# Tagged Questions

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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### Strange notation using dollar sign

In the paper Multi-Signatures in the Plain Public-Key Model and a General Forking Lemma, the authors Bellare and Neven use notation which looks like left arrow with dollar sign above it. Authors ...
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### Proof of IND-q-CCA security

I have some questions about the paper Bounded CCA2-Secure Encryption (pdf). On page eight "3.2 Construction", the authors have done a black-box construction of an IND-q-CCA security schema and then ...
135 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 ...
671 views

### What does this notation stand for when describing a code?

This code has appeared in some online course material. I understand the $(5, 4, 3)$ refers to (length, num codewords, distance) but no explanation of the $Z_2^5$ notation is given: One $(5,4,3)$ ...
44 views

### Is there a difference between $\mathbb{Z}_2^b$, $\text{GF}(2^b)$ and $\text{GF}(2)^b$?

I have read a lot about Galois Fields (GF). They are also presented in The Design of Rinjdael on page 13. In computer memory, the polynomials in $F[x]|_l$ with $F$ a finite field can be stored ...
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### Range of a number notation

If a number is chosen from $[-n,n]$ is that the same as being chosen from $\mathbb{Z}_n$? Since the operations are modular, what meaning does the negative part of the range have?
361 views

### What does 0…0 and 1…1 mean

I am very new to cryptography but can someone explain what exactly does 0...0 and 1...1 mean in general term. Is it that 1st and ...
64 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 ...
67 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'...
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### 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 ...
115 views

### 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
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### 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 ...
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### What is the recommended format/notation for crypto design?

Is there a recommended format or formal notation for documenting the combination of symmetric and asymmetric encryption, key derivation and other algorithms (and their inputs and outputs) that I think ...
1k 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 ...
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### What does the comma mean in m, c := E(K, m)

Disclaimer: I'm a beginner to cryptography. Background: I'm reading Cryptography Engineering by Ferguson, Schneier, and Kohno, where the authors use this image: Question: What do the commas mean ...
281 views

### Ciphertext notation where the ciphertext consists of two parts

I've see in several places (here or there) the notation $c = (U, V)$ or $c =\langle U, V \rangle$, where $c$ is a ciphertext (to be transmitted). But as both $U$ and $V$ are "key-like". I can't find ...
42 views

### mapping function

I have read a scientific paper which covers some security schemes in mobile ad hoc networks. I don't understand this notation: $$H_0\;\;\;\text{ Mapping }\{0,1\}^*\to \mathbb Z_p^*$$ where $p$ is a ...
118 views

### What does the probability subscript mean in Shannon's secrecy definition?

Shannon's secrecy can be defined as: $$P_M (M=m) = P_{SK,M}(M=m|E(SK,m)=c)$$ What does $P_M$ means? (same question for $P_{SK,M}$) I know that is the probability space M, M being the messages; I do ...
163 views

### Unable to understand hash function representations

I have some hash function representations, which I find it hard to understand. I have searched a lot but didn't found anything helpful. Please help me understand the hash function representations ...
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### Where can I find names for cryptographic notation I don't recognize?

I'm new to this space and find myself stumbling over come cryptographic/mathematical notation. Search engines are not very helpful when copying and pasting Greek letters. Is there any reference that ...
967 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 ...
93 views

### What is the meaning of h(r) in this protocol?

Could somebody tell me what the meaning is of $h(r)$ in the protocol below? ‎‎$A‎\leftarrow‎{B}\quad:{h(r)‎‎}{,B}{,P{_A(r,B)}}‎ \\A‎\rightarrow‎{B}\quad:r$
1k 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 ...
81 views

### Meaning of Multiplicative Group to the power n i.e. Z^n [closed]

What does $Z_q^n$ mean in this notation?      References: on the 2nd paragraph of page: http://en.wikipedia.org/wiki/Learning_with_errors
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### 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 ...
428 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 ...
606 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 ...
508 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 ...
481 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 ...
6k 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?
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 ...