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 curve...
View ArticleWhat'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...
View ArticleNotation 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, $f : \{0,1\}^n...
View ArticleWhat does this Big-O notation mean based on appendix?
I am reading the following book: Introduction to Modern Cryptography Second Edition by Jonathan Katz and Yehuda Lindell.I am going through page 533 where they list what some of the notation means, and...
View Articlewhat is meaning of operator " := " in cryptography?
I've seen := used in several cryptography papers where the this symbol has been used instead of assignment operator ($ \leftarrow $ ) or equal sign (=), but never with an accompanying explanation. It's...
View ArticleWhat does it mean for “1^n”(i.e., the security parameter written in unary)?...
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?
View ArticleWhy does key generation take an input $1^k$, and how do I represent it in...
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 key and...
View ArticleWhat 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 has...
View ArticleWhat does $\text{PK}=\text{pk}\oplus\text{H}(\text{opk})$ represent in this...
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] framework...
View ArticleHow 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...
View ArticleBig-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...
View ArticleOne 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 an...
View ArticleFor a given security parameter $\kappa$. what does $poly(\kappa)$ mean?
Let ($Gen,Enc,Dec$) be an LHE scheme with security parameter $\kappa$ andmessage space $M$. Assume that a multiplication operation exists in $M$,i.e., is a finite ring. Let $F : \{0, 1\}^s × L → M$ be...
View ArticleIn 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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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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Understanding this notation for the probability distribution of order...
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 formula...
View ArticleSuperscript 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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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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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 dictionary...
View Articlewhat 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?
View ArticlePerp notation question
What does the symbol $\perp$ mean? I saw this on a paper where some entity outputs $\perp$.
View ArticleProbability 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 Page...
View ArticleWhy would be the use of such hash function definition? What would be the...
$ 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...
View ArticleConfusing 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...
View ArticleOn 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 $S$...
View ArticleUnderstanding $\mathbb{Z}_q[X]/(X^N + 1)$ 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 please...
View ArticleQuestion about the notation $H\leftarrow\mathcal{H}_{\mathcal{K}}$ in an...
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, we have $H...
View ArticleCartesian 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, $P$...
View ArticleDoes 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 using...
View ArticleCarter-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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