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A Lattice-based Authenticated Group Key Establishment Scheme Using Secret Sharing

Karimani, Saba | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51149 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Aref, Mohammad Reza; Eghlidos, Taraneh
  7. Abstract:
  8. Secure communication among members of a group requires a shared cryptographic key. To address this issue, group key agreement and exchange schemes are introduced. In group key exchange schemes, a trusted center generates a shared key for the group and sends it securely to the group members. But in group key agreement schemes, all members of the group are involved in generating group keys. One of the useful ways in these schemes is to use secret sharing to share keys. A public key infrastructure is used to secure the distribution of the shares in secret sharing schemes. As quantum computers threat the classic cryptographic algorithms that are based on the difficulty of factoring large numbers and discrete logarithm problems, post-quantum cryptography has been considered by the cryptographic community. Among the various post-quantum domains, the lattice-based cryptography has been welcomed due to the linear structure along with the proven security based on the worst case hardness of lattice problems. On the other hand, the lattice-based cryptography schemes are introduced in order to ensure the consistency between secret sharing and group key establishment schemes and the used public key infrastructure. In this thesis, after introducing the basic concepts of lattice-based cryptography, secret sharing and key establishment, we present an LWE-based verifiable threshold secret sharing scheme. We also compare our secret sharing scheme with the existing schemes and use it to design a new lattice-based group key exchange scheme. At last, we analyze the security of a verifiable and authenticated lattice-based group key agreement scheme using the Pilaram’s multi-secret sharing scheme and compare it with the two existing schemes of classic group key agreement using secret sharing
  9. Keywords:
  10. Secret Sharing ; Lattice-Based Cryptography ; Learning with Error Problem ; Multi-Secret Shairing ; Group Key Exchange

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