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## Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE (2010)

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Venue: | In Advances in Cryptology — CRYPTO 2010, Springer LNCS 6223 |

Citations: | 50 - 10 self |

### Citations

1696 | Identity-based Encryption from the WeilPairing
- Boneh, Franklin
- 1987
(Show Context)
Citation Context ... some ℓ < k. It outputs the private key SK id for the identity id which is distributed the same as the output of Extract for id. Selective and Adaptive ID Security. The standard IBE security model of =-=[BF01]-=- allows an attacker to adaptively choose the identity it wishes to attack. A weaker notion of IBE called selective security [CHK07] forces the adversary to announce ahead of time the public key it wil... |

253 | Hierarchical ID-based cryptography - Gentry, Silverberg - 2002 |

247 | A forward-secure public-key encryption scheme
- Canetti, Halevi, et al.
- 2003
(Show Context)
Citation Context ... standard model treats identities at each level as kbit binary strings. Table 1 shows that the construction is only competitive with existing HIBEs [CHKP10,ABB10] in applications where k < ℓ (such as =-=[CHK07]-=- where k = 1). When k > ℓ the construction is not competitive due to the k 2 term in the ciphertext length (compared to kℓ in [CHKP10] and ℓ in [ABB10]). Nevertheless, this HIBE is very different from... |

216 | Efficient selective-id secure identity-based encryption without random oracles
- Boneh, Boyen
- 2004
(Show Context)
Citation Context ...struction and proof of security in [CHKP10] resembles the tree construction of Canetti et al. [CHK07]. The construction and proof of security in [ABB10] resembles the constructions of Boneh and Boyen =-=[BB04]-=- and Waters [Wat05]. The constructions in this paper have some relation to the HIBE of Boneh, Boyen, and Goh [BBG05], although the relation is not as direct. Waters [Wat09] recently proposed dualencry... |

175 |
Complexity of Lattice Problems, A Cryptographic Perspective
- Micciancio, Goldwasser
- 2002
(Show Context)
Citation Context ... := {˜s1, . . . , ˜sk} ⊂ R m denotes the Gram-Schmidt orthogonalization of the vectors s1, . . . , sk taken in that order. We refer to ‖ ˜ S‖ as the Gram-Schmidt norm of S. Micciancio and Goldwassser =-=[MG02]-=- showed that a full-rank set S in a lattice Λ can be converted into a basis T for Λ with an equally low Gram-Schmidt norm. Lemma 1 ([MG02, Lemma 7.1]). Let Λ be an m-dimensional lattice. There is a de... |

139 | Toward hierarchical identity-based encryption - Horwitz, Lynn - 2002 |

128 | Worst-case to average-case reductions based on gaussian measures
- Micciancio, Regev
(Show Context)
Citation Context ...tructions of Boneh and Boyen [BB04] and Waters [Wat05]. The constructions in this paper have some relation to the HIBE of Boneh, Boyen, and Goh [BBG05], although the relation is not as direct. Waters =-=[Wat09]-=- recently proposed dualencryption as a method to build fully secure HIBE systems from bilinear maps. It is a beautiful open problem to construct a lattice analog of that result using either the basis ... |

121 | Bonsai trees, or how to delegate a lattice basis
- Cash, Hofheinz, et al.
- 2010
(Show Context)
Citation Context ...ms of ciphertext and private key size. In terms of computation time, the encryptor in our system computes an ℓ-wise matrix product when encrypting to an identity at depth ℓ, which is not necessary in =-=[CHKP10]-=-. However, this product is not message dependent and need only be computed once per identity. Our construction in the standard model treats identities at each level as kbit binary strings. Table 1 sho... |

117 | Anonymous hierarchical identitybased encryption (without random oracles). CRYPTO - Boyen, Waters |

96 | Efficient lattice (h)ibe in the standard model
- Agrawal, Boneh, et al.
- 2010
(Show Context)
Citation Context ...KP10,ABB10] in applications where k < ℓ (such as [CHK07] where k = 1). When k > ℓ the construction is not competitive due to the k 2 term in the ciphertext length (compared to kℓ in [CHKP10] and ℓ in =-=[ABB10]-=-). Nevertheless, this HIBE is very different from the existing HIBEs and the techniques of [ABB10] can potentially be applied to improve its performance.selective secure ciphertext secret key pub. pa... |

95 | Predicting lattice reduction - Gama, Nguyen - 2008 |

95 |
Vinod Vaikuntanathan, Trapdoors for hard lattices and new cryptographic constructions
- Gentry, Peikert
- 2008
(Show Context)
Citation Context ... Z m . Properties. The following lemma from [Pei] captures standard properties of these distributions. The first property follows from Lemma 4.4 of [MR07]. The last two properties are algorithms from =-=[GPV08]-=-. Lemma 2. Let q ≥ 2 and let A be a matrix in Zn×m q with m > n. Let TA be a basis for Λ⊥ q (A) and σ ≥ ‖˜ TA‖ ω( √ log m ). Then for c ∈ Rm and u ∈ Zn q : 1. Pr [ x ∼ D Λ u q (A),σ : ‖x‖ > √ m σ ] ≤ ... |

67 | Generating shorter bases for hard random lattices. Cryptology ePrint Archive, Report 2008/521, 2008. http://eprint.iacr.org/. Joël Alwen and Chris Peikert. Generating shorter bases for hard random lattices
- Alwen, Peikert
- 2009
(Show Context)
Citation Context ...hm that, given an arbitrary basis of Λ and a full-rank set S = {s1, . . . , sm} in Λ, returns a basis T of Λ satisfying ‖ ˜ T ‖ ≤ ‖ ˜ S‖ and ‖T ‖ ≤ ‖S‖ √ m/2 Ajtai [Ajt99] and later Alwen and Peikert =-=[AP09]-=- show how to sample an essentially uniform matrix A ∈ Zn×m q with an associated basis SA of Λ⊥ q (A) with low Gram-Schmidt norm. The following follows from Theorem 3.2 of [AP09] taking δ := 1/3. The t... |

63 |
Generating hard instances of the short basis problem
- Ajtai
- 1999
(Show Context)
Citation Context ...eterministic polynomial-time algorithm that, given an arbitrary basis of Λ and a full-rank set S = {s1, . . . , sm} in Λ, returns a basis T of Λ satisfying ‖ ˜ T ‖ ≤ ‖ ˜ S‖ and ‖T ‖ ≤ ‖S‖ √ m/2 Ajtai =-=[Ajt99]-=- and later Alwen and Peikert [AP09] show how to sample an essentially uniform matrix A ∈ Zn×m q with an associated basis SA of Λ⊥ q (A) with low Gram-Schmidt norm. The following follows from Theorem 3... |

56 |
Yevgeniy Dodis, Cécile Malinaud, and Prashant Puniya. Merkle-Damg˚ard revisited: How to construct a hash function
- Coron
- 2005
(Show Context)
Citation Context ...standard” random function h : ({0, 1} ∗ ) ≤d → {0, 1} t by using h as a coin generator for the sampling process in Algorithm SampleR(1 m ). This method however is not indefferentiable in the sense of =-=[CDMP05]-=- and the analysis requires that H itself be a random oracle. 4.1 Construction The system uses a number of parameters that will be set in Section 4.2. The parameters n, m and q are fixed across the lev... |

38 | Lattice mixing and vanishing trapdoors: A framework for fully secure short signatures and - Boyen - 2010 |

27 | Hierarchical identity based encryption with polynomially many levels - Gentry, Halevi - 2009 |