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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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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1 vote
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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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1 vote
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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 ...
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1 vote
1 answer
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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 ...
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0 answers
36 views

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 $F : \{0, 1\}^s × L → M$ ...
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1 vote
1 answer
198 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 ...
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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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0 votes
1 answer
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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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2 votes
1 answer
110 views

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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2 votes
0 answers
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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?
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1 vote
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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0 votes
1 answer
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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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1 answer
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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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0 votes
1 answer
637 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 ...
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13 votes
1 answer
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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 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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2 votes
1 answer
137 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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1 vote
0 answers
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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 votes
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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1 answer
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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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16 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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2 votes
2 answers
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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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6 votes
1 answer
761 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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6 votes
1 answer
330 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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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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1 vote
1 answer
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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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1 answer
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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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2 votes
1 answer
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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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0 votes
1 answer
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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:
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1 vote
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 $x=\max(a,b,c)$?
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0 votes
1 answer
207 views

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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1 vote
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/...
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-1 votes
1 answer
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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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1 vote
1 answer
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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. ...
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0 votes
1 answer
355 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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1 vote
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?
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1 vote
1 answer
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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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4 votes
1 answer
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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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9 votes
1 answer
430 views

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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10 votes
2 answers
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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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11 votes
1 answer
2k views

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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12 votes
1 answer
13k views

Encoding vs. Compression vs. Encryption

In what ways does encryption differ from proprietary/secret compression schemes and codecs?
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2 votes
0 answers
622 views

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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1 vote
1 answer
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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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3 votes
3 answers
1k views

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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