There are a lot of people who learn and teach the RSA algorithm superficially without a sufficient grasp of the number theory to really understand what is going on. I know because I've been one of them (on both sides). The Carmichael vs. Euler totient issue confused me for a long time.

Needless to say, those people should not be implementing RSA for a system that needs actual security. I'm looking for a better way to teach "real" RSA without needing the students to be math majors or to spend a whole semester on it. Does anybody have any suggestions?

Hm, never encountered the Carmichael function before, but I have had a cursory understanding of Carmichael number.

Given a standard 2048-bit RSA modulus, the totient is still ~2048 bits. I'm not sure and haven't done or seen analysis given the reduction in size (and search space) when replaced with a Carmichael function.

I know, I'll attempt to summon cperciva.

"The efficiency gained from using Carmichael’s totient is minimal. More efficiency can be gained by using Garner’s algorithm."

The proof of which is left to the reader?

Another similar one is that we don't care for strong primes anymore and even though the standards for RSA specifically require it, it's not actually helpful at all, see https://eprint.iacr.org/2001/007

Strong primes are ones where the totient (both carmichael and euler totients) have large primes in them. This happens naturally for 2048 bit and above RSA keys in any-case, they'll statistically absolutely have primes that are larger than the bits needed to factor using elliptic curve methods (>256 bits). In general it's just not that helpful, similar to trying to require carmichael rather than Euler totient. Ok you've made the 2048 bit key 3 bits stronger, great, but let's not bother right?

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