Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
On-Line Error Detection for Bit-Serial Multipliers in GF(2m)
Journal of Electronic Testing: Theory and Applications
Multiplexer-Based Array Multipliers
IEEE Transactions on Computers
Normal bases via general Gauss periods
Mathematics of Computation
Efficient Normal Basis Multipliers in Composite Fields
IEEE Transactions on Computers
An Efficient Optimal Normal Basis Type II Multiplier
IEEE Transactions on Computers
A New Construction of Massey-Omura Parallel Multiplier over GF(2^{m})
IEEE Transactions on Computers
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
A Search of Minimal Key Functions for Normal Basis Multipliers
IEEE Transactions on Computers
Low Complexity Word-Level Sequential Normal Basis Multipliers
IEEE Transactions on Computers
Concurrent Error Detection in a Bit-Parallel Systolic Multiplier for Dual Basis of GF(2m)
Journal of Electronic Testing: Theory and Applications
Fault Detection Architectures for Field Multiplication Using Polynomial Bases
IEEE Transactions on Computers
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Concurrent Error Detection in Montgomery Multiplication over GF(2m)
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Algorithm-Based Fault Tolerance for Matrix Operations
IEEE Transactions on Computers
On concurrent detection of errors in polynomial basis multiplication
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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Successful implementation of elliptic curve cryptographic systems primarily depends on the efficient and reliable arithmetic circuits for finite fields with very large orders. Thus, the robust encryption/decryption algorithms are elegantly needed. Multiplication would be the most important finite field arithmetic operation. It is much more complex compared to the finite field addition. It is also frequently used in performing point operations in elliptic curve groups. The hardware implementation of a multiplication operation may require millions of logic gates and may thus lead to erroneous outputs. To obtain reliable cryptographic applications, a novel concurrent error detection (CED) architecture to detect erroneous outputs in multiplexer-based normal basis (NB) multiplier over GF(2 m ) using the parity prediction scheme is proposed in this article. Although various NB multipliers, depending on $$ \alpha \alpha^{{2^i }} = \sum\limits_{j = 0}^{m - 1} {t_{i,j} } \alpha^{{2^j }} $$ , have different time and space complexities, NB multipliers will have the same structure if they use a parity prediction function. By using the structure of the proposed CED NB multiplier, a CED scalable multiplier over composite fields with 100% error detection rate is also presented.