J. pelzl, T. Wollinger, J. Guajardo and C. Paar. Hyperelliptic Curve Cryptosystems: Closing The Performance Gap To elliptic Curve (Update), Cryptology ePrint Archieve, Report 2003/026, Home/Search Document Details and Download
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Hyperelliptic Curves and Cryptography - Jacobson, Jr., Menezes, Stein (2004) (1 citation) (Correct)
....processor architectures. Several authors have presented explicit formulas for performing the group law in the jacobian. These formulas are speci c to the genus 2 or genus 3 cases and improve upon Cantor s algorithm and its derivatives. A historical survey of the contributions can be found in [60]. Two recent contributions are those of Lange [47] and Pelzl et al. 60] For genus 2 curves, Lange presented addition formulas that take 1 inversion, 22 multiplications, and 3 squarings in the underlying eld, and doubling formulas that require 2 additional squarings. For genus 3 curves, Pelzl et ....
....for performing the group law in the jacobian. These formulas are speci c to the genus 2 or genus 3 cases and improve upon Cantor s algorithm and its derivatives. A historical survey of the contributions can be found in [60] Two recent contributions are those of Lange [47] and Pelzl et al. [60]. For genus 2 curves, Lange presented addition formulas that take 1 inversion, 22 multiplications, and 3 squarings in the underlying eld, and doubling formulas that require 2 additional squarings. For genus 3 curves, Pelzl et al. gave addition formulas that take 1 inversion, 70 multiplications, ....
J. Pelzl, T. Wollinger, J. Guajardo and C. Paar, \Hyperelliptic curve cryptosystems: Closing the performance gap to elliptic curve (update)", Cryptology ePrint Archive: Report
Fast Arithmetic on Jacobians of Picard Curves - Flon, Oyono (2003) (1 citation) (Correct)
....Picard curves) Still, it is most important to compute eciently in the group, and an important part of today s reseach is devoted to allowing fast arithmetic in Jacobians of curves. For instance, many papers study the case of hyperelliptic curves of genus 2 and 3 ( Lan02] MCT01] KGM 02] PWGP03] In this article, we nd explicit formulae for computing in the Jacobian of a Picard curve, basing us on some geometric aspects of these curves. Volcheck ( Vol94] Huang and Ierardi ( HI94] have already proposed general methods for computing in the Jacobians of arbitrary algebraic curves. ....
J. Pelzl, T. Wollinger, J. Guajardo, and C. Paar, Hyperelliptic curves cryptosystems: closing the performance gap to elliptic curves, Cryptology ePrint archive, 2003, http://eprint.iacr.org/.
Efficient Doubling on Genus 3 Curves over Binary Fields - Fan, Wollinger, Wang (2005) Self-citation (Wollinger) (Correct)
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J. pelzl, T. Wollinger, J. Guajardo and C. Paar. Hyperelliptic Curve Cryptosystems: Closing The Performance Gap To elliptic Curve (Update), Cryptology ePrint Archieve, Report 2003/026,
Finding Optimum Parallel Coprocessor Design for.. - Bertoni.. (2004) (1 citation) Self-citation (Wollinger Paar) (Correct)
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J. Pelzl, T. Wollinger, J. Guajardo, and C. Paar. Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves. In C . K. Koc and C. Paar, editors, Workshop on Cryptographic Hardware and Embedded Systems --- CHES
Hyperelliptic Curve Cryptosystems: Closing the.. - Pelzl, Wollinger.. (2003) (9 citations) Self-citation (Pelzl Wollinger Guajardo Paar) (Correct)
....inversion, M to multiplication, S to squaring, and M=S to multiplications or squarings, since squarings are assumed to be of the same complexity as a multiplication in these publications. For more details on previous improvements made to the explicit formulae the interested reader is referred to [PWGP03] For genus 3 hyperelliptic curves of odd characteristic the only improvement over Cantor s algorithm was presented in [KGM 02] The authors adopted the methods from [MDM 02,Har00] to obtain the speed up. The operation complexity for genus 3 curves is summarized in Table 3. Theoretical ....
....implementations of HECC. To our knowledge there has not been any work dealing with the implementation of HEC on embedded systems. The results of previous HECC software implementations are summarized in Table 2. Detailed information about previously made HECC implementations can be found in [PWGP03]. The rst HECC hardware architectures were proposed in [Wol01] The performance of a hardware based genus two hyperelliptic curve coprocessor over mixed addition Table 2. Execution times of recent HEC implementations in software. reference processor genus eld t scalarmult: in ms [Kri97] ....
