Cryptographic Backdoors: Breaking the RSA

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# Cryptographic Backdoors: Breaking the RSA - PowerPoint PPT Presentation

Cryptographic Backdoors: Breaking the RSA. Adhokshaj Mishra http://adhokshajmishraonline.in. Who am I?. A hobbyist C, C++, assembly programmer Independent Security Researcher with primary interest in cryptography, virology, crypto-virology, kleptography and mutation.

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## Cryptographic Backdoors: Breaking the RSA

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### Cryptographic Backdoors:Breaking the RSA

Who am I?
• A hobbyist C, C++, assembly programmer
• Independent Security Researcher with primary interest in cryptography, virology, crypto-virology, kleptography and mutation.
Topics To Be Covered
• RSA Revisited
• A Trivial RSA Backdoor
• Significance of PRNG Based Backdoors
• Backdoored PRNG for RSA
• Why AES + CTR?
• Proof of Correctness
• Proof of Concept (DEMO)
RSA Revisited
• Prime numbers: p, q
• N = p x q
• Phi = (p-1) x (q-1)
• e: 1 < e < Phi, gcd(e, Phi) = 1
• d: (d x e) mod Phi = 1
• Public Key: (N, e)
• Private Key: (N, d)
A Trivial RSA Backdoor
• RSA requires two randomly chosen prime numbers.
• Keep one of them fixed for all keys :D
• GCD (N1, N2) = p  constant
• Easily detectable and no forward secrecy
Why PRNG?
• Sweet and safe spot for backdoors
• Backdoors become very hard to detect
• They don’t raise eyebrows when in use
PRNG Backdoor
• Each PRNG instance contains set of parameters unique to itself.
• Seed is the only input that changes with time.
• Only seed is relayed to the attacker.
Common Uses
• PRNG is used in a lot of crypto algorithms. Backdoor the PRNG and all of them are screwed 
• Air-force fighter jets and Navy ships use Zero Knowledge Proofs. ZKP itself works on PRNG 
• PRNG backdoor can render SSL useless. Whole traffic can be recorded in plaintext, and even worse, it can be modified while in progress.