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2 Optional: approximate GCD problem: GCD attack and lattice attack The Partial Approximate Common Divisor problem consists in recovering $p$, given $x_0 = p \cdot q_0$ and polynomially many $x_i = p \cdot q_i + r_i$. 1. Implement the brute force attack on the noise. 2. Implement the improved attack from [3]. 3. Implement the lattice attack. 4. Compare the practical complexities of these attacks.

          2 Optional: approximate GCD problem: GCD attack and lattice attack
The Partial Approximate Common Divisor problem consists in recovering $p$, given $x_0 = p \cdot q_0$ and polynomially many $x_i = p \cdot q_i + r_i$.
1. Implement the brute force attack on the noise.
2. Implement the improved attack from [3].
3. Implement the lattice attack.
4. Compare the practical complexities of these attacks.

2 Optional: approximate GCD problem: GCD attack and lattice attack
The Partial Approximate Common Divisor problem consists in recovering p, given x0 = p · q0 and polynomially many xi = p · qi + ri.
1. Implement the brute force attack on the noise.
2. Implement the improved attack from [3].
3. Implement the lattice attack.
4. Compare the practical complexities of these attacks.

Added by Megan S.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

07/05/2022

Step 1

The correct value of p will satisfy the equation o = p : qo and polynomially many x; = p qi + ri. Show more…

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question is attached as an image.please ensure that code run correctly and gives you an output.Thanks!you can use sage library 2 Optional: approximate GCD problem: GCD attack and lattice attack The Partial Approximate Common Divisor problem consists in recovering p, given o = p : qo and polynomially many x; = p qi + ri. 1. Implement the brute force attack on the noise 2. Implement the improved attack from [3]. 3. Implement the lattice attack 4. Compare the practical complexities of these attacks.