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Jan Pelzl, Thomas Wollinger, Jorge Guajardo, and Christof Paar. Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves (Update). Cryptology ePrint Archive, Report 2003/026, 2003. http://eprint.iacr.org/.
Low Cost Security: Explicit Formulae for Genus 4.. - Pelzl, Wollinger, Paar (2003) (4 citations) Self-citation (Pelzl Wollinger Paar) (Correct)
....HECC Cantor [Can87] presented algorithms to perform the group operations on HEC in 1987. In recent years, there has been extensive research being performed to speed up the group operations on genus two HECC [Nag00,Har00,MCT01,MDM 02,Tak02,Lan02a,Lan02b,Lan02c] and genus three [Nag00,KGM 02,PWGP03] Only Nagao [Nag00] tried to improve Cantor s algorithm for higher genera. He mainly applied the following ideas: Division of polynomials without eld inversion Computation of the gcd with one inversion. Interleaving super uous calculations in the reduction part Expressing points on ....
.... software implementations on general purpose machines [Kri97,SS98,Sma99,SS00,MCT01,MDM 02,KGM 02,Lan02a] and publications dealing with hardware implementations of HECC [Wol01,BCLW02] Only very recently work dealing with the implementation of HECC on embedded systems was published in [Pel02,PWGP03] The results of previous genus 4 HECC software implementations are summarized in Table 1. The table entries are sorted in chronological order. All implementations use Cantor s algorithm with polynomial arithmetic. We remark that the contribution at hand is the rst genus 4 HECC implementation ....
[Article contains additional citation context not shown here]
J. Pelzl, T. Wollinger, J. Guajardo, and C. Paar. Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves (Update). Cryptology ePrint Archive, Report 2003/026, 2003. http://eprint.iacr.org/.
SPA resistant left-to-right integer recodings - Theriault (2005) (Correct)
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J. Pelzl, T. Wollinger, J. Guajardo, and C. Paar. Hyperelliptic curve cryptosystems: Closing the performance gap to elliptic curves. In Cryptographic Hardware and Embedded Systems -- CHES 2003, volume 2779 of LNCS, pages 351--365. Springer--Verlag, 2003.
Inversion-Free Arithmetic on Genus 3 Hyperelliptic Curves - Fan, Wang (2004) (Correct)
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J.pelzl, T.Wollinger, J.Guajardo and C.Paar, Hyperelliptic Curve Cryptosystems: Closing The Performance Gap To elliptic Curve (Update), Cryptology ePrint Archieve, Report
A Survey of Public-Key Cryptosystems - Koblitz, Menezes (Correct)
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J. Pelzl, T. Wollinger, J. Guajardo and C. Paar, Hyperelliptic curve cryptosystems: closing the performance gap to elliptic curves, Cryptographic Hardware and Embedded Systems --- CHES
Computing Zeta Functions Of Curves Over Finite Fields - Vercauteren (2003) (1 citation) (Correct)
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J. Pelzl, T. Wollinger, and C. Guajardo, J.and Paar. Hyperelliptic curves cryptosystems: closing the performance gap to elliptic curves. Available at http://eprint.iacr.org/2003.
Fast Addition on Non-Hyperelliptic Genus 3 Curves - Flon, Oyono, Ritzenthaler (2004) (1 citation) (Correct)
No context found.
J. Pelzl, T. Wollinger, J. Guajardo, and C. Paar. Hyperelliptic curves cryptosystems: closing the performance gap to elliptic curves. In Cryptographic Hardware and Embedded Systems - CHES 2003.
Efficient Implementation of Genus Three Hyperelliptic Curve.. - Kitamura, Katagi (2003) (Correct)
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Pelzl, J., Wollinger, T., Guajardo, J., Paar, C.: Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves. Cryptology ePrint Archive, 2003/06, IACR (2003)
Parallelizing Explicit Formula for Arithmetic in the Jacobian .. - Mishra, Sarkar (2003) (2 citations) (Correct)
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J. Pelzl, T. Wollinger, J. Guajardo and C. Paar. Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves. Cryptology ePrint Archive, Report 2003/26, 2003. http://eprint.iacr.org/.
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