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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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1answer
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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 ...
7
votes
1answer
988 views

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 ...
15
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2answers
833 views

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 ||...
2
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2answers
62 views

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^...
4
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1answer
266 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 ...
5
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1answer
138 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 ...
2
votes
1answer
167 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 ...
0
votes
1answer
55 views

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 ...
1
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1answer
199 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 ...
1
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1answer
65 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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1answer
99 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 ...
1
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1answer
43 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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1answer
54 views

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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1answer
447 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. ...
0
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1answer
254 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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2answers
693 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?
2
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1answer
147 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 ...
4
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1answer
84 views

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 $F \circ G : \mathcal{K}^2 \times \mathcal{M} \times \mathcal{M}$ ...
8
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1answer
254 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.
7
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2answers
486 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 $...
12
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1answer
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:: ...
8
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1answer
6k views

Encoding vs. Compression vs. Encryption

In what ways does encryption differ from proprietary/secret compression schemes and codecs?
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0answers
412 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 ...
1
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1answer
141 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 ...
3
votes
3answers
524 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 ? $$...
6
votes
1answer
386 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 ...
2
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0answers
146 views

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 ...
10
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1answer
424 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 ...
5
votes
1answer
707 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 $(5,4,3)$ ...
3
votes
1answer
87 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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1answer
58 views

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?
5
votes
1answer
1k 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 ...
2
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2answers
120 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 ...
3
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2answers
7k 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'...
1
vote
1answer
92 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 ...
2
votes
1answer
317 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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2answers
903 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 ...
8
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1answer
900 views

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 ...
6
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1answer
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 ...
1
vote
2answers
226 views

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 ...
4
votes
1answer
361 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 ...
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votes
2answers
108 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 ...
4
votes
1answer
736 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 ...
3
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1answer
177 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 ...
3
votes
1answer
170 views

Is there a standard notation for a message concatenated with its signature?

I'm wondering what's the standard (or canonical) notation for "a message along with its signature", i.e. $$ \mathit{Message}~\Vert~\sigma_k(\mathit{Message}) \text. $$ Here the duplicated $\mathit{...
2
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0answers
149 views

Can you explain “k out of n” from the VCS paper by Naor and Shamir

I am new to visual cryptography. I’ve just read the paper “Visual Cryptography” by Moni Naor and Adi Shamir and I'm stuck on the chapter about the “$k$ out of $n$” construction. I am aware that, on ...
2
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2answers
150 views

What is the correct way to notate elliptic curve properties

When looking through elliptic curve and modulus posts i can see many examples of people referencing $p$ and $n$, in upper and lower case, and sometimes $Q$ is written instead of $p$ or $P$, and I ...
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1answer
90 views

Explanation of vector in Visual Cryptography

I'm starting to study about visual cryptography, but I am stuck with the following problem. On paper "Visual Cryptography" by Moni Naor and Adi Shamir, on page 6. How to read/what is the meaning of $...
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0answers
103 views

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 ...
6
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2answers
4k 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 ...