# Questions tagged [notation]

Questions on the meaning, history, and usage of symbols and notation in cryptography. Please remember to mention where (book, paper, webpage, etc.) you encountered any notation you are asking about.

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22 votes
3 answers
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### Why does key generation take an input $1^k$, and how do I represent it in practice?

In my lecture, the lecturer said: Let $K$ be the key generation algorithm. Given a security parameter represented in unary, $1^k$, $K(1^k)$ will output a keypair $(pk; sk)$, known as the public ...
• 2,701
11 votes
1 answer
665 views

### How can I instantiate a generalized hash function?

I've come across a bunch of "strange" hash function notations, such as the following ones and now I don't know how to choose / instantiate them. Can you please explain me what this notation means and ...
• 46k
6 votes
1 answer
1k views

### What does the expression $1^n$ mean as a function argument?

In a paper about predicate encryption or attribute based encryption, the setup function is mentioned with the $setup(1^n)$ or $setup(1^l)$. I want to know what is meant here. Is it multiples of ones ...
14 votes
1 answer
1k views

### What the X stands for in the front of Elliptic curve names like X25519

I have seen Curve25519 and X25519, Curve448 and X448. I've seen a small note in this answer (Historical note: Originally, X25519 was called Curve25519, but now Curve25519 just means the elliptic ...
• 48.5k
29 votes
2 answers
22k views

### What exactly is a negligible (and non-negligible) function?

The mathematical definition of neglible and non-neglible functions is fairly clear-cut, but why they are important and how they are used in cryptography?
• 525
8 votes
1 answer
2k views

### What does the $\|$ operation mean in cryptographic notation?

I am studying elliptic curves problems, which also includes study of related protocols such as ECIES. The problem is that I don't understand the notation $\|$. What does this operation mean? Some ...
• 95
6 votes
1 answer
644 views

### "Power of one" as input to functions of a cryptosystem

What does $1^\lambda$ mean when you pass it as a parameter to the functions of a cryptosystem. The cryptosystem in question is this and a picture reference is this. I have been told it signifies the ...
• 273
5 votes
2 answers
16k views

### what is meaning of operator " := " in cryptography?

I've seen := used in several cryptography papers where the this symbol has been used instead of assignment operator ($\leftarrow$ ) or equal sign (=), but never with an accompanying explanation. It'...
0 votes
1 answer
1k views

### What's the difference between these hash functions H, H1 and H2?

These are hash functions, but I don't understand their notations, can anyone tell me what's the difference between H, H1 and H2? $\mathbb{G}_1$ is an additive group and $\mathbb{G}_2$ is a ...
• 125
6 votes
2 answers
3k views

### Why is this the inverse of a Enigma Machine rotor?

I am learning about how the Enigma Machine works and I found this example of one letter being encrypted by an Enigma Machine. It shows the letter "G" going through three rotors and then it goes into ...
• 163
5 votes
3 answers
2k views

### What do $0^n$ and $1^n$ mean in cryptography?

Let $f$ = $\{f_k\}$ be a pseudorandom function family. Let $G(x)$ be a pseudo-random generator such that: $G(x) = f_x(0^k)f_x(1^k)$ where $k=|x|$. I don't understand the meaning of $1^n$ and $0^n$, ...
• 183
1 vote
1 answer
215 views

### Subscript R notation for the finite fields

I'm trying to understand the notation used in the literature for Pairing-based cryptography. I know (and I hope I've understood it well) from Wikipedia that $\mathbb{Z}_p$ is the finite field of prime ...
• 200
3 votes
2 answers
820 views

### Why is a non fixed-length encryption scheme worse than a fixed-length one?

I have the following definition (highlights by me): An (efficient secret-key) encryption scheme $(Gen,Enc,Dec)$, where $Gen$ and $Enc$ are PPT algorithms and $Dec$ is a Deterministic Polytime ...
1 vote
1 answer
236 views

### One way function existence

Let $x = (x_1, x_2,...,x_n)\in\{0,1\}^n$ for $n\in\mathbb{N}$. Prove that if one-way functions (OWFs) exist, then there exists a one-way function $f$ such that for every bit $i\in[1,n]$ there exists ...
• 11
10 votes
2 answers
2k views

• 579
0 votes
1 answer
222 views

### How does this generate a permutation?

In the process of trying to answer this question, I ended up getting stuck. I found a paper which seems to solve their issue: its authors define a process which yields a pseudorandom permutation ...