# 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 $K, K_1, K_2$...
58 views

### 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 ...
59 views

### 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, $P$ ...
1 vote
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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, ...
181 views

### 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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### 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 ...
1k views

### 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 "$<\!\!<\!\!<$" 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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### 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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### 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 ...
647 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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### 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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### 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 ...