Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Elliptic curves in cryptography
Elliptic curves in cryptography
The Montgomery Modular Inverse-Revisited
IEEE Transactions on Computers - Special issue on computer arithmetic
Synthesis and Optimization of Digital Circuits
Synthesis and Optimization of Digital Circuits
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
Efficient Implementation of Elliptic Curve Cryptosystems on an ARM7 with Hardware Accelerator
ISC '01 Proceedings of the 4th International Conference on Information Security
Dual-Field Arithmetic Unit for GF(p) and GF(2m)
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
A Scalable Dual-Field Elliptic Curve Cryptographic Processor
IEEE Transactions on Computers
A Unified Method for Iterative Computation of Modular Multiplication and Reduction Operations
ICCD '99 Proceedings of the 1999 IEEE International Conference on Computer Design
Scalable VLSI Architecture for GF(p) Montgomery Modular Inverse Computation
ISVLSI '02 Proceedings of the IEEE Computer Society Annual Symposium on VLSI
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
A Full RNS Implementation of RSA
IEEE Transactions on Computers
ASAP '04 Proceedings of the Application-Specific Systems, Architectures and Processors, 15th IEEE International Conference
Synthesis of Arithmetic Circuits: FPGA, ASIC and Embedded Systems
Synthesis of Arithmetic Circuits: FPGA, ASIC and Embedded Systems
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
Comparing Subtraction-Free and Traditional AMI
DDECS '06 Proceedings of the 2006 IEEE Design and Diagnostics of Electronic Circuits and systems
A high speed coprocessor for elliptic curve scalar multiplications over Fp
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Area-time efficient multi-modulus adders and their applications
Microprocessors & Microsystems
The CRNS framework and its application to programmable and reconfigurable cryptography
ACM Transactions on Architecture and Code Optimization (TACO) - Special Issue on High-Performance Embedded Architectures and Compilers
Improving modular inversion in RNS using the plus-minus method
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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Elliptic curve point multiplication is considered to be the most significant operation in all elliptic curve cryptography systems, as it forms the basis of the elliptic curve discrete logarithm problem. Designs for elliptic curve cryptography point multiplication are area demanding and time consuming. Thus, the efficient realization of point multiplication is of fundamental importance for the performance of an elliptic curve system. In this paper, a hardware architecture of an elliptic curve point multiplier is proposed that exploits the intrinsic parallelism of the residue number system (RNS), in order to speed up the elliptic curve point calculations and minimize the area complexity of the elliptic curve point multiplier. The architecture proves to be the fastest among all known design approaches, while complexity is less than half of that of previous efforts. This architecture also supports the required input (binary-to-RNS) and output (RNS-to-binary) conversions. Through a graph-oriented approach, the area of the elliptic curve point multiplier is minimized, by optimizing the point addition and doubling algorithms. Also, through this approach, the number of execution steps for point addition is matched to the number of execution steps for point doubling. Additionally, the impact of various RNS bases, in terms of number of moduli and their bit lengths, on the area and speed of the proposed implementation is analyzed, in an effort to define the potential for using RNS in elliptic curve cryptography.