Leakage Resilient Secret Sharing and Applications

A secret sharing scheme allows a dealer to share a secret among a set of n parties such that any authorized subset of the parties can recover the secret, while any unauthorized subset learns no information about the secret. A leakage-resilient secret sharing scheme (introduced in independent works by Goyal and Kumar, STOC ’18 and Benhamouda, Degwekar, Ishai and Rabin, CRYPTO ’18) additionally requires the secrecy to hold against every unauthorized set of parties even if they obtain some bounded leakage from every other share. The leakage is said to be local if it is computed independently for each share. So far, the only known constructions of local leakage resilient secret sharing schemes are for threshold access structures for very low (O(1)) or very high (\(n -o(\log n)\)) thresholds.

[1]  Yehuda Lindell,et al.  Secure Computation on the Web: Computing without Simultaneous Interaction , 2011, IACR Cryptol. ePrint Arch..

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

[3]  Nir Bitansky,et al.  Leakage-Tolerant Interactive Protocols , 2012, TCC.

[4]  Yael Tauman Kalai,et al.  Multiparty computation secure against continual memory leakage , 2012, STOC '12.

[5]  Oded Goldreich,et al.  Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity , 1988, SIAM J. Comput..

[6]  Yael Tauman Kalai,et al.  Secure Computation against Adaptive Auxiliary Information , 2013, CRYPTO.

[7]  Vinod Vaikuntanathan,et al.  Protecting Circuits from Leakage: the Computationally-Bounded and Noisy Cases , 2010, EUROCRYPT.

[8]  David Chaum,et al.  Multiparty Unconditionally Secure Protocols (Extended Abstract) , 1988, STOC.

[9]  Yuval Ishai,et al.  On the Local Leakage Resilience of Linear Secret Sharing Schemes , 2018, Journal of Cryptology.

[10]  G. R. BLAKLEY.  Safeguarding cryptographic keys , 1979, 1979 International Workshop on Managing Requirements Knowledge (MARK).

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

[12]  Divya Gupta,et al.  Constant-rate Non-malleable Codes in the Split-state Model , 2017, IACR Cryptol. ePrint Arch..

[13]  Bhavana Kanukurthi,et al.  Non-malleable Randomness Encoders and their Applications , 2018, IACR Cryptol. ePrint Arch..

[14]  Anat Paskin-Cherniavsky,et al.  Non-Interactive Secure Multiparty Computation , 2014, IACR Cryptol. ePrint Arch..

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

[16]  Guy N. Rothblum,et al.  How to Compute under ${\cal{AC}}^{\sf0}$ Leakage without Secure Hardware , 2012, CRYPTO.

[17]  Amit Sahai,et al.  Multi-Input Functional Encryption , 2014, IACR Cryptol. ePrint Arch..

[18]  Moni Naor,et al.  Public-Key Cryptosystems Resilient to Key Leakage , 2009, SIAM J. Comput..

[19]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[20]  Silvio Micali,et al.  Physically Observable Cryptography (Extended Abstract) , 2004, TCC.

[21]  Xin Li,et al.  Improved non-malleable extractors, non-malleable codes and independent source extractors , 2016, Electron. Colloquium Comput. Complex..

[22]  Vipul Goyal,et al.  Non-malleable secret sharing , 2018, IACR Cryptol. ePrint Arch..

[23]  Yuval Ishai,et al.  Bounded-Communication Leakage Resilience via Parity-Resilient Circuits , 2016, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS).

[24]  Yael Tauman Kalai,et al.  Program Obfuscation with Leaky Hardware , 2011, IACR Cryptol. ePrint Arch..

[25]  Vinod Vaikuntanathan,et al.  Simultaneous Hardcore Bits and Cryptography against Memory Attacks , 2009, TCC.

[26]  Vipul Goyal,et al.  Non-malleable Secret Sharing for General Access Structures , 2018, CRYPTO.

[27]  Amit Sahai,et al.  Leakage-Resilient Secret Sharing , 2018, Electron. Colloquium Comput. Complex..

[28]  Ivan Damgård,et al.  Stronger Leakage-Resilient and Non-Malleable Secret-Sharing Schemes for General Access Structures , 2019, IACR Cryptol. ePrint Arch..

[29]  Divesh Aggarwal,et al.  Optimal Computational Split-state Non-malleable Codes , 2016, TCC.

[30]  Ariel J. Feldman,et al.  Lest we remember: cold-boot attacks on encryption keys , 2008, CACM.

[31]  Yael Tauman Kalai,et al.  Leakage-resilient coin tossing , 2011, Distributed Computing.

[32]  R. Ostrovsky,et al.  Smooth Histograms for Sliding Windows , 2007, FOCS 2007.

[33]  Amit Sahai,et al.  Leakage-Resilient Zero Knowledge , 2011, CRYPTO.

[34]  Amos Beimel,et al.  Secret-Sharing Schemes: A Survey , 2011, IWCC.

[35]  Saikrishna Badrinarayanan,et al.  Revisiting Non-Malleable Secret Sharing , 2019, IACR Cryptol. ePrint Arch..

[36]  Ivan Damgård,et al.  Leakage Resilient Secure Two-Party Computation , 2011, IACR Cryptol. ePrint Arch..

[37]  Yuval Ishai,et al.  Private Circuits: Securing Hardware against Probing Attacks , 2003, CRYPTO.

[38]  Yuval Ishai,et al.  Secure Multiparty Computation with General Interaction Patterns , 2016, IACR Cryptol. ePrint Arch..

[39]  Moti Yung,et al.  How to share a function securely , 1994, STOC '94.

[40]  Moni Naor,et al.  A minimal model for secure computation (extended abstract) , 1994, STOC '94.

[41]  Mark Simkin,et al.  Lower Bounds for Leakage-Resilient Secret Sharing , 2020, IACR Cryptol. ePrint Arch..

[42]  Suela Kodra.  Fuzzy extractors : How to generate strong keys from biometrics and other noisy data , 2015 .

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

[44]  Hugo Krawczyk,et al.  Robust Non-Interactive Multiparty Computation Against Constant-Size Collusion , 2017, IACR Cryptol. ePrint Arch..

[45]  Michael Hamburg,et al.  Spectre Attacks: Exploiting Speculative Execution , 2018, 2019 IEEE Symposium on Security and Privacy (SP).

[46]  Yair Frankel,et al.  A Practical Protocol for Large Group Oriented Networks , 1990, EUROCRYPT.

[47]  GuruswamiVenkatesan,et al.  Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes , 2009 .

[48]  Silvio Micali,et al.  A Completeness Theorem for Protocols with Honest Majority , 1987, STOC 1987.

[49]  Enkatesan G Uruswami.  Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes , 2008 .

[50]  Yvo Desmedt,et al.  Threshold Cryptosystems , 1989, CRYPTO.

[51]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.

[52]  Yevgeniy Dodis,et al.  Survey: Leakage Resilience and the Bounded Retrieval Model , 2009, ICITS.