Question

Solve the discrete logarithm problem 5^{x}\equiv 22 (mod 47) using Baby-Step, Giant-Step algorithm.

10 Mar 2024
Answer :
Word Count : 598
To solve the discrete logarithm problem \( 5^x \equiv 22 \ (\text{mod} \ 47) \) using the Baby-Step, Giant-Step algorithm, we'll go through the following steps: ### 1. Preprocessing: We need to choose an integer \( m \) for the Baby-Step and Giant-Step algorithm. A common choice for \( m \) is approximately \( \sqrt{p} \), where \( p \) is the modulus. In our case, \( p = 47 \), so: \[ m = \lceil \sqrt{47} \rceil = 7 \] This means we will compute \( m = 7 \) baby steps and \( m \) giant steps. ### 2. Baby Steps: Compute and store the values of \( 5^j \ \ (\text{mod} \ 47) \) for \( ________ ________ ____ ____ _____ ______ ______ _______ __________ _________.
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