(Hierarchical) Identity Based Encryption (IBE/HIBE)

Identity based encrypton (IBE) is one of the main applications of strong lattice trapdoors, and the first lattice based IBE (in the random oracle model) was proposed by Gentry, Peikert and Vaikuntanathan (1) in 2008. Substantial improvements can be obtained using the same approach, but with better lattice trapdoor generation and gaussian preimage sampling algorithms.

  1. Trapdoors for Hard Lattices and New Cryptographic Constructions
    (Gentry, Peikert & Vaikuntanathan - STOC 2008)

Follow up work gives both IBE schemes in the standard model, and Hierarchical IBE (HIBE) schemes, i.e., IBE supporting delegation. IBE and HIBE can be seen as an important special case of (hierarchical) functional encryption. As for functional encryption, most IBE and HIBE schemes target the selective security model, where the adversary selects the identity/function under attack in advance.

  1. Expressive Encryption Systems from Lattices - (Abstract from the Invited Lecture)
    (Boyen - CNS 2011)

  2. Bonsai Trees, or How to Delegate a Lattice Basis
    (Cash, Hofheinz, Kiltz & Peikert - J.Crypto 2012/Eurocrypt 2010)

  3. Efficient Lattice (H)IBE in the Standard Model
    (Agrawal, Boneh, Boyen, Eurocrypt 2010)

  4. Lattice Basis Delegation in Fixed Dimension and Shorter-Ciphertext Hierarchical IBE
    (Agrawal, Boneh, Boyen, Crypto 2010)

  5. Adaptively Secure Efficient Lattice (H)IBE in Standard Model with Short Public Parameters
    (Singh, PanduRangan & Banerjee - SPACE 2012)

  6. Efficient Lattice HIBE in the Standard Model with Shorter Public Parameters
    (Singh, PanduRangan & Banerjee - ICT 2014)

Other Variants and Extensions

  1. Circular and KDM Security for Identity-Based Encryption
    (Alperin-Sheriff & Peikert - PKC 2012)

  2. Revocable Identity-Based Encryption from Lattices
    (Chen, Lim, Ling, Wang & Nguyen - ISP 2012)

  3. Deterministic Public Key Encryption and Identity-Based Encryption from Lattices in the Auxiliary-Input Setting
    (Xie, Xue & Zhang - SCN 2012)

  4. Adaptive-ID Secure Revocable Identity-Based Encryption from Lattices via Subset Difference Method
    (Cheng & Zhang - ISPE 2015)

Recent papers

  1. Adaptively Secure Identity-Based Encryption from Lattices with Asymptotically Shorter Public Parameters
    (Yamada - EuroCrypt 2016)

  2. Towards Tightly Secure Lattice Short Signature and Id-Based Encryption
    (Boyen & Li - Asiacrypt 2016)

  3. Partitioning via Non-linear Polynomial Functions: More Compact IBEs from Ideal Lattices and Bilinear Maps (Katsumata & Yamada - Asiacrypt 2016)