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A Lattice-base Threshold Secret Sharing Scheme

Asaad, Saba | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45937 (05)
  4. University: Sharif University of Technology
  5. Department: Electical Engineering
  6. Advisor(s): Aref, Mohammad Reza; Eghlidos, Taraneh
  7. Abstract:
  8. In order to provide both security and availability for a given secret, one way is to distribute it among a number of parties called participants. The distribution should be accomplished in such a way that any subset of participants, the size of which is at least equal to a given number, be able to reconstruct the secret, using their shares. More specifically, a (t, n)-threshold secret sharing scheme refers to the procedure of assigning each of the n participants a private share, such that every subset of at least t participants could recover the secret. Due to the possibility of quantum attacks in future, we need to construct secure channels for transmitting secret shares. Such channels could be modeled by a lattice based public key cryptosystem whose security is based on hardness of lattice problems. Because of both security and efficiency of lattice construction, we propose a lattice based threshold secret sharing scheme that is compatible with the platform on which the cryptosystem is built. In this thesis, after reviewing basics in lattice and some features of threshold secret sharing scheme, two variants of (t, n) threshold secret sharing scheme is realized using a lattice model. Compared to the existing lattice based secret sharing schemes by Bansarkhani et al. and Georgescu, both papers address to (t, n) schemes, which requires all shareholders pooling their shares to recover the secret, while in the proposed schemes any set of qualified shareholders are able to recover the secret. In the first mode, we use Learning with error problem for distributing the shares amongst shareholders and the security of the second scheme is based on shortest vector problem. For both cases, it is shown that the proposed scheme is correct and asymptotically perfect from information theoretic point of view
  9. Keywords:
  10. Secret Sharing ; Lattice Based Secret Sharing ; Learning with Error Problem ; Shortest Vector Problem

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