scholarly journals Efficient Explicit Formulae for Genus 2 Hyperelliptic Curves over Prime Fields and Their Implementations

2007 ◽  
pp. 155-172 ◽  
Author(s):  
Xinxin Fan ◽  
Guang Gong
Keyword(s):  
Hyperelliptic Curves ◽  
Genus 2 ◽  
Prime Fields ◽  
Explicit Formulae

scholarly journals Cryptographic aspects of real hyperelliptic curves

2010 ◽  
Vol 47 (1) ◽  
pp. 31-65 ◽  
Author(s):  
Michael J. Jacobson ◽  
Renate Scheidler ◽  
Andreas Stein
Keyword(s):  
Hyperelliptic Curve ◽  
Discrete Logarithm ◽  
Mathematical Structure ◽  
Hyperelliptic Curves ◽  
Cryptographic Protocols ◽  
Discrete Logarithm Problem ◽  
Explicit Formulas ◽  
Genus 2

Abstract In this paper, we give an overview of cryptographic applications using real hyperelliptic curves. We review previously proposed cryptographic protocols and discuss the infrastructure of a real hyperelliptic curve, the mathematical structure underlying all these protocols. We then describe recent improvements to infrastructure arithmetic, including explicit formulas for divisor arithmetic in genus 2, and advances in solving the infrastructure discrete logarithm problem, whose presumed intractability is the basis of security for the related cryptographic protocols.

scholarly journals Explicit formulas for real hyperelliptic curves of genus 2 in affine representation

2011 ◽  
Vol 5 (4) ◽  
pp. 623-666 ◽  
Author(s):  
Stefan Erickson ◽  
Michael Jacobson, Jr. ◽  
Andreas Stein
Keyword(s):  
Hyperelliptic Curves ◽  
Explicit Formulas ◽  
Genus 2
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