The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Computer arithmetic: algorithms and hardware designs
Computer arithmetic: algorithms and hardware designs
The Montgomery Modular Inverse-Revisited
IEEE Transactions on Computers - Special issue on computer arithmetic
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
New Algorithm for Classical Modular Inverse
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
Efficient Computation of Multiplicative Inverses for Cryptographic Applications
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
High speed modular divider based on GCD algorithm
ICICS'07 Proceedings of the 9th international conference on Information and communications security
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A new carry-free Montgomery inversion algorithm which is suitable for hardware implementation is presented. The algorithm utilizes a new redundant sign digit (RSD) representation and arithmetic to avoid carry propagation in addition and subtraction, which are the atomic operations in the Montgomery inversion algorithm. The proposed algorithm is described in such a way that its hardware realization is straightforward. The algorithm enables very fast computation of multiplicative inversion in GF(p), which is the most time-consuming operation in elliptic and hyperelliptic curve cryptography. Complexity analysis and a gate level implementation of the algorithm reveal that the proposed algorithm provides a speedup of at least 1.95 over the original Montgomery inversion algorithm.