Shor's Algorithm on Qiskit 1.0
400 USD Since IBM only has 127 qubits available, the implementation will likely be sufficient only for a 32-bit group order. The group order may be as follows:
Pcurve = 4294967311
N = 4294843068
Acurve = 0,
Bcurve = 7
Gx = 2502914690 Gy = 3608000288
The task involves solving the elliptic curve discrete logarithm problem (ECDLP) using quantum computations to determine a scalar value (k), such that (k multiplied by G = Q), where (G) is the generator point on the elliptic curve, and (Q) is the given point. Here is a brief description of the approach and key considerations:
1. Operations on elliptic curve: Focus on point addition operations on the elliptic curve, avoiding multiplication or inversion operations that require significant quantum resources.
2. Quantum superposition: Use quantum superposition to parallelize the computation of all possible point additions (G, G + G, G + G + G, up to N additions), speeding up the process compared to the classical sequential approach.
3. Quantum phase estimation (QPE): Apply quantum phase estimation to determine the scalar value (k) by analyzing the superposition results that relate the known point (Q) to the computed points from repeated sums (G).
4. Optimization: Minimize the use of quantum registers, focusing on the (x)-coordinates of points (Qx), allowing for efficient comparisons and reducing quantum resources compared to storing complete point information.
5. Efficiency and quantum advantage: Use quantum parallelism and QPE to achieve significant acceleration in finding (k) compared to classical methods, maintaining the quantum advantage in solving ECDLP.
This approach aims to harness the potential of quantum computing for ECDLP without the complexities and resource requirements associated with full point operations, focusing on a simplified method using point addition and phase estimation.
*If this understanding is correct.
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7 days750 USD
8778 60 0 1 7 days750 USDGood day!
I am ready to implement Shor's algorithm for finding discrete logarithm on elliptic curves with maximum optimization.
I code in Python and I hold the 16th place in this language.
I am eager to start collaborating!
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