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.
Questions tagged [notation]
105 questions
7
votes
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Why is the BSI not using powers of two?
In their Technical Guideline TR-02102-2 Cryptographic Mechanisms: Recommendations and Key Lengths the BSI is giving minimal key lengths for - e.g. the TLS handshake protocol. All of these are not integers that are a power of two. I always thought,…
Tom K.
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6
votes
1 answer
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 or representing something else?
Also, why is this…
s.venkatesan
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6
votes
1 answer
What are the curly brackets in this cryptographic hash function definition?
Reading the Schnorr signature Wikipedia page, I stumbled upon the following statement:
All users agree on a cryptographic hash function $H:\{0,1\}^*\to\mathbb{Z}_q$.
What do these curly brackets mean here and how exactly is the hash function's…
Paul Razvan Berg
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5
votes
3 answers
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 $0^n$, and the differences between them, in that…
Yoni Hassin
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5
votes
2 answers
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's not exactly possible to search the precise…
Sumit Jaiswal
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3
votes
2 answers
What does $\langle A, B\rangle$ mean?
I'm reading about CL-PKC and in Al-Riyami's FullIndent, I find some notations I must be sure to understand, to well explain it in my report.
This algorithm takes paramsand $A$'s secret value $x_A$ as input and
constructs $A$'s public Key $P_A$…
3isenHeim
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3
votes
1 answer
Understanding $\mathbb{Z}_q[X]/(X^N + 1)$ notation in cryptography paper
I can't seem to understand what $A_{N,q}$ represents in this paper (Section 2.1 - Notations). More specifically, I'm struggling to grasp the meaning of $\mathbb{Z}_q[X]/(X^N + 1)$. Could someone please explain it to me?
$\lfloor . \rfloor$…
Al A
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2
votes
1 answer
What does a vertical bar mean in this context?
I'm doing a few exercises regarding Schnorr's identification scheme.
I have the exercise starting off like this, with the values defined:
Let $p = 311$ and $r = 31\ |\ (p - 1)$. Let $g = 169$, which has order $r$.
I just really can't figure out…
Garsty100
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votes
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What is the meaning of the notation $\langle a, b\rangle$ in certain cryptography papers?
I'm trying to understand a paper from Brakerski and Vaikuntanathan. In it, they use the notation $\langle a,b \rangle$ but they don't explain what that means.
The answers on this question say that it's just another way to write a tuple, but I don't…
Mahkoe
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2
votes
0 answers
What is the difference between =, ←, and := in crypto?
I have seen all of the following notations used to denote the encryption of a message $m$ with the key $k$ to produce the ciphertext $c$:
$c = E(k,m)$
$c \leftarrow E(k,m)$
$c := E(k,m)$
Is there any difference between them?
M. Al
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2
votes
1 answer
Top notation as exponent
In cryptography, what does the Top notation mean? It resembles a capital T: T
In particular, I saw it in the follwing context:
$c = (c_1,c_2)^\top$
where $c_1$ and $c_2$ are homomorphic ciphertexts
dfsdf sdfdsf
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2
votes
1 answer
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 ?
Mahdi Khosravi
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1
vote
0 answers
what is the notation of nth power of 1?
when reading theoretical materials, it is often seen that "a common input 1^n..." what does it mean? Are there any similar questions and answers previously in StackExchange?
oxear08
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1
vote
1 answer
Big-Omega and small-Omega question
I found this on page 538 (resp. 576) of Introduction to Modern Cryptography 2nd (resp 3rd) edition by Katz and Lindell. The third bullet point under Example A.6 says:
$$\begin{array}{l}\text{Let }f(n)=n^4+3n+500.\text{…
questioner
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1
vote
1 answer
Multi-argument Poly Notation
In complexity theory, how do you interpret multi-argument poly notation, such as $poly(a,b)$ or $poly(a,b,c)$?
Does it mean $poly(x)$ for $x=\max(a,b,c)$?
Joseph Johnston
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