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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15
votes
2answers
2k 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?
5
votes
3answers
335 views

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

EDIT : I added more context. Let $f$ = {$f_k$} be a pseudo random 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 ...
4
votes
1answer
238 views

What is meant by $\tilde\Omega(\lambda^4)$?

I'm currently reading the paper (Leveled) fully homomorphic encryption without bootstrapping , and the following paragraph was near the start: What is meant by the symbol used? Is it merely to ...
3
votes
1answer
254 views

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 ...
3
votes
3answers
153 views

Hash Family Example

I am reading my lecture and I found this definition: Let be $F$ be a family of hash functions, that is, a parameterized set $$F=\{g_k:\{0,1\}^{*}\rightarrow\{0,1\}^{n}|k\in K\},$$ where $n\in ...
2
votes
2answers
354 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 ...
2
votes
1answer
90 views

How do these figures represent a boolean function?

In the Wikipedia article "Bent functions", there are some figures representing those Bent functions: How do these figures represent a boolean function ?
2
votes
1answer
315 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 ...
2
votes
0answers
104 views

SIMONs Cryptoanalysis

I'm reading Cryptanalysis of the SIMON Family of Block Ciphers. In Section 3.1, it says: For SIMON, consider an n-bit input difference $\alpha= x\oplus x'$ to $F$ of Hamming weight one. As the ...
1
vote
2answers
128 views

Standard symbol / notation for “x knows y”, or the inverse

What's the standard way to express "$x$ knows about $y$", or "$x$ has no knowledge of $y$" in cryptographic notation? Example (PRNG predictor): $\exists f : P(f(G(k)|_{0..n}) = G(k)|_{n+1}) \geq 0.5 ...
1
vote
1answer
365 views

ECIES protocol - what does the || operation mean?

I am studying elliptic curves problems, which also includes study of related protocols such as ECIES. A there is a problem I don't understand operation $||$. What this operation mean? Some stuff is ...
1
vote
1answer
100 views

What is meant by this notation in the ElGamal key generation process?

Alice chooses i) A large prime $p_A$ (say 200 to 300 digits) ii) A primitive element $\alpha_A$ modulo $p_A$, iii) A (possibly random) integer $d_A$ with $2 \le d_A \le p_A-2$. Alice ...
1
vote
1answer
305 views

What does $(\mathbb{Z}_n^*)^2$ mean?

In a paper they write once, $(\mathbb{Z}_n^*)^2$. Is this the group of quadratic residues or is it something else? Here the theorem: Under the strong RSA assumption, given a modulus $n$, along with ...
1
vote
1answer
36 views

Undefined $E_y(1,r_{i,j,1})$ notation in cryptography paper, suspect ElGamal-like

I'm trying to understand a paper that uses the notation $E_y(1,r_{i,j,1})$ (full text available in link, used just once on Page #35, 6th page of pdf, Section 3.3, Step 1c) in the context of an ...
1
vote
0answers
58 views

What does the notation $1^n$ stand for? [duplicate]

I'm seeing this all over my Katz and Lindell book and I don't see where they introduced it.