TY - JOUR

T1 - Robust fuzzy extractors and authenticated key agreement from close secrets

AU - Dodis, Yevgeniy

AU - Kanukurthi, Bhavana

AU - Katz, Jonathan

AU - Reyzin, Leonid

AU - Smith, Adam

N1 - Funding Information:
Manuscript received June 24, 2011; revised April 18, 2012; accepted April 21, 2012. Date of publication May 19, 2012; date of current version August 14, 2012. This work was supported by the Louis L. and Anita M. Perlman Fellowship. Y. Dodis was supported by the NSF under Grants #0133806, #0311095, and #0515121. B. Kanukurthi was supported by the NSF under Grants #0311485, #0515100, #0546614, #0831281, #1012910, and #1012798. J. Katz was supported by the NSF under Grants #0310751, #0447075, and #0627306. L. Reyzin was supported by the NSF under Grants #0311485, #0515100, #0546614, #0831281, #1012910, and #1012798. This paper was presented in part at Advances in Cryptology—Crypto 2006 and in part at the 6th International Conference on Security and Cryptography for Networks (SCN). This is an expanded and corrected version of [15] and [23].

PY - 2012

Y1 - 2012

N2 - Consider two parties holding samples from correlated distributions W and W′, respectively, where these samples are within distance t of each other in some metric space. The parties wish to agree on a close-to-uniformly distributed secret key R by sending a single message over an insecure channel controlled by an all-powerful adversary who may read and modify anything sent over the channel. We consider both the keyless case, where the parties share no additional secret information, and the keyed case, where the parties share a long-term secret {\ssr SK Ext that they can use to generate a sequence of session keys {R j} using multiple pairs {(W j, W′ j)}. The former has applications to, e.g., biometric authentication, while the latter arises in, e.g., the bounded-storage model with errors. We show solutions that improve upon previous work in several respects. 1) The best prior solution for the keyless case with no errors (i.e., t=0) requires the min-entropy of W to exceed 2n/3 , where n is the bit length of W. Our solution applies whenever the min-entropy of W exceeds the minimal threshold n/2, and yields a longer key. 2) Previous solutions for the keyless case in the presence of errors (i.e., t < 0) required random oracles. We give the first constructions (for certain metrics) in the standard model. 3) Previous solutions for the keyed case were stateful. We give the first stateless solution.

AB - Consider two parties holding samples from correlated distributions W and W′, respectively, where these samples are within distance t of each other in some metric space. The parties wish to agree on a close-to-uniformly distributed secret key R by sending a single message over an insecure channel controlled by an all-powerful adversary who may read and modify anything sent over the channel. We consider both the keyless case, where the parties share no additional secret information, and the keyed case, where the parties share a long-term secret {\ssr SK Ext that they can use to generate a sequence of session keys {R j} using multiple pairs {(W j, W′ j)}. The former has applications to, e.g., biometric authentication, while the latter arises in, e.g., the bounded-storage model with errors. We show solutions that improve upon previous work in several respects. 1) The best prior solution for the keyless case with no errors (i.e., t=0) requires the min-entropy of W to exceed 2n/3 , where n is the bit length of W. Our solution applies whenever the min-entropy of W exceeds the minimal threshold n/2, and yields a longer key. 2) Previous solutions for the keyless case in the presence of errors (i.e., t < 0) required random oracles. We give the first constructions (for certain metrics) in the standard model. 3) Previous solutions for the keyed case were stateful. We give the first stateless solution.

KW - Fuzzy extractors

KW - information reconciliation

KW - information-theoretic cryptography

KW - key-agreement

KW - weak secrets

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U2 - 10.1109/TIT.2012.2200290

DO - 10.1109/TIT.2012.2200290

M3 - Article

AN - SCOPUS:84865393678

VL - 58

SP - 6207

EP - 6222

JO - IRE Professional Group on Information Theory

JF - IRE Professional Group on Information Theory

SN - 0018-9448

IS - 9

M1 - 6203415

ER -