The Side Channel

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SEJPM

9:01 AM

@Eddie in a technical sense commutative only applies to operators (AFAIK)

you could call the RSA core primitive (fixed exponent modular exponentiation) commutative

Also note that in most implementation order for these keys matters a lot for security

as e is usually small (and thus easily brute-forced)

perhaps you're looking for Permutation here?

i.e. "the RSA keygen gives you two keys which parametrize the core primitive to be a permutation"?

6 hours later…

Eddie

2:40 PM

@SEJPM Makes sense.

I appreciate the rest of what you suggested. But I'm wondering if that goes "too deep" for my audience. Mostly I'm trying to compare DH and RSA (and even DSA). DH let's you establish a shared secret over an unsecure medium. DSA let's you generate and verify signatures. And RSA creates a set of keys which _______________________ (looking for the right phrase which succinctly highlights two sets of keys which allow you to encrypt with one key and decrypt with the other.

It's possible the right phrase doesn't exist, and that's cool too. I can explain it with longer phras…

SEJPM

3:10 PM

@Eddie "And RSA creates a set of keys which lets you either decrypt or encrypt but not necessarily both"?

Eddie

@SEJPM I may just leave it as "RSA creates a set of keys which let you encrypt with one and decrypt with the other". Mostly what I had before, but I'll remove the "commutative" term since it doesn't seem to be accurate.

SEJPM

@Eddie well technically you can derive the encryption key (usually) from the decryption key, but in practice nobody does that

so yeah, it should be close enough

Eddie

Yea. I mean, doesn't 99% of SSL certificates out there use the same public key, 65537? What matters is the modulus... which, at this point in the class I'm writing the student's aren't ready to hear about =)

2 hours later…

Squeamish Ossifrage

5:14 PM

@Eddie What you are describing is a dangerous misconception about how RSA works: the public and private exponents are very much not interchangeable. I would strongly urge you to avoid trying to characterize it this way, especially for a lay audience that may have difficulty distinguishing (a) things that are technically symmetries in obscure formulas deep in the guts of a mathematics paper, and (b) things that are actually interchangeable in practice.

See crypto.stackexchange.com/a/70530 for details on what can go horribly wrong if you try to interchange the public and private exponents, and crypto.stackexchange.com/a/50440 for what can go horribly wrong if you naively treat the obscure formulas deep in the guts of a mathematical paper as a real cryptosystem which you hope to have application-relevant security properties.

kelalaka

@SqueamishOssifrage welcome back! just a visit?

Squeamish Ossifrage

Yes. Still waiting for Stack Exchange, Inc., to do anything to pull themselves out of the hole they dug themselves into last year. So far I've only seen that they've decided to stop digging.

Recognizing the Law of Holes is a good start, but they burned a lot of bridges that they haven't begun to repair yet as far as I can see.

@Eddie If you really want to go into the mathematical guts, the term you're probably looking for is that RSA is a family of trapdoor permutations. But this technical concept is relevant only to people who are actually working in the mathematical guts; what the lay audience should know about is what security property public-key (anonymous) encryption means and how to do it, or what security property public-key signature means and how to do it.

2 hours later…