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Extracting discrete logarithms from a forger
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Classroom Contents
On the Exact Security of Schnorr-Type Signatures
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- 1 Introduction
- 2 Outline
- 3 Forger adversary against Schnorr signatures
- 4 Extracting discrete logarithms from a forger
- 5 Multiple invocations of the forger forking
- 6 Success probability of the reduction: the Forking Lemma
- 7 The concept of meta-reduction
- 8 The One More Discrete Logarithm (OMDL) problem
- 9 Restriction to algebraic reductions
- 10 Meta-reduction main idea
- 11 Meta-reduction: the general strategy
- 12 Extraction of DLog(A) by the meta-reduction
- 13 A bad event which makes the meta-reduction fail
- 14 Simulation of the forger choice of the forgery index
- 15 Main theorem
- 16 A thought experiment
- 17 The new meta-reduction
- 18 Probability of event Bad
- 19 Expected-time and queries forgers
- 20 Extensions
- 21 Conclusion
