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Study mode:
on
1
Intro
2
Outline
3
Generalized Birthday Problem(s)
4
Applications
5
Wagner's algorithm in a single slide
6
An example with k = 4
7
Known quantum complexities
8
Previous exponents (with QAQM)
9
Quantum search
10
Classical merging as a sampling procedure
11
Depth-first traversal of Wagner's tree
12
Quantum merging
13
4-xor example
14
We have to re-optimize the tree
15
General strategy
16
Merging 4 lists with a single solution
17
Schroeppel and Shamir's 4-list method
18
From classical to quantum
19
Time complexity of this example
20
General comparison
21
Conclusion
Description:
Explore quantum algorithms for solving k-xor and k-sum problems in this conference talk presented at Eurocrypt 2020. Delve into the Generalized Birthday Problem and its applications, examining Wagner's algorithm and known quantum complexities. Learn about classical merging as a sampling procedure and depth-first traversal of Wagner's tree. Discover quantum merging techniques, including a 4-xor example and the re-optimization of the tree structure. Investigate the general strategy for merging 4 lists with a single solution, comparing Schroeppel and Shamir's 4-list method to quantum approaches. Analyze time complexities and gain insights into the transition from classical to quantum algorithms in this field.

Optimal Merging in Quantum K-XOR and K-Sum Algorithms

TheIACR
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