TAILIEUCHUNG - Acceleration of the Elliptic Cryptography with Vector Finite Fields

Implementation of the cryptographic algorisms based on elliptic curves (ECs) over VFFs provides significantly higher performance than the implementation of the EC-based algorithms, in which the ECs are defined over the ground fields and extension finite fields of polynomials. | International Journal of Network Security Sept. 2009 180 Acceleration of the Elliptic Cryptography with Vector Finite Fields Nikolay A. Moldovyan Specialized Center of Program Systems SPECTR Kantemirovskaya 10 St-Petersburg 197342 Russia Email spectrz@ Received Oct. 16 2008 revised and accepted Feb. 9 2009 Abstract Special form of finite fields FFs called vector FFs VFFs is defined in the vector spaces over the ground finite field GF p using particular types of the multiplication operation over vectors. Implementation of the cryptographic algorisms based on elliptic curves ECs over VFFs provides significantly higher performance than the implementation of the EC-based algorithms in which the ECs are defined over the ground fields and extension finite fields of polynomials. Keywords Digital signature elliptic curve finite field finite vector field 1 Introduction The most computationally efficient digital signature DS algorithms are based on elliptic curves ECs over finite fields 6 9 . The well known DS standards ECDSA 5 and GOST R 4 specify EC-based algorithms over the ground fields GF p . However in many cases of the practical use of DS algorithms there are required the DS schemes providing higher performance in hardware and in software. To meet such requirements there have been proposed different approaches to accelerated the EC-based cryptographic algorithms 7 8 . These approaches can be categorized into two groups i high-level algorithm that manage the ECs selection and ii low-level algorithm that manage the finite field operation. Especially much attention in these researches is paid to the EC-based algorithms implementation using the finite fields GF 2m GF 2m s and GF pm because of their efficiency in hardware implementation 1 2 3 . This paper proposes another approach to acceleration of the EC-based cryptographic algorithms. The new approach consists in implementing the ECs using new form of the extension fields GF pm 10

• An ninh - Bảo mật
• Finite Fields in Vector Spaces
• Vector Finite Fields
• The Elliptic Cryptography
• Finite Vector Spaces
• Vector Finite Fields
• Different Finite Fields
• Abstract algebra
• Matrix groups and symmetry
• Group actions
• The sylow theorems
• Integral domains
• Lattices and boolean algebras
• Vector spaces
• Finite fields