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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
Description:
Explore a detailed analysis of the security of Schnorr-type signatures in the Random Oracle Model through this conference talk presented at Eurocrypt 2012. Delve into topics such as forger adversaries, discrete logarithm extraction, the Forking Lemma, meta-reductions, and the One More Discrete Logarithm problem. Examine the intricacies of algebraic reductions, the main strategy for meta-reduction, and the extraction of DLog(A). Investigate the simulation of forger choice, the main theorem, and a thought experiment leading to a new meta-reduction. Consider the probability of bad events, expected-time and queries forgers, and potential extensions of the presented concepts. Gain valuable insights into advanced cryptographic theory and its practical implications for signature schemes.

On the Exact Security of Schnorr-Type Signatures

TheIACR
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