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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Carter-Wegman MAC different notations

While studying Carter-Wegman message authentication codes MAC, I got two different notations for the broader concept and have problems with understanding the difference, if any exist. Let $K, K_1, K_2$...
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Does this protocol description and design look sound?

I am working on a tool that uses password derived keys for AES and a selectable modes of operation to encrypt (and later decrypt) text for storage on an insecure media. The tool is constrained to ...
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Cartesian Product Notation for Encryption and Decryption

I'm learning about encryption $(E)$ and decryption $(D)$ algorithms and am wondering what the following notation means, specifically the cartesian product for $E$ and $D$. $k$ represents key, $P$ ...
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Question about the notation $H\leftarrow\mathcal{H}_{\mathcal{K}}$ in an IND-CCA security experiment

In the paper "Hybrid Key Encapsulation Mechanisms and Authenticated Key Exchange" by Bindel et al., I looked at the IND-CCA security experiment (figure 3). In the first line of the game, ...
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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 ...
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On the construction and notation of a certain OWF

I am studying a little bit about one-way functions from Dr Goyal's notes. He constructs the following OWF: Let $D=\Bbb Z_2^{n^3}$ and $R=\Bbb Z_2^{2 n}$. Given $x \in D$, $f$ interprets $x$ as a set $...
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Confusing notation in signature scheme

In the paper Efficient and Secure Pairing-Free Certificateless Aggregate Signature Scheme for Healthcare Wireless Medical Sensor Networks, on the signature generation part (Page 5), there is an ...
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Why would be the use of such hash function definition? What would be the input of these functions?

$ G \space is \space an \space elliptic \space curve \space group \space G \space with \space order \space q$ and three hash functions are defined as this: $$ H_1: \{0,1\}^*\times G \rightarrow Z^*_q ...
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2 answers
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Probability conventions in cryptography

I am working on Victor Shoup's tutorial on game-based security proof and want to figure out some notions from the perspective of probability theory. Consider the following PRF advantage defined on ...
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Perp notation question

What does the symbol $\perp$ mean? I saw this on a paper where some entity outputs $\perp$.
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what is the notation of nth power of 1? [duplicate]

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?
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Can you identify these cryptographic algorithmic symbols?

I am mostly self taught and have limited knowledge of the symbology in the image below. It is a diagram of a sub block the RIPEMD-160 algorithm: Are such symbols standardized? Is there a good ...
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Notation question: Dividing 2 Elliptic Curve Points producing a third point

I'm working my way through some papers and ran across what seems to be division of two points that produce a third point. I'm new to ECC and am having a terrible time trying to figure out what this ...
David Rusu's user avatar
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Superscript vs subscript notation in cryptographic formulation

I'm currently reading this paper [PDF]. On page 4, I bumped into these notations : \begin{equation} \text { Experiment } \operatorname{Exp}_{\mathcal{F} \mathcal{E}, A}^{\text {ind-mode }}(k) \text { :...
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Understanding this notation for the probability distribution of order preserving encryption

I'm reading this PDF: https://link.springer.com/content/pdf/10.1007/978-3-642-01001-9_13.pdf about order preserving encryption functions and there's this on page 9 (or 232): It's describing the ...
Guerlando OCs's user avatar
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For a given security parameter $\kappa$. what does $poly(\kappa)$ mean?

Let ($Gen,Enc,Dec$) be an LHE scheme with security parameter $\kappa$ and message space $M$. Assume that a multiplication operation exists in $M$, i.e., is a finite ring. Let $F : \{0, 1\}^s × L → M$ ...
dev1610's user avatar
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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 ...
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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)=...
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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 ...
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1 answer
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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 ...
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What does it mean for “1^n”(i.e., the security parameter written in unary)? [duplicate]

As it is mentioned above, I am confused about “Gen takes as input $1^n$ and outputs a key“. Does it mean that the input of Gen is 1111....111 with length of n?
Xinyu Tu's user avatar
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1 answer
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What does $\text{PK}=\text{pk}\oplus\text{H}(\text{opk})$ represent in this paper?

In Lu, Au and Zhang's 2019 paper (Linkable) Ring Signature from Hash-Then-One-Way Signature, they …extend [M. Abe, M. Ohkubo, and K. Suzuki's 2019 1-out-of-n signatures from a variety of keys] ...
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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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14 votes
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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 ...
kelalaka's user avatar
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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 ...
Wild Tarzan's user avatar
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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'...
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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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In DES : Matsui's notation(LC) vs Biham's notation(DC)

I'm doing linear attack for 8 rounds DES. And I just wondering about the difference between Matsui's notation and Biham's notation. In Matsui's paper, numbers bits from 0 to 63 from right to left. In ...
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1 answer
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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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7 votes
1 answer
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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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17 votes
2 answers
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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^...
oniki's user avatar
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6 votes
1 answer
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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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"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
2 votes
1 answer
197 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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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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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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Discrete Logarithm Notation

I'm studying for my final, and some of the practice problems that I have found have discrete logarithms in this notation $L_n(p)$. What does this notation equate to? For example:
Jeg's user avatar
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1 answer
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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's user avatar
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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 ...
NNN's user avatar
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1 answer
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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/...
MSJ's user avatar
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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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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. ...
venturemoo's user avatar
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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?
Frustrated's user avatar
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2 answers
2k views

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?
Ishan's user avatar
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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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