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Efficient Logarithm Computation with Pollard's Rho Algorithm

Learn about the Pollard's Rho algorithm for computing discrete logarithms, a randomized method with minimal storage requirements and practical efficiency. This handbook provides an introduction, algorithm pseudocode, and a detailed example of this algorithm. Compared to the baby-step giant-step algorithm, Pollard's Rho is ideal for practical problems. The document focuses on cyclic groups with prime order. For further reference, explore the provided link.

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Efficient Logarithm Computation with Pollard's Rho Algorithm

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  1. Handbook of Applied Cryptography- CH3, 3.6.3 Kwang-Wook Yun 2017. 9.18

  2. Agenda • 3.6.3 Pollard’s rho algorithm for logarithms • Introduction • Algorithm pseudocode • Example

  3. 3.6.3 Introduction • Pollard’s rho algorithm(Algorithm3.60) for computing discrete logarithms is a randomized algorithm with the same expected running time as the baby-step giant-step algorithm. • But, Pollard’s rho algorithm requires a negligible amount of storage. • it is far preferable to baby-step giant-step algorithm for problems of practical interest. For simplicity, it is assumed in this subsection that G is a cyclic group whose order n is prime.

  4. 3.6.3 Introduction

  5. 3.6.3 Algorithm pseudocode

  6. 3.6.3 Example

  7. 4.2.1 Fermat’s test • 4.11

  8. 참조 • Pollard’s rho algorithm for logarithms: https://en.m.wikipedia.org/wiki/Pollard%27s_rho_algorithm_for_logarithms

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