Exponentiation in Pairing-Friendly Groups Using Homomorphisms

نویسندگان

  • Steven D. Galbraith
  • Michael Scott
چکیده

We present efficiently computable homomorphisms of the groups G2 and GT for pairings G1 × G2 → GT . This allows exponentiation in G2 and GT to be accelerated using the Gallant-Lambert-Vanstone method.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Final Exponentiation for Calculating Pairings on Ordinary Elliptic Curves

When performing a Tate pairing (or a derivative thereof) on an ordinary pairing-friendly elliptic curve, the computation can be looked at as having two stages, the Miller loop and the so-called final exponentiation. As a result of good progress being made to reduce the Miller loop component of the algorithm (particularly with the discovery of “truncated loop” pairings like the R-ate pairing [18...

متن کامل

Reducing Pairing Inversion to Exponentiation Inversion using Non-degenerate Auxiliary Pairing

The security of pairing-based cryptosystems is closely related to the difficulty of the pairing inversion problem. Building on previous works, we provide further contributions on the difficulty of pairing inversion. In particular, we revisit the approach of Kanayama-Okamoto who modified exponentiation inversion and Miller inversion by considering an “auxiliary” pairing. First, by generalizing a...

متن کامل

Efficient zero knowledge proofs of knowledge for homomorphisms

Efficient zero-knowledge proofs of knowledge for homomorphisms are a key building block in a vast number of constructions in applied cryptography. Examples are: identification-, signature-, group signature-, anonymous credential-, and identity escrow-schemes as well as voting systems, e-cash, multi-party computations, and trusted computing. This dissertation studies efficient zero-knowledge pro...

متن کامل

Efficient zero-knowledge proofs of knowledge for homomorphisms

Efficient zero-knowledge proofs of knowledge for homomorphisms are a key building block in a vast number of constructions in applied cryptography. Examples are: identification-, signature-, group signature-, anonymous credential-, and identity escrow-schemes as well as voting systems, e-cash, multi-party computations, and trusted computing. This dissertation studies efficient zero-knowledge pro...

متن کامل

Pairing Cryptography Meets Isogeny: A New Framework of Isogenous Pairing Groups

We put forth a new mathematical framework called Isogenous Pairing Groups (IPG) and new intractable assumptions in the framework, the Isogenous DBDH (Isog-DBDH) assumption and its variants. Three operations, i.e., exponentiation, pairing and isogeny on elliptic curves are treated under a unified notion of trapdoor homomorphisms, and combinations of the operations have potential new cryptographi...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008