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Bootstrapping Classical and Quantum Query Lower Bounds for Finding Tarski Fixed Points
Tongyang Li, Weiran Ma, Ziyi Yang +1
The Tarski fixed-point problem asks for a fixed point of a monotone map on a -dimensional grid lattice of width and has applications in game theory, economics, and verificat…
Quantum Query Complexity of Finding a Tarski Fixed Point on a High-Dimensional Grid
Tongyang Li, Weiran Ma, Ziyi Yang +1
The Knaster-Tarski fixed-point theorem states that every monotone function over a complete lattice has a fixed point. Beyond its fundamental role in order theory, the theorem and i…
Quantum Algorithm for Elliptic Curve Discrete Logarithms with Space-Efficient Point Addition
Han Luo, Ziyi Yang, Jingquan Luo +5
The Elliptic Curve Discrete Logarithm Problem (ECDLP) is a fundamental problem in cryptography, and reducing the resource requirements of quantum algorithms for solving ECDLP is an…
Space-Efficient Quantum Algorithm for Elliptic Curve Discrete Logarithms with Resource Estimation
Han Luo, Ziyi Yang, Ziruo Wang +2
Solving the Elliptic Curve Discrete Logarithm Problem (ECDLP) is critical for evaluating the quantum security of widely deployed elliptic-curve cryptosystems. Consequently, minimiz…