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High Performance Arithmetic for Hyperelliptic Curve Cryptosystems of Genus Two
, 2003
"... Nowadays, there exists a manifold variety of cryptographic applications: from low level embedded crypto implementations up to high end cryptographic engines for servers. The latter require a exible implementation of a variety of cryptographic primitives in order to be capable of communicating wi ..."
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Cited by 13 (6 self)
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Nowadays, there exists a manifold variety of cryptographic applications: from low level embedded crypto implementations up to high end cryptographic engines for servers. The latter require a exible implementation of a variety of cryptographic primitives in order to be capable of communicating with several clients. On the other hand, on the client it only requires an implementation of one speci c algorithm with xed parameters such as a xed eld size or xed curve parameters if using ECC/ HECC. In particular for embedded environments like PDAs or mobile communication devices, xing these parameters can be crucial regarding speed and power consumption. In this contribution, we propose a highly ecient algorithm for a hyperelliptic curve cryptosystem of genus two, well suited for these constraint devices.
Rethinking low genus hyperelliptic jacobian arithmetic over binary fields: Interplay of field arithmetic and explicit formulae
"... Abstract. In this paper, we present several improvements on the best known explicit formulæ for hyperelliptic curves of genus three and four in characteristic two, including the issue of reducing memory requirements. To show the effectiveness of these improvements and to allow a fair comparison of t ..."
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Cited by 12 (5 self)
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Abstract. In this paper, we present several improvements on the best known explicit formulæ for hyperelliptic curves of genus three and four in characteristic two, including the issue of reducing memory requirements. To show the effectiveness of these improvements and to allow a fair comparison of the curves of different genera, we implement all formulæ using a highly optimized software library for arithmetic in binary fields. This library was designed to minimize the impact of a whole series of overheads which have a larger significance as the genus of the curves increases. The current state of the art in attacks against the discrete logarithm problem is taken into account for the choice of the field and group sizes. Performance tests are done on two personal computers with very different architectures. Our results can be shortly summarized as follows: Curves of genus three provide performance similar, or better, to that of curves of genus two, and these two types of curves can perform faster than elliptic curves – indeed on some processors often twice as fast. Curves of genus four attain a performance level comparable to elliptic curves. A large choice of curves is therefore available for the deployment of curvebased cryptography, with curves of genus three and four providing their own advantages as larger cofactors can be allowed for the group order.
Elliptic & hyperelliptic curves on embedded µp
 ACM Transactions in Embedded Computing Systems (TECS), 2003. Special Issue on Embedded Systems and Security
"... To appear in the special issue on Embedded Systems and Security of the ..."
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Cited by 10 (4 self)
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To appear in the special issue on Embedded Systems and Security of the
High Performance Arithmetic for Special Hyperelliptic Curve Cryptosystems of Genus Two
 In International Conference on Information Technology: Coding and Computing  ITCC 2004. IEEE Computer Society
, 2004
"... Regarding the overall speed and power consumption, cryptographic applications in embedded environments like PDAs or mobile communication devices can benefit from specially designed cryptosystems with fixed parameters. In this contribution, we propose a highly efficient algorithm for a hyperelliptic ..."
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Cited by 6 (4 self)
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Regarding the overall speed and power consumption, cryptographic applications in embedded environments like PDAs or mobile communication devices can benefit from specially designed cryptosystems with fixed parameters. In this contribution, we propose a highly efficient algorithm for a hyperelliptic curve cryptosystem (HECC) of genus two, well suited for these applications on constrained devices. This work presents a major improvement of HECC arithmetic for certain nonsupersingular curves defined over fields of characteristic two. We optimized the group doubling operation and managed to speed up the whole cryptosystem by approximately 27 % compared to the previously known most efficient case. Furthermore, an actual implementation of the new formulae on an embedded processor shows its practical relevance. A scalar multiplication can be performed in approximately 50¢¤ £ on an 80MHz embedded device. 1.
S.: Tree parity machine rekeying architectures
 IEEE Transactions on Computers
, 2005
"... The necessity to secure the communication between hardware components in embedded systems becomes increasingly important with regard to the secrecy of data and particularly its commercial use. We suggest a lowcost (i.e. small logicarea) solution for flexible security levels and short key lifetimes ..."
