Pairing based non-repudiation protocols in cryptography

Thesis Type: Doctorate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Institute of Applied Mathematics, Turkey

Approval Date: 2017




Bilinear pairing on an elliptic curve is a mapping of a pair of elements on an elliptic curve into an element of a finite field. It is called symmetric when two elements of the domain are in the same group, it is called asymmetric otherwise. Generally symmetric pairings classified as Type-I and asymmetric pairings as Type-III. Type-II is a special case of Type-III which we don't consider in this thesis. Although the first use of bilinear pairings in cryptography has the intention to attack elliptic curve cryptosystems, in recent years they have been widely used to construct new encryption and signature schemes. As a main building block for non-repudiation protocols, signatures with different properties are implemented by using pairings on elliptic curves. Verifiably encrypted signature scheme due to Chen and Gu is a typical example for such a pairing based implementations. In the first part of this thesis, we propose an adaptation of certificateless public key cryptography to hybrid verifiably encrypted signature scheme due to Chen and Gu. This is called CL-HVESS. Then we expand CL-HVESS to Type-III pairings to mitigate the risks of recent attacks on Type-I pairings. In addition to this, we also present a replay attack to Chen and Gu protocol. In the second part we propose a non-repudiation protocol which has a new structure based on pairing based cryptography. The hybrid structure consists of two rounds; first round runs with an online Trusted Third Party (TTP) then second and next rounds run with offline TTP. Our contribution here is the usage of signed Joux Tri-partite key exchange scheme in the first round as a security enhancing method. In the third part we propose a new scheme that combines signcryption and verifiably encrypted signatures which we call VESigncrypt. We use it in a fair secret contract signing protocol. VESigncrypt has single recipient, multi recipient and publicly verifiable versions. To the best of our knowledge, this scheme is the first of its kind in the literature. In the last part of the thesis we first present a survey for isogeny based cryptography. Then, we propose a new verifiably encrypted probabilistic signature scheme based on isogenies. Finally we present new signature and verifiably encrypted signature schemes based on isogeny pairing groups.