A VLSI Architecture for Fast Inversion in GF(2/sup m/)
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
Introduction to Digital Systems
Introduction to Digital Systems
Computer
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
A Scalable and Unified Multiplier Architecture for Finite Fields GF(p) and GF(2m)
CHES '00 Proceedings of the Second 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
New hardware algorithms and designs for montgomery modular inverse computation in galois fields gf(p) and gf(2n)
Efficient scalable VLSI architecture for Montgomery inversion in GF(p)
Integration, the VLSI Journal
A Carry-Free Architecture for Montgomery Inversion
IEEE Transactions on Computers
Improvement to Montgomery Modular Inverse Algorithm
IEEE Transactions on Computers
Parallel Itoh---Tsujii multiplicative inversion algorithm for a special class of trinomials
Designs, Codes and Cryptography
A parallel version of the Itoh-Tsujii multiplicative inversion algorithm
ARC'07 Proceedings of the 3rd international conference on Reconfigurable computing: architectures, tools and applications
Finite field arithmetic for cryptography
IEEE Circuits and Systems Magazine
A fast inversion algorithm and low-complexity architecture over GF(2m)
CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part II
Accelerating inverse of GF(2n) with precomputation
ISPEC'10 Proceedings of the 6th international conference on Information Security Practice and Experience
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Computing the inverse of a number in finite fields GF(p) or GF(2n) is equally important for cryptographic applications. This paper proposes a novel scalable and unified architecture for a Montgomery inverse hardware that operates in both GF(p) and GF(2n) fields. We adjust and modify a GF(2n) Montgomery inverse algorithm to accommodate multi-bit shifting hardware, making it very similar to a previously proposed GF(p) algorithm. The architecture is intended to be scalable, which allows the hardware to compute the inverse of long precision numbers in a repetitive way. After implementing this unified design it was compared with other designs. The unified hardware was found to be eight times smaller than another reconfigurable design, with comparable performance. Even though the unified design consumes slightly more area and it is slightly slower than the scalable inverter implementations for GF(p) only, it is a practical solution whenever arithmetic in the two finite fields is needed.