Card-based Cryptography with Dihedral Symmetry

Abstract It is known that secure computation can be done by using a deck of physical cards. This area called card-based cryptography. Shinagawa et al. (in: Provable security—9th international conference, ProvSec 2015, Kanazawa, Japan, 2015) proposed regular n -sided polygon cards enable to compute functions over $${\mathbb {Z}}/n{\mathbb {Z}}$$ Z / n . In particular, they designed efficient protocols for linear (e.g. addition and constant multiplication) Here, efficiency measured the number used in protocol. this paper, we propose new type cards, dihedral as natural generalization Based on them, construct various interesting such carry addition, equality, greater-than, whose construction has not been before. Beside this, introduce protocol framework captures wide class card types including binary so on.