On the Generic Hardness of DDH-II

The well known Decisional Diffie-Hellman assumption states that given g, g and g, for random a, b, the element g is pseudo-random. Canetti in [Can97] introduced a variant of this assumption in which b is still random but a is drawn according to some well-spread distribution. In this paper we prove that his assumption holds in the generic group model and demonstrate its broad applicability in the context of leakage resilient cryptography.

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

[2]  Serge Vaudenay,et al.  The Black-Box Model for Cryptographic Primitives , 1998, Journal of Cryptology.

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

[4]  Stefan Dziembowski,et al.  Leakage-Resilient Cryptography From the Inner-Product Extractor , 2011, IACR Cryptol. ePrint Arch..

[5]  Paul C. Kocher,et al.  Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems , 1996, CRYPTO.

[6]  Ronald Cramer,et al.  A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack , 1998, CRYPTO.

[7]  Richard J. Lipton,et al.  On the Importance of Checking Cryptographic Protocols for Faults (Extended Abstract) , 1997, EUROCRYPT.

[8]  Nigel P. Smart.  The Exact Security of ECIES in the Generic Group Model , 2001, IMACC.

[9]  Silvio Micali,et al.  Probabilistic encryption & how to play mental poker keeping secret all partial information , 1982, STOC '82.

[10]  Hovav Shacham,et al.  A Cramer-Shoup Encryption Scheme from the Linear Assumption and from Progressively Weaker Linear Variants , 2007, IACR Cryptol. ePrint Arch..

[11]  Victor Shoup,et al.  Lower Bounds for Discrete Logarithms and Related Problems , 1997, EUROCRYPT.

[12]  Ueli Maurer,et al.  Lower Bounds on Generic Algorithms in Groups , 1998, EUROCRYPT.

[13]  Allison Bishop,et al.  Achieving Leakage Resilience through Dual System Encryption , 2011, TCC.

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

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

[16]  Yael Tauman Kalai,et al.  On cryptography with auxiliary input , 2009, STOC '09.

[17]  Brent Waters,et al.  Functional Encryption for Regular Languages , 2012, CRYPTO.

[18]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[19]  Yevgeniy Dodis,et al.  Efficient Public-Key Cryptography in the Presence of Key Leakage , 2010, ASIACRYPT.

[20]  Matthew K. Franklin,et al.  Identity-Based Encryption from the Weil Pairing , 2001, CRYPTO.

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

[22]  Yevgeniy Dodis,et al.  Leakage-Resilient Public-Key Cryptography in the Bounded-Retrieval Model , 2009, CRYPTO.

[23]  Yael Tauman Kalai,et al.  Public-Key Encryption Schemes with Auxiliary Inputs , 2010, TCC.

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

[25]  Jean-Jacques Quisquater,et al.  ElectroMagnetic Analysis (EMA): Measures and Counter-Measures for Smart Cards , 2001, E-smart.

[26]  Eike Kiltz,et al.  Leakage Resilient ElGamal Encryption , 2010, ASIACRYPT.

[27]  Eike Kiltz,et al.  Secure Hybrid Encryption from Weakened Key Encapsulation , 2007, CRYPTO.

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

[29]  Yael Tauman Kalai,et al.  Overcoming the Hole in the Bucket: Public-Key Cryptography Resilient to Continual Memory Leakage , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[30]  Keisuke Tanaka,et al.  Randomness Leakage in the KEM/DEM Framework , 2011, ProvSec.

[31]  Guy N. Rothblum,et al.  Leakage-Resilient Signatures , 2010, TCC.

[32]  Brent Waters,et al.  Full-Domain Subgroup Hiding and Constant-Size Group Signatures , 2007, Public Key Cryptography.

[33]  Hovav Shacham,et al.  Short Group Signatures , 2004, CRYPTO.

[34]  Vinod Vaikuntanathan,et al.  Signature Schemes with Bounded Leakage Resilience , 2009, ASIACRYPT.

[35]  Shai Halevi,et al.  After-the-Fact Leakage in Public-Key Encryption , 2011, IACR Cryptol. ePrint Arch..

[36]  Paul C. Kocher,et al.  Differential Power Analysis , 1999, CRYPTO.

[37]  Taher ElGamal,et al.  A public key cyryptosystem and signature scheme based on discrete logarithms , 1985 .

[38]  Alexander W. Dent,et al.  The Hardness of the DHK Problem in the Generic Group Model , 2006, IACR Cryptol. ePrint Arch..

[39]  Jung Hee Cheon,et al.  Security Analysis of the Strong Diffie-Hellman Problem , 2006, EUROCRYPT.

[40]  Zvika Brakerski,et al.  Circular and Leakage Resilient Public-Key Encryption Under Subgroup Indistinguishability (or: Quadratic Residuosity Strikes Back) , 2010, IACR Cryptol. ePrint Arch..

[41]  Eli Biham,et al.  Differential Fault Analysis of Secret Key Cryptosystems , 1997, CRYPTO.

[42]  Ran Canetti,et al.  Towards Realizing Random Oracles: Hash Functions That Hide All Partial Information , 1997, CRYPTO.