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21
An EnergyEfficient Reconfigurable PublicKey Cryptogrphy Processor
 IEEE Journal of solidstate circuits
, 2001
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Highradix Montgomery modular exponentiation on reconfigurable hardware
 IEEE Transactions on Computers
, 2001
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Hardware Implementation of Elliptic Curve Processor over GF(p)
 International Journal of Embedded Systems
, 2003
"... This paper describes a hardware implementation of an arithmetic processor which is efficient for bitlengths suitable for both commonly used types of Public Key Cryptography (PKC), i.e., Elliptic Curve (EC) and RSA Cryptosystems. The processor consists of special operational blocks for Montgomery Mo ..."
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Cited by 36 (6 self)
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This paper describes a hardware implementation of an arithmetic processor which is efficient for bitlengths suitable for both commonly used types of Public Key Cryptography (PKC), i.e., Elliptic Curve (EC) and RSA Cryptosystems. The processor consists of special operational blocks for Montgomery Modular Multiplication, modular addition/substraction, EC Point doubling/addition, modular multiplicative inversion, EC point multiplier, projective to affine coordinates conversion and Montgomery to normal representation conversion.
A Scalable GF(p) Elliptic Curve Processor Architecture for Programmable Hardware
"... This work proposes a new elliptic curve processor architecture for the computation of point multiplication for curves defined over fields GF (p). This is a scalable architecture in terms of area and speed specially suited for memoryrich hardware platforms such a field programmable gate arrays ( ..."
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Cited by 31 (2 self)
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This work proposes a new elliptic curve processor architecture for the computation of point multiplication for curves defined over fields GF (p). This is a scalable architecture in terms of area and speed specially suited for memoryrich hardware platforms such a field programmable gate arrays (FPGAs). This processor uses a new type of highradix Montgomery multiplier that relies on the precomputation of frequently used values and on the use of multiple processing engines.
Security on FPGAs: State of the art implementations and attacks
 ACM. Trans. Embedd. Comput. Syst
, 2004
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Implementation Options for Finite Field Arithmetic for Elliptic Curve Cryptosystems,” Invited presentation at
 the 3rd Workshop on Elliptic Curve Cryptography (ECC ’99
, 1999
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Efficient Elliptic Curve Processor Architectures for Field Programmable Logic
, 2002
"... Elliptic curve cryptosystems offer security comparable to that of traditional asymmetric cryptosystems, such as those based on the RSA encryption and digital signature algorithms, with smaller keys and computationally more efficient algorithms. The ability to use smaller keys and computationally mor ..."
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Cited by 8 (0 self)
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Elliptic curve cryptosystems offer security comparable to that of traditional asymmetric cryptosystems, such as those based on the RSA encryption and digital signature algorithms, with smaller keys and computationally more efficient algorithms. The ability to use smaller keys and computationally more efficient algorithms than traditional asymmetric cryptographic algorithms are two of the main reasons why elliptic curve cryptography has become popular. As the popularity of elliptic curve cryptography increases, the need for efficient hardware solutions that accelerate the computation of elliptic curve point multiplications also increases. This dissertation introduces elliptic curve processor architectures suitable for the computation of point multiplications for curves defined over fields GF (2m) and curves defined over fields GF (p). Each of the processor architectures presented here allows designers to tailor the performance and hardware requirements according to their performance and cost goals. Moreover, these architectures are well suited for implementation in modern field programmable gate arrays (FPGAs). This point was proved with prototyped implementations. The fastest prototyped GF (2m) processor
Towards an FPGA Architecture Optimized for PublicKey Algorithms
 in The SPIE’s Symposium on Voice, Video, and Data Communications
, 1999
"... Cryptographic algorithms are constantly evolving to meet security needs, and modular arithmetic is an integral part of these algorithms, especially in the case of publickey cryptosystems. To achieve optimal system performance while maintaining physical security, it is desirable to implement cryptog ..."
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Cited by 5 (1 self)
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Cryptographic algorithms are constantly evolving to meet security needs, and modular arithmetic is an integral part of these algorithms, especially in the case of publickey cryptosystems. To achieve optimal system performance while maintaining physical security, it is desirable to implement cryptographic algorithms in hardware. However, many publickey cryptographic algorithms require the implementation of modular arithmetic, specifically modular multiplication, for operands of 1024 bits in length. Additionally, algorithm agility is required to support algorithm independent protocols, a feature of most modern security protocols. Reprogrammability, particularly insystem reprogrammability, is critical in enabling the switching between cryptographic algorithms required for algorithm independent protocols. Field Programmable Gate Arrays (FPGAs) are a viable option for achieving this goal. Ideally, the targeted FPGA will have been designed with the architectural requirements for wideoper...
Fast BlumBlumShub Sequence Generation Using Montgomery Multiplication
 In IEEE Proceedings of Computers and Digital Techniques
, 2000
"... VLSI modules are proposed for fast, efficient generation of highthroughput BlumBlumShub (BBS) and BBSlike sequences using Montgomery Multiplication, where postprocessing associated with Montgomery’s algorithm can be eliminated. 2 1 ..."
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Cited by 2 (0 self)
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VLSI modules are proposed for fast, efficient generation of highthroughput BlumBlumShub (BBS) and BBSlike sequences using Montgomery Multiplication, where postprocessing associated with Montgomery’s algorithm can be eliminated. 2 1
Applications of the Montgomery exponent
 International Conference on Information Technology: Coding and Computing
, 2005
"... We define here the Montgomery Exponent of order s, modulo the odd integer N, by MEXP = MEXP(A, X, N, s) = A X 2 −s(X−1) (mod N), and illustrate some properties and usage of this operator. We show how A X (mod N) can be obtained from MEXP(A, X, N, s) by one Montgomery multiplication. This provides a ..."
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We define here the Montgomery Exponent of order s, modulo the odd integer N, by MEXP = MEXP(A, X, N, s) = A X 2 −s(X−1) (mod N), and illustrate some properties and usage of this operator. We show how A X (mod N) can be obtained from MEXP(A, X, N, s) by one Montgomery multiplication. This provides a new modular exponentiation algorithm that uses one Montgomery multiplication less than the number required with the standard method. The resulting reduction in the computation time and code size is significant when the exponent X is short (e.g., modular squaring and RSA verification). We also illustrate the potential advantage in performance and code size when known cryptographic applications are modified to allow for using MEXP as the analogue of modular exponentiation.