Key distribution system, terminal device, key distribution method, and program

Abstract

With respect to a key distribution system including N terminal devices Uand a key distribution server used for exchanging a session key, the key distribution system includes an isogeny calculating unit configured to calculate a first public value using a basis of a first torsion subgroup of a predetermined elliptic curve at an odd-numbered terminal device Uand calculate a second public value using a basis of a second torsion subgroup of the predetermined elliptic curve at an even-numbered terminal device U, when N is an even number, a distributing unit configured to distribute the first public value calculated at the odd-numbered terminal device Uto a terminal device Uand a terminal device U, and distribute the second public value calculated at the even-numbered terminal device Uto a terminal device Uand a terminal device U, from the key distribution server, a key generating unit configured to use second public values distributed by the distributing unit to generate the session key at the odd-numbered terminal device U, and use first public values distributed by the distributing unit to generate the session key at the even-numbered terminal device U, wherein the isogeny calculating unit calculates the first public value using the basis of the first torsion subgroup and the second public value using the basis of the second torsion subgroup at a predetermined terminal device Uamong the terminal devices U, when N is an odd number.