Hardware Implementation of Montgomery's Modular Multiplication Algorithm
IEEE Transactions on Computers
Space/Time Trade-Offs for Higher Radix Modular Multiplication Using Repeated Addition
IEEE Transactions on Computers
Montgomery Multiplication in GF(2^k
Designs, Codes and Cryptography
The Montgomery Modular Inverse-Revisited
IEEE Transactions on Computers - Special issue on computer arithmetic
ARM System Architecture
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
IEEE Micro
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
A Scalable Architecture for Montgomery Multiplication
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Simplifying Quotient Determination in High-Radix Modular Multiplication
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Design and Implementation of a Coprocessor for Cryptography Applications
EDTC '97 Proceedings of the 1997 European conference on Design and Test
Montgomery in Practice: How to Do It More Efficiently in Hardware
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics in Cryptology
High-Radix Design of a Scalable Modular Multiplier
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
A Bit-Serial Unified Multiplier Architecture for Finite Fields GF(p) and GF(2m)
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
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
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
Relationship between GF(2^m) Montgomery and Shifted Polynomial Basis Multiplication Algorithms
IEEE Transactions on Computers
VLSI Implementation of a Functional Unit to Accelerate ECC and AES on 32-Bit Processors
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
A high-performance unified-field reconfigurable cryptographic processor
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Full-custom VLSI design of a unified multiplier for elliptic curve cryptography on RFID tags
Inscrypt'09 Proceedings of the 5th international conference on Information security and cryptology
Hardware/software co-design of elliptic curve cryptography on an 8051 microcontroller
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
Instruction set extensions for pairing-based cryptography
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
International Journal of Information and Computer Security
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We describe a scalable and unified architecture for a Montgomery multiplication module which operates in both types of finite fields GF(p) and GF(2m). The unified architecture requires only slightly more area than that of the multiplier architecture for the field GF(p). The multiplier is scalable, which means that a fixed-area multiplication module can handle operands of any size, and also, the wordsize can be selected based on the area and performance requirements. We utilize the concurrency in the Montgomery multiplication operation by employing a pipelining design methodology. The upper limit on the precision of the scalable and unified Montgomery multiplier is dictated only by the available memory to store the operands and internal results, and the module is capable of performing infinite-precision Montgomery multiplication in both types of finite fields.