# Requirements for the modulus in the Massey-Omura three pass protocol

In the Massey-Omura three pass protocol:

• How many bits long should the prime modulus $M$ be in order to be secure?
• Should the $M$ be secret?
• Should the $M$ be generated every time or it could be reused to generate new keys?
• I'd guess that it works like DH in that regard, you can use a shared public modulus, as long as it's big enough. 2048 bits or so. – CodesInChaos Jul 14 '15 at 10:46

How many bits long should the prime modulus $M$ be in order to be secure?
The modulus $M$ should be long enough to prevent discrete logarithms from being computable. As of 2015 this means 2048 bits length is fine, but for other (official) recommendations you should consult keylength.com
Should the $M$ be secret?
You can make $M$ secret but making it public shouldn't affect security as long as it's large enough to prevent any discrete logarithm computations from succeeding.