VLSI Architectures for Computing Multiplications and Inverses in GF(2m)
IEEE Transactions on Computers
A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
RSA chips (past/present/future)
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A course in number theory and cryptography
A course in number theory and cryptography
VLSI implementation of public-key encryption algorithms
Proceedings on Advances in cryptology---CRYPTO '86
THOMAS—A complete single chip RSA device
Proceedings on Advances in cryptology---CRYPTO '86
A Comparison of VLSI Architecture of Finite Field Multipliers Using Dual, Normal, or Standard Bases
IEEE Transactions on Computers
Fast RSA-hardware: dream or reality
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Optimal normal bases in GF(pn)
Discrete Applied Mathematics
A VLSI Architecture for Fast Inversion in GF(2/sup m/)
IEEE Transactions on Computers
An Algorithm to Design Finite Field Multipliers Using a Self-Dual Normal Basis
IEEE Transactions on Computers
Generalized Signed-Digit Number Systems: A Unifying Framework for Redundant Number Representations
IEEE Transactions on Computers
A single chip 1024 bits RSA processor
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
A fast elliptic curve cryptosystem
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
VICTOR: an efficient RSA hardware implementation
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
A survey of hardware implementations of RSA (abstract)
CRYPTO '89 Proceedings on Advances in cryptology
Modular exponentiation using recursive sums of residues
CRYPTO '89 Proceedings on Advances in cryptology
A fast modular-multiplication algorithm based on a higher radix
CRYPTO '89 Proceedings on Advances in cryptology
IEEE Transactions on Computers
A Radix-4 Modular Multiplication Hardware Algorithm for Modular Exponentiation
IEEE Transactions on Computers - Special issue on computer arithmetic
IEEE Transactions on Computers - Special issue on computer arithmetic
Bit-Serial Systolic Divider and Multiplier for Finite Fields GF(2/sup m/)
IEEE Transactions on Computers - Special issue on computer arithmetic
IEEE Transactions on Computers
Hardware Implementation of Montgomery's Modular Multiplication Algorithm
IEEE Transactions on Computers
Modulo Reduction in Residue Number Systems
IEEE Transactions on Parallel and Distributed Systems
Redundant Integer Representations and Fast Exponentiation
Designs, Codes and Cryptography - Special issue dedicated to Gustavus J. Simmons
VLSI array algorithms and architectures for RSA modular multiplication
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
Low Complexity Bit-Parallel Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
Systolic Array Implementation of Euclid's Algorithm for Inversion and Division in GF (2m)
IEEE Transactions on Computers
A survey of fast exponentiation methods
Journal of Algorithms
IEEE Transactions on Computers
Mastrovito Multiplier for All Trinomials
IEEE Transactions on Computers
New Low-Complexity Bit-Parallel Finite Field Multipliers Using Weakly Dual Bases
IEEE Transactions on Computers
An improved Montgomery's algorithm for high-speed RSA public-key cryptosystem
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Two systolic architectures for modular multiplication
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Mastrovito Multiplier for General Irreducible Polynomials
IEEE Transactions on Computers
The State of Elliptic Curve Cryptography
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
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Look-Up Table-Based Large Finite Field Multiplication in Memory Constrained Cryptosystems
IEEE Transactions on Computers - Special issue on computer arithmetic
The Montgomery Modular Inverse-Revisited
IEEE Transactions on Computers - Special issue on computer arithmetic
New Systolic Arrays for C + AB2, Inversion, and Division in GF(2m)
IEEE Transactions on Computers
Efficient Normal Basis Multipliers in Composite Fields
IEEE Transactions on Computers
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
An Efficient Optimal Normal Basis Type II Multiplier
IEEE Transactions on Computers
IEEE Transactions on Computers
A Fast Algorithm for Multiplicative Inversion in GF(2m) Using Normal Basis
IEEE Transactions on Computers
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IEEE Transactions on Computers
High-Radix Montgomery Modular Exponentiation on Reconfigurable Hardware
IEEE Transactions on Computers
Handbook of Applied Cryptography
Handbook of Applied Cryptography
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A New Construction of Massey-Omura Parallel Multiplier over GF(2^{m})
IEEE Transactions on Computers
Montgomery Multiplier and Squarer for a Class of Finite Fields
IEEE Transactions on Computers
Examining Smart-Card Security under the Threat of Power Analysis Attacks
IEEE Transactions on Computers
Equally Spaced Polynomials, Dual Bases, and Multiplication in F2^n
IEEE Transactions on Computers
General-Purpose Systolic Arrays
Computer
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IEEE Transactions on Computers
Systolic Modular Multiplication
IEEE Transactions on Computers
On Computing Multiplicative Inverses in GF(2/sup m/)
IEEE Transactions on Computers
A Systolic, Linear-Array Multiplier for a Class of Right-Shift Algorithms
IEEE Transactions on Computers
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
GF(2m) Multiplication and Division Over the Dual Basis
IEEE Transactions on Computers
IEEE Transactions on Computers
A Search of Minimal Key Functions for Normal Basis Multipliers
IEEE Transactions on Computers
Modular Arithmetic Using Low Order Redundant Bases
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Exponentiation Using Division Chains
IEEE Transactions on Computers
An RNS Montgomery Modular Multiplication Algorithm
IEEE Transactions on Computers
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Precise Bounds for Montgomery Modular Multiplication and Some Potentially Insecure RSA Moduli
