RSA Cracking

Implementation of the well-known RSA cracking tech, Common Factor Attacks.

Tech

• Using Node.js to implement Common Factor Attacks
• Big Number Computation
• RSA key generation and restoration

Procedure and Mathematical Computation

• Collect enough quantity of RSA public keys

• Import all public key files

  • extract and stroe their modulus and exponent value

• The value is in the big number form (supported by jsbn)

• Traversal all the possible combination of 12 modulus value

  • to see if there exist a GCD greater then 1

• Store the GCD p and the other factor q of the two modulus respectively

Calculate φ( n ) = (p-1)*(q-1)
Calculate d = e modinverse φ( n )
Calculate dp = d mod (p-1)
Calculate dq = d mod (q-1)
Calculate coeff (A.K.A. invQ) = q modinverse p
Generate private key with modulus, exponent, p, q, dp, dq, invQ and d
Export the private key to pem form

Dependencies

• jsbn: ^1.1.0
• node-rsa: ^1.0.7

Usage

npm ci
npm start
npm test