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Cited by 6 (3 self)
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The necessity to secure the communication between hardware components in embedded systems becomes increasingly important with regard to the secrecy of data and particularly its commercial use. We suggest a lowcost (i.e. small logicarea) solution for flexible security levels and short key lifetimes. The basis is an approach for symmetric key exchange using the synchronization of Tree Parity Machines. Fast successive key generation enables a key exchange within a few milliseconds, given realistic communication channels with a limited bandwidth. For demonstration we evaluate characteristics of a standardcell ASIC design realization as IPcore in ¢¡¤£¦¥¨§ Index Termstechnology. K.4.4.f Security, K.6.5.a Authentication, B.7.1.b Algorithms implemented in hardware, C.3.h Ubiquitous computing, J.9.d Pervasive computing I.
CRYPTOGRAPHIC PROTOCOLS ON REAL HYPERELLIPTIC CURVES
"... (Communicated by Edlyn Teske) Abstract. We present publickey cryptographic protocols for key exchange, digital signatures, and encryption whose security is based on the presumed intractability of solving the principal ideal problem, or equivalently, the distance problem, in the real model of a hype ..."
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Cited by 6 (3 self)
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(Communicated by Edlyn Teske) Abstract. We present publickey cryptographic protocols for key exchange, digital signatures, and encryption whose security is based on the presumed intractability of solving the principal ideal problem, or equivalently, the distance problem, in the real model of a hyperelliptic curve. Our protocols represent a significant improvement over existing protocols using real hyperelliptic curves. Theoretical analysis and numerical experiments indicate that they are comparable to the imaginary model in terms of efficiency, and hold much more promise for practical applications than previously believed. 1.
Effects of Optimizations for Software Implementations of Small Binary Field Arithmetic. To appear
 in Proceedings of WAIFI 2007, International Workshop on the Arithmetic of Finite Fields
, 2007
"... Abstract. We describe an implementation of binary field arithmetic written in the C programming language. Even though the implementation targets 32bit CPUs, the results can be applied also to CPUs with different granularity. We begin with separate routines for each operand size in words to minimize ..."
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Cited by 5 (4 self)
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Abstract. We describe an implementation of binary field arithmetic written in the C programming language. Even though the implementation targets 32bit CPUs, the results can be applied also to CPUs with different granularity. We begin with separate routines for each operand size in words to minimize performance penalties that have a bigger relative impact for shorter operands – such as those used to implement modern curve based cryptography. We then proceed to use techniques specific to operand size in bits for several field sizes. This results in an implementation of field arithmetic where the curve representing field multiplication performance closely resembles the theoretical quadratic bitcomplexity that can be expected for small inputs. This has important practical consequences: For instance, it will allow us to compare the performance of the arithmetic on curves of different genera and defined over fields of different sizes without worrying about penalties introduced by field arithmetic and concentrating on the curve arithmetic itself. Moreover, the cost of field inversion is very low, makingthe use of affine coordinates in curve arithmetic more interesting. These applications will be mentioned.
Explicit formulas for real hyperelliptic curves of genus 2
 in affine representation, in “International Workshop on the Arithmetic of Finite Fields – WAIFI 2007,” Lect. Notes Comput. Sci
, 2007
"... Abstract. In this paper, we present for the first time efficient explicit formulas for arithmetic in the degree 0 divisor class group of a real hyperelliptic curve. Hereby, we consider real hyperelliptic curves of genus 2 given in affine coordinates for which the underlying finite field has characte ..."
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Cited by 5 (1 self)
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Abstract. In this paper, we present for the first time efficient explicit formulas for arithmetic in the degree 0 divisor class group of a real hyperelliptic curve. Hereby, we consider real hyperelliptic curves of genus 2 given in affine coordinates for which the underlying finite field has characteristic> 3. These formulas are much faster than the optimized generic algorithms for real hyperelliptic curves and the cryptographic protocols in the real setting perform almost as well as those in the imaginary case. We provide the idea for the improvements and the correctness together with a comprehensive analysis of the number of field operations. Finally, we perform a direct comparison of cryptographic protocols using explicit formulas for real hyperelliptic curves with the corresponding protocols presented in the imaginary model.
Finding Optimum Parallel Coprocessor Design for Genus 2 Hyperelliptic Curve Cryptosystems
, 2004
"... Hardware accelerators are often used in cryptographic applications for speeding up the highly arithmeticintensive publickey primitives, e.g. in highend smart cards. One of these emerging and very promising publickey scheme is based on HyperElliptic Curve Cryptosystems (HECC). In the open literatu ..."
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Cited by 4 (2 self)
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Hardware accelerators are often used in cryptographic applications for speeding up the highly arithmeticintensive publickey primitives, e.g. in highend smart cards. One of these emerging and very promising publickey scheme is based on HyperElliptic Curve Cryptosystems (HECC). In the open literature only a few considerations deal with hardware implementation issues of HECC.