Pohlig Hellman Attack Example

[nicole-graus]

Pohlig Hellman Attack Example

Description

This PR adds an implementation that demonstrates the Pohlig-Hellman algorithm for solving the discrete logarithm problem on subgroups of elliptic curves.

In this example we chose to work with a subgroup of the BLS12-381 Elliptic Curve of order
$$s = 96192362849 = 11 \cdot 10177 \cdot 859267.$$

This attack is significantly more efficient than attempting to solve the discrete logarithm problem using brute-force search. Using the Pohlig-Hellman attack, the logarithm can be recovered in under one second, whereas a brute-force approach could take several days.

This highlights the importance of avoiding groups with small primes order factorization in cryptographic applications.

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 72.05%. Comparing base (ca84326) to head (8750d90).

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #995   +/-   ##
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  Coverage   72.05%   72.05%           
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  Files         160      160           
  Lines       35122    35122           
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  Hits        25306    25306           
  Misses       9816     9816           

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[pablodeymo]

Suggested change

	let x = chinese_remainder_theorem(&equations)?;
	Ok(x as u128)
	chinese_remainder_theorem(&equations).and_then(|x| x as u128)

[nicole-graus]

Thanks, we changed it here.