VLSI Architectures for Computing Multiplications and Inverses in GF(2m)
IEEE Transactions on Computers
A VLSI Architecture for Fast Inversion in GF(2/sup m/)
IEEE Transactions on Computers
Systolic Array Implementation of Euclid's Algorithm for Inversion and Division in GF (2m)
IEEE Transactions on Computers
Elliptic curves in cryptography
Elliptic curves in cryptography
The Montgomery Modular Inverse-Revisited
IEEE Transactions on Computers - Special issue on computer arithmetic
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Introduction to Digital Systems
Introduction to Digital Systems
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
GF(2m) Multiplication and Division Over the Dual Basis
IEEE Transactions on Computers
Elliptic Curves over Fp Suitable for Cryptosystems
ASIACRYPT '92 Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
A Scalable Architecture for Montgomery Multiplication
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Efficient Computation of Multiplicative Inverses for Cryptographic Applications
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Scalable VLSI Architecture for GF(p) Montgomery Modular Inverse Computation
ISVLSI '02 Proceedings of the IEEE Computer Society Annual Symposium on VLSI
Scalable and Unified Hardware to Compute Montgomery Inverse in GF(p) and GF(2)
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Combined circuit architecture for computing normal basis and montgomery multiplications over GF(2m)
Mobility '08 Proceedings of the International Conference on Mobile Technology, Applications, and Systems
Scalable and Systolic Montgomery Multipliers over GF(2m)
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Combined circuit architecture for computing normal basis and Montgomery multiplications over GF(2m)
International Journal of Autonomous and Adaptive Communications Systems
| Hi-index | 0.00 |
The multiplicative inversion operation is a fundamental computation in several cryptographic applications. In this work, we propose a scalable VLSI hardware to compute the Montgomery modular inverse in GF(p). We suggest a new correction phase for a previously proposed almost Montgomery inverse algorithm to calculate the inversion in hardware. We also propose an efficient hardware algorithm to compute the inverse by multi-bit shifting method. The intended VLSI hardware is scalable, which means that a fixed-area module can handle operands of any size. The word-size, which the module operates, can be selected based on the area and performance requirements. The upper limit on the operand precision is dictated only by the available memory to store the operands and internal results. The scalable module is in principle capable of performing infinite-precision Montgomery inverse computation of an integer, modulo, a prime number. This scalable hardware is compared with a previously proposed fixed (fully parallel) design showing very attractive results.