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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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 ...
juaninf's user avatar
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11 votes
1 answer
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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 ...
SEJPM's user avatar
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6 votes
1 answer
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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 ...
s.venkatesan's user avatar
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 ...
kelalaka's user avatar
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29 votes
2 answers
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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?
Nico Bellic's user avatar
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 ...
eXPi's user avatar
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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 ...
Papa Delta's user avatar
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'...
Sumit Jaiswal's user avatar
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 ...
Chai Ma's user avatar
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6 votes
2 answers
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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 ...
michaelpri's user avatar
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 $0^n$, ...
Yoni Hassin's user avatar
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 ...
3isenHeim's user avatar
  • 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 ...
Alan Bletchley's user avatar
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 ...
maryam's user avatar
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10 votes
2 answers
2k views

Why is the polynomial of an LFSR called so?

As far as I understand, the "polynomial" of the LFSR tells us the positions of the register where taps are situated. However, the natural way to look at the positions would be to think of them as $...
Agnishom Chattopadhyay's user avatar
7 votes
2 answers
7k views

What does ⊕ mean in cryptography?

Can someone please help me with the question below? Explain why 0 ⊕ x ≠ 1 ⊕ x, whatever the value of the bit x. Hence, explain why flipping a bit in the plaintext produces a predictable change in the ...
user avatar
6 votes
1 answer
2k views

Confusing XOR notation in textbook sample solution

I am preparing for the midterm exam in my Data Security class so I am trying to read and understand the textbook's exercise questions. The sample solution at the end the textbook makes this problem ...
Node.JS's user avatar
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3 votes
2 answers
475 views

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 ...
3isenHeim's user avatar
  • 200
2 votes
2 answers
2k views

Understanding Hash function notations

I am implementing a Certificateless Cryptography Algorithm by referencing the paper An Efficient Certificateless Encryption for Secure Data Sharing in Public Clouds. In this paper on page no. 4 during ...
Vighanesh Gursale's user avatar
1 vote
1 answer
2k 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 ...
user4811's user avatar
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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 ...
JamesTheAwesomeDude's user avatar