报告题目：Tutorial Talk on Polynomial-based Cryptography
报告人：Lein Harn 教授
This tutorial talk will cover following topics.
(1) What is polynomial-based cryptography?
▪ Univariate polynomial has been used in (t, n) secret sharing scheme.
▪ Bivariate polynomials, including both symmetric and asymmetric bivariate polynomials, have been used to establish pairwise keys of users.
▪ The threshold of bivariate polynomials.
(2) Why do we study polynomial-based cryptography?
▪ Polynomial-based cryptography is suitable for future development (after quantum computing).
▪ Polynomial-based cryptography is suitable for current development (faster than public-key computation).
(3) Why polynomial evaluation is much faster than public-key evaluations?
▪ The complexity of polynomial evaluation based on Horner’s rule is compared with modular exponentiation based on square-and-multiplication.
▪ I will include both theoretical and experimental results to support above claims.
(4) What polynomial-based cryptography can provide?
▪ Secure secret reconstruction with confidentiality
▪ Secret sharing over network
▪ Threshold changeable secret sharing
▪ Group authentication and group key establishment
▪ Enhance key establishment in wireless sensor network with probabilistic sensor capture attack
(5) What is the limitation of polynomial-based cryptography?
▪ After capturing t or more than t shares, attacker can recover the secret polynomial.
(6) Future research
▪ Research in extension to threshold cryptography based on bivariate polynomial including threshold signature and threshold encryption.
▪ Research in secret sharing based on bivariate polynomial including multi-secret secret sharing, verifiable secret sharing, rational secret sharing.
▪ Research in group-oriented cryptography based on bivariate polynomial including what other group-oriented protocols can be developed based on bivariate polynomials.
▪ Research on multi-variable polynomial cryptography including general extension to multi-variate polynomials.
▪ Research on network applications based on bivariate polynomial including cloud computing, distributed database, IoT, wireless sensor networks, vehicle networks.
Lein Harn received the B.S. degree in electrical engineering from the National Taiwan University in 1977, the M.S. degree in electrical engineering from the State University of New York-Stony Brook in 1980, and the Ph.D. degree in electrical engineering from the University of Minnesota in 1984. In 1984, he joined the Department of Electrical and Computer Engineering, University of Missouri- Columbia as an Assistant Professor, and in 1995, he has been promoted as a Full Professor, University of Missouri, Kansas City (UMKC). While at UMKC, he went on development leave to work in Racal Data Group, Florida for a year. His research interests include cryptography, network security, and wireless communication security. He has published over hundred research journal papers on digital signature design and applications, and wireless and network security. He has written two books on security. He is currently investigating new ways of using secret sharing in various applications.