A Veriﬁable (k,n,m)-Threshold Multi-secret Sharing
Scheme Based on NTRU Cryptosystem
Ali Nakhaei Amroudi
Published online: 26 April 2017
Ó Springer Science+Business Media New York 2017
Abstract The existing secret sharing schemes suffer from resistance against quantum
attacks or requirement to a secure channel. In this paper, we introduce a veriﬁable multi-
secret sharing scheme using NTRU cryptosystem which is a post quantum cryptosystem.
Our scheme is based on multivariate polynomials and uses hash functions for veriﬁcation.
In addition, our scheme does not require a secure channel and all public data are resistant
against quantum attacks.
Keywords Secret sharing schemes Á NTRU cryptosystem Á Multivariate
Polynomial Á Insecure channel
Mathematics Subject Classiﬁcation 94A60 Á 94A62
Secret sharing scheme was introduced by Shamir  and Blakley  independently in
1979. In a multi-secret sharing scheme, there are multiple secrets to be shared during one
secret sharing process [10, 15, 30].
& Ali Nakhaei Amroudi
Department of Mathematics and Cryptography, Malek Ashtar University of Technology, Isfahan,
Department of Electrical Engineering, Islamic Azad University, Isfahan (Khorasgan) Branch,
Wireless Pers Commun (2017) 96:1393–1405