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics in Cryptology
MIST: An Efficient, Randomized Exponentiation Algorithm for Resisting Power Analysis
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics in Cryptology
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
Efficient elliptic curve exponentiation
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Systolic Modular Multiplication
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Faster Modular Multiplication by Operand Scaling
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Efficient Algorithms for Elliptic Curve Cryptosystems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Fast RSA-Type Cryptosystem Modulo pkq
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Extending the GHS Weil Descent Attack
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Low Cost Attacks on Tamper Resistant Devices
Proceedings of the 5th International Workshop on Security Protocols
Optimal Finite Field Multipliers for FPGAs
FPL '99 Proceedings of the 9th International Workshop on Field-Programmable Logic and Applications
Selecting Cryptographic Key Sizes
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Low Complexity Bit-Parallel Finite Field Arithmetic Using Polynomial Basis
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Montgomery's Multiplication Technique: How to Make It Smaller and Faster
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Highly Regular Architectures for Finite Field Computation Using Redundant Basis
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Fast Multiplication in Finite Fields GF(2N)
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Elliptic Curve Scalar Multiplier Design Using FPGAs
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
A Scalable Architecture for Montgomery Multiplication
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Some Security Aspects of the M IST Randomized Exponentiation Algorithm
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Fault Attacks on RSA with CRT: Concrete Results and Practical Countermeasures
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Modular Exponent Realization on FPGAs
FPL '98 Proceedings of the 8th International Workshop on Field-Programmable Logic and Applications, From FPGAs to Computing Paradigm
The Chinese Remainder Theorem and its application in a high-speed RSA crypto chip
ACSAC '00 Proceedings of the 16th Annual Computer Security Applications Conference
Performance-Scalable Array Architectures for Modular Multiplication
ASAP '00 Proceedings of the IEEE International Conference on Application-Specific Systems, Architectures, and Processors
ASYNC '00 Proceedings of the 6th International Symposium on Advanced Research in Asynchronous Circuits and Systems
Simplifying Quotient Determination in High-Radix Modular Multiplication
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Montgomery Modular Exponentiation on Reconfigurable Hardware
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
Comparison of arithmetic architectures for Reed-Solomon decoders in reconfigurable hardware
FCCM '97 Proceedings of the 5th IEEE Symposium on FPGA-Based Custom Computing Machines
A Compact Fast Variable Key Size Elliptic Curve Cryptosystem Coprocessor
FCCM '99 Proceedings of the Seventh Annual IEEE Symposium on Field-Programmable Custom Computing Machines
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
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FCCM '00 Proceedings of the 2000 IEEE Symposium on Field-Programmable Custom Computing Machines
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ICCD '99 Proceedings of the 1999 IEEE International Conference on Computer Design
Scalable VLSI Architecture for GF(p) Montgomery Modular Inverse Computation
ISVLSI '02 Proceedings of the IEEE Computer Society Annual Symposium on VLSI
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RSP '01 Proceedings of the 12th International Workshop on Rapid System Prototyping
Tamper resistance: a cautionary note
WOEC'96 Proceedings of the 2nd conference on Proceedings of the Second USENIX Workshop on Electronic Commerce - Volume 2
On the importance of checking cryptographic protocols for faults
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Fast arithmetic architectures for public-key algorithms over Galois fields GF((2n)m)
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EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Efficient semisystolic architectures for finite-field arithmetic
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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Proceedings of the 14th ACM Great Lakes symposium on VLSI
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Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
Design and Evaluation of a Security Scheme for Sensor Networks
ISQED '05 Proceedings of the 6th International Symposium on Quality of Electronic Design
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Integration, the VLSI Journal
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Mobile Networks and Applications
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IEEE Design & Test
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IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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CARDIS'06 Proceedings of the 7th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Applications
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International Journal of Information Security and Privacy
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This paper presents an overview of hardware implementations for the two commonly used types of public key cryptography, i.e. RSA and elliptic curve cryptography, both based on modular arithmetic. We first discuss the mathematical background and the algorithms to implement these cryptosystems. Next an overview is given of the different hardware architectures which have been proposed in the literature.