Some comments from my notepad, not sure what's the best way to put these edits though.
**** What is cryptography section:
A little abstract, but I was thinking we could distill the main goals to just two,
secrecy - we want to keep the information in encrypted messages private,
i.e. we do not want adversaries to learn information from
our ciphertexts (encrypted texts). So we encrypt messages before sending them, the goal
being to make encrypted messages "indistinguishable".
integrity - we want to be able to check that messages have not
been tampered with, i.e. if an adversary tampers with a message, the
receiver will be able detect it, our tool is authentication,
goal is to make our messages "unforgeable"
(not sure if slightly more explanation of indistinguishability
or unforgeability would be overkill here, I think the examples
will make the notions clearer anyway)
Who are our "adversaries"?
It turns out that in the real world we only need to worry about adversaries that
are "computationally bounded" - i.e. real world computers that can only solve "tractable" problems (problems that are computable in polynomial time). If we had to worry about computers
with the power to solve "harder" problems things would be much trickier.
**** The RSA part
(more math-y speak if needed)
g is chosen from integers between 1 and p-1
(the finite field of order p - this just means the set {1, 2, ..., p-1} together with an
addition and multiplication operation satisfy some rules - in this case, addition and
multiplication are what they usually are for whole numbers, just take the remainder if the number
gets too big)
g is a primitive root modulo p which means that for every number a
that is coprime to p, there exists an exponent x where g^x mod p is
congruent to a mod p
(i.e. g^x cycles through all the integers between 1 and p-1 as
we vary x)
**** Discrete log problem
Seems a little odd to put discrete log at the end of the Merkle tree part, it could go with the RSA part.
Some comments from my notepad, not sure what's the best way to put these edits though.
**** What is cryptography section: A little abstract, but I was thinking we could distill the main goals to just two,
secrecy - we want to keep the information in encrypted messages private, i.e. we do not want adversaries to learn information from our ciphertexts (encrypted texts). So we encrypt messages before sending them, the goal being to make encrypted messages "indistinguishable".
integrity - we want to be able to check that messages have not been tampered with, i.e. if an adversary tampers with a message, the receiver will be able detect it, our tool is authentication, goal is to make our messages "unforgeable"
(not sure if slightly more explanation of indistinguishability or unforgeability would be overkill here, I think the examples will make the notions clearer anyway)
Who are our "adversaries"?
It turns out that in the real world we only need to worry about adversaries that are "computationally bounded" - i.e. real world computers that can only solve "tractable" problems (problems that are computable in polynomial time). If we had to worry about computers with the power to solve "harder" problems things would be much trickier.
**** The RSA part
(more math-y speak if needed) g is chosen from integers between 1 and p-1 (the finite field of order p - this just means the set {1, 2, ..., p-1} together with an addition and multiplication operation satisfy some rules - in this case, addition and multiplication are what they usually are for whole numbers, just take the remainder if the number gets too big)
**** Discrete log problem
Seems a little odd to put discrete log at the end of the Merkle tree part, it could go with the RSA part.