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1

Mathematically speaking it should be, but don't forget the weakest chain here : Diffie-Hellman is vulnerable to MitM attacks... So something in addition must be used to ensure your security.

1

ElGamal works for any ring. What is badly specified is the glue between the protocols (some network packets) and the exact implementation variants in the math library. C25519 use arithmetic over Montgomery curves. Ed25519 use arithmetic over twisted Edwards curves. Huff curves implementations can be "faster", but there are not in the repository of curves ...

1

Through repeated DH attempts, could Alice and Bob build a large random key for use as a one-time pad? No, since that is not how a one time pad works. You can use your idea to create cryptographic material to encrypt plaintext using XOR, what you are describing is an asymmetric stream cipher of some sorts. A one time pad requires an "offline" exchange ...

1

Guess the catch in the video is in how the participants exchange details 'publicly'. If the Man-In-The-Middle can intercept and manipulate what is being 'publicly' shared, then the attempt to eavesdrop would still be successful.

5

$\mathbb{Z}^*_{13}$ is a group with 12 elements, not 13. A group is defined by a set of elements, and a "law". The law combines two elements and yields a third one within the set. You get a group if the law fulfils some properties (the law is associative, there is a neutral element, each element has an opposite in the group). $\mathbb{Z}_{13}$ is a group ...

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