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A Lattice based Threshold Multi-Secret Sharing Scheme and its Application to Threshold Cryptography

Pilaram, Hossein | 2017

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 50409 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Eghlidos, Taraneh
  7. Abstract:
  8. Secret sharing schemes are used for storage and management of sensitive data such as cryptographic keys and bank account numbers. These schemes provide both confidentiality and reliability. Advances in quantum computers have threatened the security of currently used public-key cryptographic algorithms. In this thesis, for designing quantum resistant cryptographic schemes, we construct a lattice based threshold multi-stage secret sharing (TMSSS) scheme. Using a lattice based one-way function, even after some secrets are revealed, the computational security of the unrecovered secrets is provided against quantum computers. The scheme is multi-use and verifiable meaning that the participants can verify the shares received from the dealer and the recovered secrets from the combiner, using public information. Furthermore, we propose a threshold increasing algorithm for our lattice based TMSSS scheme in such a way that more number of participants are required to recover the secret. Finally, we use the TMSSS scheme to propose a lattice based threshold public key encryption scheme and a lattice based threshold signature scheme in such a way that certain number of the participants can decrypt or sign the message, respectively . The security of the proposed schemes is based on the hardness of lattice problems, which are believed to resist against the quantum computers
  9. Keywords:
  10. Threshold Secret Sharing ; Threshold Cryptography ; Lattice-Based Cryptography ; Lattice Based Secret Sharing

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