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A special case: quadratic extensions in odd char
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Classroom Contents
Cover and Decomposition Index Calculus on Elliptic Curve
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- 1 Intro
- 2 The discrete logarithm problem on elliptic curve Use the group of points of an elliptic curve defined over a finite field
- 3 Basic outline of index calculus methods
- 4 Transfer of the ECDLP via cover maps Weil de
- 5 The GHS construction
- 6 Decomposition attack
- 7 Nagao's approach for decompositions
- 8 Analysis of Nagao's approach
- 9 Modified index calculus
- 10 A special case: quadratic extensions in odd char
- 11 The sieving technique Fact: solutions of the polynomial system only give the polynomial
- 12 Second ingredient: the combined attack
- 13 The sextic extension case
- 14 A concrete attack on a 150-bit curve
- 15 Scaling data for our implementation
