TAILIEUCHUNG - Low-Power Elliptic Curve Cryptography Using Scaled Modular Arithmetic

We introduce new modulus scaling techniques for transforming a class of primes into special forms which enables efficient arithmetic. The scaling technique may be used to improve multiplication and inversion in finite fields. We present an efficient inversion algorithm that utilizes the structure of scaled modulus. | Low-Power Elliptic Curve Cryptography Using Scaled Modular Arithmetic E. Oztlirk1 B. Sunar1 and E. Savas2 1 Department of Electrical Computer Engineering Worcester Polytechnic Institute Worcester MA 01609 USA erdinc sunar@ 2 Faculty of Engineering and Natural Sciences Sabanci University Istanbul Turkey TR-34956 erkays@ Abstract. We introduce new modulus scaling techniques for transforming a class of primes into special forms which enables efficient arithmetic. The scaling technique may be used to improve multiplication and inversion in finite fields. We present an efficient inversion algorithm that utilizes the structure of scaled modulus. Our inversion algorithm exhibits superior performance to the Euclidean algorithm and lends itself to efficient hardware implementation due to its simplicity. Using the scaled modulus technique and our specialized inversion algorithm we develop an elliptic curve processor architecture. The resulting architecture successfully utilizes redundant representation of elements in GF p and provides a low-power high speed and small footprint specialized elliptic curve implementation. 1 Introduction Modular arithmetic has a variety of applications in cryptography. Many publickey algorithms heavily depend on modular arithmetic. Among these RSA encryption and digital signature schemes discrete logarithm problem DLP based schemes such as the Diffie-Helman key agreement 4 and El-Gamal encryption and signature schemes 8 and elliptic curve cryptography 6 7 play an important role in authentication and encryption protocols. The implementation of RSA based schemes requires the arithmetic of integers modulo a large integer that is in the form of a product of two large primes n p q. On the other hand implementations of Diffie-Helman and El-Gamal schemes are based on the arithmetic of integers modulo a large prime p. While ECDSA is built on complex algebraic structures the underlying arithmetic operations are either modular .

• An ninh - Bảo mật
• Elliptic Curve Cryptography
• Scaled Modular Arithmetic
• Modulus Scaling Techniques
• Scaled Modular Inversion
• The Elliptic Curve Architecture
• Block diagram of the arithmetic
• Elliptic Curves
• Elliptic Curve Cryptosystems
• Implementation of ECC
• An toàn thông tin
• Bảo mật thông tin
• An Implementation Guide
• Discrete Logarithm Problem
• The Point multiplication
• Elliptic Curve Domain parameters
• EC on Prime field
• An Implementation Tutorial
• The Finite Fields
• Elliptic and hyperelliptic curve cryptography
• Hyperelliptic curve cryptography
• Cohomological background on point counting
• Background on pairings
• Background on weil descent
• A course in number theory
• Elliptic curve primality test
• Elliptic curve factorization
• The quadratic sieve method
• Natural science
• Data sequence
• Discrete logarithm
• Elliptic curve
• Elliptic curve cryptosystem
• Public key
• natural sciences
• science and technology
• scientific reports
• research projects
• scientific research
• ECDSA for digital signature
• A Hardware Architecture
• Lossless Data Compression
• Architecture of the system
• Implementation and Results
• Tạp chí Khoa học
• Mã hóa bất đối xứng
• Smart Auto parking
• QR code
• Applications to Cryptography
• Efficient Software Implementation
• The Basis Representation
• Addition and Subtraction
• Network security
• Lecture notes on Computer and network security
• Computer security
• Digital rights management
• Digital signature
• Tate pairing
• Weil pairing
• Menezes Okamoto Vanstone
• Communication security
• Information security
• System security
• Public key cryptography
• Chaos based information security
• Architecture of the Circuit
• ECC processor architecture
• Hierarchy of operations in ECC
• The Implementation Approaches
• The Implementation Results
• Future Work and Conclusion
• International Journal of Computer Networks and Communications Security
• Secure mutual authentication protocol
• Session key agreement