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Multicore curvebased cryptoprocessor with reconfigurable modular arithmetic logic units over GF(2 n
 IEEE Transactions on Computers
"... Abstract—This paper presents a reconfigurable curvebased cryptoprocessor that accelerates scalar multiplication of Elliptic Curve Cryptography (ECC) and HyperElliptic Curve Cryptography (HECC) of genus 2 over GFð2nÞ. By allocating copies of processing cores that embed reconfigurable Modular Arithme ..."
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Cited by 11 (4 self)
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Abstract—This paper presents a reconfigurable curvebased cryptoprocessor that accelerates scalar multiplication of Elliptic Curve Cryptography (ECC) and HyperElliptic Curve Cryptography (HECC) of genus 2 over GFð2nÞ. By allocating copies of processing cores that embed reconfigurable Modular Arithmetic Logic Units (MALUs) over GFð2nÞ, the scalar multiplication of ECC/HECC can be accelerated by exploiting InstructionLevel Parallelism (ILP). The supported field size can be arbitrary up to ðn þ 1Þ 1. The superscaling feature is facilitated by defining a single instruction that can be used for all field operations and point/divisor operations. In addition, the cryptoprocessor is fully programmable and it can handle various curve parameters and arbitrary irreducible polynomials. The cost, performance, and security tradeoffs are thoroughly discussed for different hardware configurations and software programs. The synthesis results with a 0:13 m CMOS technology show that the proposed reconfigurable cryptoprocessor runs at 292 MHz, whereas the field sizes can be supported up to 587 bits. The compact and fastest configuration of our design is also synthesized with a fixed field size and irreducible polynomial. The results show that the scalar multiplication of ECC over GFð2163Þ and HECC over GFð283Þ can be performed in 29 and 63 s, respectively. Index Terms—Multiprocessor systems, processor architectures, reconfigurable hardware, arithmetic and logic units, public key cryptosystems. Ç 1
On Parallelization of HighSpeed Processors for Elliptic Curve Cryptography
 IEEE Transaction on Very Large
"... permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Helsinki University of Technology's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or pr ..."
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Cited by 9 (3 self)
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permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Helsinki University of Technology's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubspermissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
Robust software partitioning with multiple instantiation
 INFORMS Journal on Computing
, 2012
"... The purpose of software partitioning is to assign code segments of a given computer program to a range of execution locations such as general purpose processors or specialist hardware components. These execution locations differ in speed, communication characteristics, and in size. In particular, ha ..."
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Cited by 2 (2 self)
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The purpose of software partitioning is to assign code segments of a given computer program to a range of execution locations such as general purpose processors or specialist hardware components. These execution locations differ in speed, communication characteristics, and in size. In particular, hardware components offering high speed tend to accommodate only few code segments. The goal of software partitioning is to find an assignment of code segments to execution locations that minimizes the overall program run time and respects the size constraints. In this paper we demonstrate that an additional speedup is obtained if we allow code segments to be instantiated on more than one location. We further show that the program run time not only depends on the execution frequency of the code segments but also on their execution order if there are multiply instantiated code segments. Unlike frequency information, however, sequence information is not available at the time when the software partition is selected. This motivates us to formulate the software partitioning problem as a robust optimization problem with decisiondependent uncertainty. We transform this problem to a mixedinteger linear program of moderate size and report on promising numerical results. Key words: robust optimization; software partitioning; decisiondependent uncertainty; multiple instance partitioning 1.
A New Double Point Multiplication Method and its Implementation on Binary Elliptic Curves with . . .
, 2012
"... Efficient and highperformance implementation of point multiplication is crucial for elliptic curve cryptosystems. In this paper, we present a new double point multiplication algorithm based on differential addition chains. We use our scheme to implement single point multiplication on binary ellipti ..."
