Number theory used in cryptography

Question

I am entering the realm of cryptography and encountering Number Theory related stuff a lot (As expected). I have a good knowledge and background on mathematics but I have been away for a while. So if anyone can give me a refresher (basic, not deep) about the below it would be perfect. (links to proper explanations are also a good idea)

1. B : {0, 1} ^d --> {0, 1}^d
2. A Є {0, 1}^d
3. uniform distribution

Answer 1

$$\{0,1\}$$ is the set that contains 0 and 1, which you should think of as the possible values of a bit. $$\{0,1\}^d$$ is the set of words made of exactly $d$ bits. For example, $\{0,1\}^4$ includes the word 1011.

$$b: \{0,1\}^d\to \{0,1\}^d$$ means that $b$ is a function that takes one of these words and yields a word.

$$A\in \{0,1\}^d$$ means that $A$ is oe of those words of $d$ bits.

A uniform distribution means that you select randomly from some set of things and each thing in the set is equally likely to be chosen.