Faster Compact Diffie-Hellman: Endomorphisms on the x-line

Diffie-Hellman type key exchange protocols based on isogenies

‎In this paper‎, ‎we propose some Diffie-Hellman type key exchange protocols using isogenies of elliptic curves‎. ‎The first method which uses the endomorphism ring of an ordinary elliptic curve $ E $‎, ‎is a straightforward generalization of elliptic curve Diffie-Hellman key exchange‎. ‎The method uses commutativity of the endomorphism ring $ End(E) $‎. ‎Then using dual isogenies‎, ‎we propose...

A NEW PROTOCOL MODEL FOR VERIFICATION OF PAYMENT ORDER INFORMATION INTEGRITY IN ONLINE E-PAYMENT SYSTEM USING ELLIPTIC CURVE DIFFIE-HELLMAN KEY AGREEMENT PROTOCOL

Two parties that conduct a business transaction through the internet do not see each other personally nor do they exchange any document neither any money hand-to-hand currency. Electronic payment is a way by which the two parties transfer the money through the internet. Therefore integrity of payment and order information of online purchase is an important concern. With online purchase the cust...

Public key exchange using extensions by endomorphisms and matrices over a Galois field

In this paper, we describe a public key exchange protocol based on an extension of a semigroup by automorphisms (more generally, by endomorphisms). One of its special cases is the standard DiffieHellman protocol, which is based on a cyclic group. However, when our protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffi...

Fast Digital Signature Schemes as Secure as Diffie-Hellman Assumptions

This paper presents two fast digital signature schemes based on Diffie-Hellman assumptions. In the random oracle model, the first scheme S1 has a tight security reduction to the computational Diffie-Hellman (CDH) problem; and the second scheme S2 has a tight security reduction to the decisional Diffie-Hellman (DDH) problem. Comparing with existing signature schemes (whose security is tightly re...

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra