Resilience Via the Bounded-Storage Model , 2006, TCC.

[26]  Stefan Dziembowski,et al.  On Forward-Secure Storage , 2006, CRYPTO.

[27]  Yonatan Aumann,et al.  Information Theoretically Secure Communication in the Limited Storage Space Model , 1999, CRYPTO.

[28]  Stefan Dziembowski,et al.  Intrusion-Resilient Secret Sharing , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[29]  Bart Preneel,et al.  Location verification using secure distance bounding protocols , 2005, IEEE International Conference on Mobile Adhoc and Sensor Systems Conference, 2005..

[30]  Michael O. Rabin,et al.  Hyper-Encryption and Everlasting Security , 2002, STACS.

[31]  Stefan Dziembowski,et al.  Leakage-Resilient Cryptography , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[32]  Yuguang Fang,et al.  Secure localization and authentication in ultra-wideband sensor networks , 2006, IEEE Journal on Selected Areas in Communications.

[33]  Rafael Pass,et al.  New and Improved Constructions of Nonmalleable Cryptographic Protocols , 2008, SIAM J. Comput..

[34]  Ueli Maurer,et al.  On Generating the Initial Key in the Bounded-Storage Model , 2004, EUROCRYPT.

[35]  Ran Raz,et al.  Extracting all the randomness and reducing the error in Trevisan's extractors , 1999, STOC '99.

[36]  David Cash,et al.  Intrusion-Resilient Key Exchange in the Bounded Retrieval Model , 2007, TCC.

[37]  Yael Tauman Kalai,et al.  One-Time Programs , 2008, CRYPTO.

[38]  Cédric Lauradoux,et al.  Distance Bounding Protocols on TH-UWB Radios , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[39]  Chi-Jen Lu.  Encryption against Storage-Bounded Adversaries from On-Line Strong Extractors , 2003, Journal of Cryptology.

[40]  Laurent Bussard.  Trust establishment protocols for communicating devices , 2004 .