Results 151 to 160 of about 216 (184)
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Hyperelliptic Curves with Compact Parameters
Designs, Codes and Cryptography, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ezra Brown +2 more
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Arithmetic of Hyperelliptic Curves
2005In Chapter 1 we introduced the discrete logarithm problem and showed that the main operation in a public-key cryptosystem is the computation of scalar multiples in a cyclic group. Chapter 9 showed how the computation of scalar multiples can be reduced to a sequence of additions and doublings in the group.
Duquesne, S., Lange, T.
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Hyperelliptic Curve Coprocessors on a FPGA
Lecture Notes in Computer Science, 2005Cryptographic algorithms are used in a large variety of different applications to ensure security services. It is, thus, very interesting to investigate various implementation platforms. Hyperelliptic curve schemes are cryptographic primitives to which a lot of attention was recently given due to the short operand size compared to other algorithms ...
Thomas Wollinger +2 more
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Evolution of Hyperelliptic Curve Cryptosystems
2010Due to short operand size, Hyperelliptic Curve Cryptosystem (HECC) of genus 3 is well suited for all kinds of embedded processor architectures, where resources such as storage, time or power are constrained. In the implementation of HECC, a significant step is the selection of secure hyperelliptic curves on which the Jacobian is constructed and speed ...
Kakali Chatterjee, Daya Gupta
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Omega Pairing on Hyperelliptic Curves
2014The omega pairing is proposed as a variant of Weil pairing on special elliptic curves using automorphisms. In this paper, we generalize the omega pairing to general hyperelliptic curves and use the pairing lattice to construct the optimal omega pairing which has short Miller loop length and simple final exponentiation.
Shan Chen +3 more
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Decoding of codes on hyperelliptic curves
1991In 1989, R. Pellikaan gave an algorithm which decodes geometric codes up to \(\left\lfloor {\left( {\frac{{d^* - 1}}{2}} \right)} \right\rfloor\)-errors, where d* is the designed distance of the code. Unfortunately this algorithm is not completely effective.
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Hyperelliptic Curves and Their Jacobians
2011The theory of algebraic curves and their Jacobians is a vast subject with a long history and huge applications. In this chapter, we are going to present only some basic notions and facts, as necessary for further use. Balancing a reasonable length of an introductory chapter and the wish to provide a self-contained exposition, we refer the reader to ...
Vladimir Dragović, Milena Radnović
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Fast scalar multiplication of degenerate divisors for hyperelliptic curve cryptosystems
Applied Mathematics and Computation, 2021Zhi Hu, Dongdai Lin, Chang-An Zhao
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Affine Variety Codes over a Hyperelliptic Curve
Problems of Information Transmission, 2021Sanjay Kumar Singh
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