Principles of CMOS VLSI design: a systems perspective
Principles of CMOS VLSI design: a systems perspective
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A Comparison of VLSI Architecture of Finite Field Multipliers Using Dual, Normal, or Standard Bases
IEEE Transactions on Computers
Optimal normal bases in GF(pn)
Discrete Applied Mathematics
Journal of Cryptology
A VLSI Architecture for Fast Inversion in GF(2/sup m/)
IEEE Transactions on Computers
IEEE Transactions on Computers
VLSI design for exponentiation in GF(2n)
AUSCRYPT '90 Proceedings of the international conference on cryptology on Advances in cryptology
IEEE Transactions on Computers - Special issue on computer arithmetic
A subexponential algorithm for discrete logarithms over all finite fields
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Finite field inversion over the dual basis
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
GF(2m) Multiplication and Division Over the Dual Basis
IEEE Transactions on Computers
IEEE Transactions on Computers
VLSI Designs for Multiplication over Finite Fields GF (2m)
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Massively Parallel Computation of Discrete Logarithms
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
A Fast Software Implementation for Arithmetic Operations in GF(2n)
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents
IEEE Transactions on Computers
Efficient Rijndael Encryption Implementation with Composite Field Arithmetic
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
A Super-Serial Galois Fields Multiplier for FPGAs and its Application to Public-Key Algorithms
FCCM '99 Proceedings of the Seventh Annual IEEE Symposium on Field-Programmable Custom Computing Machines
Hardware architectures for public key cryptography
Integration, the VLSI Journal
Efficient hardware for the tate pairing calculation in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
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This contribution describes a new class of arithmetic architectures for Galois fields GF(2k). The main applications of the architecture are public-key systems which are based on the discrete logarithm problem for elliptic curves. The architectures use a representation of the field GF(2k) as GF((2n)m), where k = nċm. The approach explores bit parallel arithmetic in the subfield GF(2n), and serial processing for the extension field arithmetic. This mixed parallel-serial (hybrid) approach can lead to very fast implementations. The principle of these approach was initially suggested by Mastrovito. As the core module, a hybrid multiplier is introduced and several optimizations are discussed. We provide two different approaches to squaring which, in conjunction with the multiplier, yield fast exponentiation architectures. The hybrid architectures are capable of exploring the time-space trade-off paradigm in a flexible manner. In particular, the number of clock cycles for one field multiplication, which is the atomic operation in most public-key schemes, can be reduced by a factor of n compared to all other known realizations. The acceleration is achieved at the cost of an increased computational complexity. We describe a proof-of-concept implementation of an ASIC for exponentiation in GF((2n)m), m variable.