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Efficient and highperformance implementation of point multiplication is crucial for elliptic curve cryptosystems. In this paper, we present a new double point multiplication algorithm based on differential addition chains. We use our scheme to implement single point multiplication on binary elliptic curves with efficiently computable endomorphisms. Our proposed scheme has a uniform structure and has some degree of builtin resistance against side channel analysis attacks. We design a cryptoprocessor based on the proposed algorithm for double point multiplication and evaluate its area and time efficiency on FPGA. To the best of the authors’ knowledge, this is the first hardware implementation of single point multiplication (using double point multiplication) on elliptic curves with efficiently computable endomorphisms. Our analysis and timing results show that the expected acceleration in point multiplication is considerable. Prototypes of the proposed architectures are implemented and experimental results are presented.
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"... Abstract—Elliptic Curve Cryptography (ECC) is a sort of publickey cryptosystem that is an alternative to other publickey algorithms like DSA, ElGamal, and Rabin. It is widely accepted because of the usage of smaller parameters than other public key cryptosystems but with same level of security. Th ..."
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Abstract—Elliptic Curve Cryptography (ECC) is a sort of publickey cryptosystem that is an alternative to other publickey algorithms like DSA, ElGamal, and Rabin. It is widely accepted because of the usage of smaller parameters than other public key cryptosystems but with same level of security. The basic building blocks of an ECC over (FP) are computations of addition and scalar point multiplication kP mod m, where P is a elliptic curve point, k is arbitrary integer in the range 1 < k < ord(p), and m is a modulus. Although, several methods have been proposed for computing kP, to speed up the modular arithmetic operation which is a key operation in all the methods is not focused. To perform modular operation, normally trail division is used and the hardware implementation of such trail division is very expensive and it may slow down the process. Thus, to speed up the modular operations, a novel fuzzy modular arithmetic is taken in this paper. In fuzzy modular arithmetic, instead of performing division for modulus operation, repeated subtraction is used. Further, an algorithm running on a general computer has only limited physical security and software implementation of cryptographic algorithms is not secured in all time. To overcome, hardware encryption is thought of. Hardware encryption performs cryptographic operations with high speed and has encapsulated security. Thus, this paper focuses on hardware implementation of ECC with fuzzy modular arithmetic using AT89C51 microcontroller.
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"... ©2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other wo ..."
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©2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. ” GF (2 m) Arithmetic Modules for Elliptic Curve Cryptography
A Run Time Reconfigurable CoProcessor for Elliptic Curve Scalar Multiplication
"... This paper reports a runtime reconfigurable coprocessor for scalar multiplication in elliptic curve cryptography. By reconfiguration, the coprocessor can support various finite field orders and hence, different security levels. This is a contribution to solve the current interoperability problems ..."
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This paper reports a runtime reconfigurable coprocessor for scalar multiplication in elliptic curve cryptography. By reconfiguration, the coprocessor can support various finite field orders and hence, different security levels. This is a contribution to solve the current interoperability problems in elliptic curve cryptography. We report the coprocessor hardware organization and the cost in terms of area and speed of the reconfigurable solution compared to a static implementation. 1.
An Efficient Multiplier/Divider Design for Elliptic Curve Cryptosystem over GF(2^m)
, 2009
"... Using the concept of reciprocal polynomial, this paper shows that a field multiplication over GF(2 m) can be implemented by extended Stein’s algorithm, one of the algorithms used to accomplish division. In this way, a field multiplier can be efficiently embedded into a divider with very little hardw ..."
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Using the concept of reciprocal polynomial, this paper shows that a field multiplication over GF(2 m) can be implemented by extended Stein’s algorithm, one of the algorithms used to accomplish division. In this way, a field multiplier can be efficiently embedded into a divider with very little hardware overhead for operand selection based on a fundamental change at the algorithmic level. When applying the developed combined multiplication and division (CMD) algorithm to Elliptic Curve Cryptography (ECC) using affine coordinates, we achieve about 13.8 % reduction on the area requirement with almost no performance degradation compared to the one implemented with two distinct components. Experimental results also demonstrate that not only our CMD circuit has the area advantage (up to 12.7%) in comparison with other lowcost design but also the resulting areaefficient design of ECC system exhibits considerable improvement on the areatime (AT) complexity of previous work.