Fully Secure Doubly-Spatial Encryption under Simple Assumptions

Recently, Hamburg improved the notion of spatial encryption by presenting a variant called doubly-spatial encryption. As a generalization of the spatial encryption, the doubly-spatial encryption is more powerful and expressive. More useful cryptography systems can be built from it, such as attribute-based encryption, etc. However, the only presented doubly-spatial encryption scheme can only be proved to be selectively secure. In this paper, we primarily focus on the full security of doubly-spatial encryption. A doubly-spatial encryption scheme has been proposed. We apply the dual system methodology proposed by Waters in the security proof. Our scheme can be proved adaptively secure under standard assumptions, the decisional linear assumption and the decisional bilinear Diffe-Hellman assumption, over prime order groups in the standard model. Our scheme is the first fully secure construction of doubly-spatial encryption. As an independent interest, we also propose a fully secure spatial encryption with weak anonymity and constant ciphertext size in the composite order group settings.

[1]  A. Miyaji,et al.  Pairing-Based Cryptography - Pairing 2010 , 2011 .

[2]  Adi Shamir,et al.  Identity-Based Cryptosystems and Signature Schemes , 1984, CRYPTO.

[3]  Allison Bishop,et al.  Revocation Systems with Very Small Private Keys , 2010, 2010 IEEE Symposium on Security and Privacy.

[4]  Huaxiong Wang,et al.  Fully Secure Spatial Encryption under Simple Assumptions with Constant-Size Ciphertexts , 2011, IACR Cryptol. ePrint Arch..

[5]  Brent Waters,et al.  Attribute-based encryption for fine-grained access control of encrypted data , 2006, CCS '06.

[6]  Tal Rabin.  Advances in Cryptology - CRYPTO 2010, 30th Annual Cryptology Conference, Santa Barbara, CA, USA, August 15-19, 2010. Proceedings , 2010, CRYPTO.

[7]  Hiroshi Doi,et al.  A Fully Secure Spatial Encryption Scheme , 2011, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[8]  Michael Hamburg,et al.  Spatial Encryption , 2011, IACR Cryptol. ePrint Arch..

[9]  Allison Bishop,et al.  New Techniques for Dual System Encryption and Fully Secure HIBE with Short Ciphertexts , 2010, IACR Cryptol. ePrint Arch..

[10]  Josef Pieprzyk,et al.  Advances in Cryptology - ASIACRYPT 2008, 14th International Conference on the Theory and Application of Cryptology and Information Security, Melbourne, Australia, December 7-11, 2008. Proceedings , 2008, ASIACRYPT.

[11]  Brent Waters,et al.  Fuzzy Identity-Based Encryption , 2005, EUROCRYPT.

[12]  Ran Canetti,et al.  A Forward-Secure Public-Key Encryption Scheme , 2003, Journal of Cryptology.

[13]  Allison Bishop,et al.  Fully Secure Functional Encryption: Attribute-Based Encryption and (Hierarchical) Inner Product Encryption , 2010, EUROCRYPT.

[14]  Shai Halevi.  Advances in Cryptology - CRYPTO 2009, 29th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2009. Proceedings , 2009, CRYPTO.

[15]  Ronald Cramer,et al.  Advances in Cryptology - EUROCRYPT 2005, 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Aarhus, Denmark, May 22-26, 2005, Proceedings , 2005, EUROCRYPT.

[16]  Nuttapong Attrapadung,et al.  Functional Encryption for Inner Product: Achieving Constant-Size Ciphertexts with Adaptive Security or Support for Negation , 2010, Public Key Cryptography.

[17]  Martijn Stam.  Beyond Uniformity: Better Security/Efficiency Tradeoffs for Compression Functions , 2008, CRYPTO.

[18]  Ran Canetti,et al.  An Efficient Threshold Public Key Cryptosystem Secure Against Adaptive Chosen Ciphertext Attack , 1999, EUROCRYPT.

[19]  Dan Boneh,et al.  Generalized Identity Based and Broadcast Encryption Schemes , 2008, ASIACRYPT.

[20]  Zhenfu Cao,et al.  Spatial Encryption under Simpler Assumption , 2009, ProvSec.

[21]  Felix Schlenk,et al.  Proof of Theorem 2 , 2005 .

[22]  David Mandell Freeman,et al.  Converting Pairing-Based Cryptosystems from Composite-Order Groups to Prime-Order Groups , 2010, EUROCRYPT.

[23]  David Pointcheval,et al.  Dynamic Threshold Public-Key Encryption , 2008, CRYPTO.

[24]  Henri Gilbert,et al.  Advances in Cryptology - EUROCRYPT 2010, 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Monaco / French Riviera, May 30 - June 3, 2010. Proceedings , 2010, EUROCRYPT.

[25]  Tatsuaki Okamoto,et al.  Fully Secure Functional Encryption with General Relations from the Decisional Linear Assumption , 2010, IACR Cryptol. ePrint Arch..

[26]  Angelo De Caro,et al.  Fully Secure Anonymous HIBE and Secret-Key Anonymous IBE with Short Ciphertexts , 2010, Pairing.

[27]  Brent Waters,et al.  Dual System Encryption: Realizing Fully Secure IBE and HIBE under Simple Assumptions , 2009, IACR Cryptol. ePrint Arch..