- [PVW08-C] Chris Peikert, Vinod Vaikuntanathan, and Brent Waters: A framework for efficient and composable oblivious transfer. CRYPTO 2008
- UC-secure OT from LWE; static corruption, single-use CRS.

- [PV08-C] Chris Peikert and Vinod Vaikuntanathan: Noninteractive statistical zero-knowledge proofs for lattice problems. CRYPTO 2008
- NISZK for SIVP, GapCRP, GapGSMP, and coGapSVP with approximation factors O~(\sqrt{n}).

- Ruckert and Peikert: CT-RSA
- It mentioned a simple key exchange from LWE, although there is no proof on correctness and security.

- [Ding12-eP] Jintai Ding: A Simple Provably Secure Key Exchange Scheme Based on the Learning with Errors Problem. ePrint 2012/688
- I cannot agree his proof.

- [Geo13-Tatra] Adela Georgescu: An LWE-based key transfer protocol with anonymity. Tatra Mountains Mathematical Publications. Vol. 53, Issue 1
- I cannot agree the correctness of ``An LWE Diffie-Hellman Key Exchange.''

- [BCDP13-eP] Olivier Blazy and Céline Chevalier and Léo Ducas and Jiaxin Pan: Errorless Smooth Projective Hash Function based on LWE. ePrint 2013/821
- Now, I can agree the proof. the ratio B/q matters.

- [KV09-AC] Jonathan Katz and Vinod Vaikuntanathan: Password-based authenticated key exchange based on lattices. ASIACRYPT 2009
- 3-move in the BPR model

- [DF11-CIS] Yi Ding and Lei Fan: Efficient Password-Based Authenticated Key Exchange from Lattices.
- 3-move in the BPR model

- [BCDP13-eP] Olivier Blazy and Céline Chevalier and Léo Ducas and Jiaxin Pan: Errorless Smooth Projective Hash Function based on LWE. ePrint 2013/821
- q is superpolynomial
- 2-move in the BPR model
- 3-move in the UC model

- [FSXY12-PKC] Atsushi Fujioka, Koutarou Suzuki, Keita Xagawa, Kazuki Yoneyama: Strongly Secure Authenticated Key Exchange from Factoring, Codes, and Lattices. PKC 2012, ePrint 2012/211

- [Geo11-IJCA] Adela Georgescu: A LWE-based Secret Sharing Scheme. IJCA Special Issue on Network Security and Cryptography NSC(3), pp.27-29, December 2011
- She (I think she) proposed an n-out-of-n secret sharing based on LWE. Let us consider a large prime p and a generator g of GF(p). (Note: She seems to set q as an order of <g> implicitly).
- Consider a secret s in Z_q^d.
- For i = 1,..,d-1, we choose (a_i,b_i) = (a_i, a_i s_i + e_i) as an LWE sample.
- For i = d, we set (a_d, b_d) = (a_d, a_d s_d + e_d), where e_d = -(e_1+e_2+...+e_{d-1}).

- A share for i is S_i = (g^{a_i}, g^{b_i}).

- [BM12-WISTP] Rachid El Bansarkhani and Mohammed Meziani: An Efficient Lattice-Based Secret Sharing Construction. WISTP 2012
- verifiable secret sharing.

Last-modified: 2014-01-04 (Sat) 14:32:49 (1511d)