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Micali-Schnorr Generator (MS-DRBG) Part III - Zero Knowledge Proof Wanted!!

See  also Part I and Part II  of this series
This is going to be a short blog post about the (in)famous Micali-Schnorr  Random Number Generator (MS-DRBG). See Part I and Part II  of this series  for more information about this topic.



WHO: NIST published the specification for Micali-Schnorr  Random Number Generator (MS-DRBG) in NIST Special Publication 800-90 ISO 18031.  Along with the explanation of the core algorithm the documents contains the specification's moduli with the claim to be of the form  n = pq with p = 2p1 + 1, q = 2q1 + 1, where p1 and q1 are (lg(n)/2 – 1)-bit primes.

N.B. a prime of the form p = 2p1 + 1 where p1 is also a prime goes under the name of Safe Prime and they are often used in cryptography for both RSA and DH.

WHAT: Now we can look at the NIST Special Publication 800-90 ISO 18031's moduli and simply believe that those modulis are of the claimed form but maybe is not a great idea (see the WHY section). Going to N(SA)IST and just asking for the factorization is not a great idea either. In the first instance because this will never happen, secondly even if there is not even a single hint that let believe so, having the factorization of the moduli might jeopardize the security of the DRBG. So WHAT?. Well it turns out there is a really beautiful paper from 1998 by Camenisch and Michels where is possible to Proving in Zero-Knowledge that a Number is the Product of Two Safe Primes.
 
WHY: So why we should not trust a priori the aforementioned claim? Well let's say that what happened in the Dual_EC_DRBG case where the presence of a backdoor is now a certainty make us at least raise an eyebrow.


WHEN: Well ideally this should had happened already when the specification (that includes the modulis) was redacted (let's remember that the Camenisch/Michels's paper predates the spec by many years) but Hey is never too late for a nice  Zero Knowledge Proof  :p

WHERE: I wonder where/how this could ever happen.... any idea ?

Having such a ZK proof would be a really win-win in an ideal World. I know this will never happen for this specific case but in my humble opinion this should be the way to go for future specifications!


That's all folks. For more crypto goodies, follow me on Twitter.



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