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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

Cryptographic Backdoors:Breaking the RSA

AdhokshajMishra

http://adhokshajmishraonline.in

who am i
Who am I?
  • A hobbyist C, C++, assembly programmer
  • Independent Security Researcher with primary interest in cryptography, virology, crypto-virology, kleptography and mutation.
  • Facebook: AdhokshajMishra
  • Twitter: @adhokshajmishra
  • Blog: http://adhokshajmishraonline.in
topics to be covered
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
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
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
Why PRNG?
  • Sweet and safe spot for backdoors
  • Backdoors become very hard to detect
  • They don’t raise eyebrows when in use
prng backdoor
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
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.