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An Elliptic Curve Processor Suitable For RFID Tags
"... RFIDTags are small devices used for identification purposes in many applications nowadays. It is expected that they will enable many new applications and link the physical and the virtual world in the near future. Since the processing power of these devices is low, they are often in the line of re ..."
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Cited by 19 (1 self)
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. In particular, we show how secure identification protocols based on the DL problem on elliptic curves are implemented on a constrained device such as an RFIDTag requiring between 8,500 and 14,000 gates, depending on the implementation characteristics. We investigate the case of elliptic curves over F2p with p
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
A microcoded elliptic curve processor using FPGA technology
 IEEE Transactions on VLSI Systems
, 2002
"... Abstract—The implementation of a microcoded elliptic curve processor using fieldprogrammable gate array technology is described. This processor implements optimal normal basis field operations in P. The design is synthesized by a parameterized module generator, which can accommodate arbitrary and a ..."
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Cited by 22 (0 self)
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Abstract—The implementation of a microcoded elliptic curve processor using fieldprogrammable gate array technology is described. This processor implements optimal normal basis field operations in P. The design is synthesized by a parameterized module generator, which can accommodate arbitrary
A Scalable and High Performance Elliptic Curve Processor with Resistance to Timing Attacks
"... This paper presents a high performance and scalable elliptic curve processor which is designed to be resistant against timing attacks. The point multiplication algorithm (doubleaddsubtract) is modified so that the processor performs the same operations for every 3 bits of the scalar k independent ..."
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Cited by 4 (0 self)
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This paper presents a high performance and scalable elliptic curve processor which is designed to be resistant against timing attacks. The point multiplication algorithm (doubleaddsubtract) is modified so that the processor performs the same operations for every 3 bits of the scalar k independent
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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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
A HighPerformance Reconfigurable Elliptic Curve Processor for GF(2 m )
, 2000
"... . This work proposes a processor architecture for elliptic curves cryptosystems over fields GF(2 m ). This is a scalable architecture in terms of area and speed that exploits the abilities of reconfigurable hardware to deliver optimized circuitry for different elliptic curves and finite fields. ..."
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Cited by 83 (6 self)
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. This work proposes a processor architecture for elliptic curves cryptosystems over fields GF(2 m ). This is a scalable architecture in terms of area and speed that exploits the abilities of reconfigurable hardware to deliver optimized circuitry for different elliptic curves and finite fields
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
Guide to Elliptic Curve Cryptography
, 2004
"... Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not a threat.) Elliptic curves ..."
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Cited by 593 (18 self)
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Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not a threat.) Elliptic curves
Modular elliptic curves and Fermat’s Last Theorem
 ANNALS OF MATH
, 1995
"... When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n> 2 such that a n + b n = c n ..."
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Cited by 612 (1 self)
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n. The object of this paper is to prove that all semistable elliptic curves over the set of rational numbers are modular. Fermat’s Last Theorem follows as a corollary by virtue of previous work by Frey, Serre and Ribet.
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k
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