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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59 views

What does this Big-O notation mean based on appendix?

I am reading the following book: Introduction to Modern Cryptography Second Edition by Jonathan Katz and Yehuda Lindell. I am going through page 533 where they list what some of the notation means, ...
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Notation for commitment schemes

I was reading this set of lecture notes on commitment schemes, where they define a commitment scheme $\text{Com}(b, r) = f(r), h(r) \oplus b$ as a secure commitment scheme. In this case, $f : \{0,1\}^...
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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 ...
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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 ...
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what is meaning of this (def=) operator in cryptography? [duplicate]

$$t \stackrel{def}{=} \lfloor \sqrt q \rfloor$$ I've found this operator on The Baby-Step/Giant-Step Algorithm
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66 views

What does the “x” operator stands for in cryptography?

I am studying commitment scheme and in of the notes from the class this statement comes up. I'd like to know exactly what the X = M x R mean, since I don't seem to understand how the "x" operator ...
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1answer
118 views

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'...
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How to interpret a specific mathematical notation in “FIPS 202” (SHA-3 / Keccak)

tl;dr What does "d <= |Z|" mean in the context of bit array manipulations? As a learning exercise I'm working on an implementation of SHA-3. I am not a cryptography specialist in any way but I ...
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Meaning of “trans” in crypto algorithm

The paper Snarky signatures: Minimal Signatures of Knowledge from Simulation-Extractable SNARKs by Jens Groth contains this line (on page 16): $$\eta \in (\mathbb{Z})^{\left|Q\right|} \leftarrow \...
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RIBE Scheme Implementation - How to encrypt message

This question is regarding "A Fully Secure Revocable ID-Based Encryption in the Standard Model" - Tung-Tso TSAI, Yuh-Min TSENG, Tsu-Yang WU The encryption method specifies part of the encryption ...
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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 ...
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How did || come to be used in crypto texts to represent concatenation?

In RFC5647, NIST SP 800-38D, etc., || is used to denote concatenation. How did that come to be? In most programming languages ||...
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Rational exponents on group generators

In elementary concepts, mostly scalar exponents shows up in group operations: $g^x$ As one may encounter in more advanced papers, there are rational exponents over generators. Simply seems like: $g^...
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588 views

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 ...
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221 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 ...
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187 views

local collisions in SHA 0

I have found interesting for me paper about constructing collisions in SHA 0. On page 60 the author determines M variable which is a concatenation of 32-bits vectors $M^{(i)}$, but I can't find any ...
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122 views

What does the〈 〉notation mean in this situation?

I was looking at solutions for a problem but I noticed it said $\langle2\rangle$ and was unsure of what that meant. From Homework 5 (PDF)
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A file chunk in a group/field

I am reading a paper by Shacham and Waters on Compact Proofs of Retrievability. In this paper on page number 3 under section 1.1 in the very first line the author states that an encoded file is broken ...
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589 views

How to select elements randomly from a multiplicative group Zn*

I am working on a problem in which I have two large safe primes say p and q randomly selected each of 512 bits. I have generated ...
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1answer
107 views

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 $x=\max(a,b,c)$?
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Why are they called “commitment”, “challenge”, and “response”?

I'm reading Proof Systems for General Statements about Discrete Logarithms, and I think I'll have a better understanding of the process if I can understand where the terms come from. They give a basic ...
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1answer
49 views

What does St denote?

I am reading a paper and notice that the term St is used without being defined. I suspect it is a common notation that I am not aware of. It is used in the following paper: https://eprint.iacr.org/...
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What does fullstop mean in this context?

I'm having difficulties figuring out, what the 'full stop' means in the paper John Almeida - SHADOW NUMBERS PUBLIC KEY ENCRYPTION. Appreciated if someone can elaborate on it or have a list of similar ...
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1k views

ANSI X9.31 AES pseudocode or algorithm explanation

I want to write a program that will generate random data by using ANSI X9.31 with AES 128 bit, however I could find the standart only with cryptographic notation, and I did not understand it clearly. ...
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318 views

What operation does $\|$ denote in ANSI X9.63 KDF? [duplicate]

Can someone tell me in laymens terms what this is? $$K_i = \mathrm{Hash}(Z \| \mathit{Counter} \| [\mathit{SharedInfo}])$$ What do the double pipes represent?
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How to encrypt this using caesar cipher?

I recently had an exercise that read: Encrypt the message "easy question" using Caesar Cipher defined as: C=E(P)=(Pi+3) mod 26 What is this formula and how to solve it?
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287 views

Vertical bar and comma in hash function input

I came across to a definition of a term PMKID while studying 4-way handshake in IEEE 802.11i. It is defined as: PMKID = H(PMK,"PMK name"||AA||SPA) I know the vertical bar || in the input of the hash ...
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Definition of Cascade for Blockciphers

I have seen that given blockciphers $F,G : \mathcal{K} \times \mathcal{M} \to \mathcal{M}$, their cascade $F \circ G$ is defined to be $F \circ G : \mathcal{K}^2 \times \mathcal{M} \times \mathcal{M}$ ...
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What does “$<\!\!<\!\!<$” mean?

What does the symbol $<\!\!<\!\!<$ mean? It is normally followed by a number. An example: It would be appreciated if you could explain it in fairly basic terms.
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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 $...
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Why do crypto tools display key components in such an unusual format?

openssl x509 (v1.0.1f) displays public key moduli as arrays of hex-encoded bytes, 15 columns wide, starting with a leading 00:: ...
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Encoding vs. Compression vs. Encryption

In what ways does encryption differ from proprietary/secret compression schemes and codecs?
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What is the difference between =, ←, and := in crypto? [closed]

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 ...
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193 views

Message space of substitution cipher

I know that the message space is the set of all possible messages, but I'm not sure how to generally define it, rather than for a specific cipher. For example, I've seen $$\{\forall c \in A\}$$, where ...
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Finding the probability of a message encrypting to a given ciphertext

I have been watching a crypto course and when they wanted to prove that the OTP is a secure cipher they refer to the probability and what I can't get so far is the understanding of this notation ? $$...
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810 views

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 ...
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1answer
551 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 ...
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1answer
713 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 $(5,4,3)$ ...
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160 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 The Design of Rijndael: AES - The Advanced Encryption Standard on pages 13 and 14. In computer memory, the polynomials in $...
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1answer
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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?
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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 ...
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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 ...
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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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1answer
126 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 ...
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1answer
813 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 ...
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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 ...