RSA cryptanalysis

RSA Attack Playground

Explore how mathematically valid RSA keys fail when parameters are badly chosen. These demos use tiny teaching-size numbers only and render each recovery as a step trace.

Formula trace

Each row shows the rule, the substituted values, and the teaching note.

#	Label	Formula	Substitution	Note
1	Start from ceil(sqrt(n))	a = ceil(sqrt(n))	a = 10008	If p and q are close, a is close to (p + q) / 2.
2	Iteration 0	b² = a² - n	1 = 10008² - 100160063	b² is a perfect square, so factors are recovered.

Mitigation notes

Generate RSA primes with approved libraries and sufficient separation.
Use e = 65537 and never choose unusually small private exponents.
Never reuse the same RSA modulus across different users.
Use randomized padding such as OAEP for encryption and PSS for signatures.
Do not send the same unpadded message to multiple recipients.
Use modern standards and prefer audited cryptographic implementations.

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