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A Lattice based Secret Sharing Scheme with Changeable Threshold

Amini Khorasgani, Hamidreza | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 46302 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Aref, Mohammad Reza; Eghlidos, Taraneh
  7. Abstract:
  8. The need to protect the key in cryptosystems has been a motivation of studying secret sharing schemes. A secret sharing scheme is a method for sharing a secret data (key) by distributing some values, called shares, to a number of participants in such a way that only some authorized subset of them can recover the secret. In a threshold secret sharing scheme, authorized subsets are those whose size are at least a given value called threshold of the scheme. Increasing the attacker capabilities in achieving the participants’ shares, requires an increase in the threshold parameter. In a changeable threshold secret sharing scheme, participants ate able to compute new shares from their old shares such that in the new scheme, more new shares are required for recovering the secret.
    In secret sharing schemes, the dealer uses secure channels for transmitting the shares to the participants. These secure channels apply public key infrastructures which their security are based on hard problems in number theory such as prime factorization and discrete logarithms. These hard problems are solved by the shor’s algorithm on a quantum computer. Therefore, the advent of quantum computers in future will lead to the substitution of classical public key infrastructures for structures resistant to quantum computing attacks such as lattice based structures. Therefore, proposing a lattice based threshold secret sharing scheme is of particular importance.
    In this thesis, we propose two lattice based threshold secret sharing schemes. We show that the first scheme, in which we use the nearest plane algorithm for recovering the secret, is asymptotically correct and secure. Our second proposed scheme is inspired by the Chinese remainder theorem based secret sharing scheme. We show that this scheme is correct and is almost secure. Finally, we propose a second scheme that doubles the threshold parameter.
  9. Keywords:
  10. Threshold Secret Sharing ; Chinese Remainder Theorem ; Lattice Based Secret Sharing ; Lattice Theory ; Threshold Changeability

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