# Tagged Questions

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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### What does $\mathbb Z_p^*$ contain?

I have a prime $p = 7$ and was tasked to select a random value in $\mathbb Z_p^*$ in my signature scheme. What does the full range of $\mathbb Z_p^*$ contain in this case? Is it $\{0...7\}$ or ...
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### What is the value of Q such that Q|P-1 where P is a prime number?

For my crypto assignment, I'm asked to enter a prime P and generate Q such that Q|P-1 Can anyone guide me what is Q|P-1?
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### What does $\to$ mean in the following definition of a block cipher?

In the following picture $\kappa$ is the key length and $n$ is the block size. I understand that $\{0,1\}^\kappa$ means all possible combination of keys and $\{0,1\}^n$ means all possible combination ...
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### SIMONs Cryptoanalysis

I'm reading Cryptanalysis of the SIMON Family of Block Ciphers. In Section 3.1, it says: For SIMON, consider an n-bit input difference $\alpha= x\oplus x'$ to $F$ of Hamming weight one. As the ...
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### Undefined $E_y(1,r_{i,j,1})$ notation in cryptography paper, suspect ElGamal-like

I'm trying to understand a paper that uses the notation $E_y(1,r_{i,j,1})$ (full text available in link, used just once on Page #35, 6th page of pdf, Section 3.3, Step 1c) in the context of an ...
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### What does the notation $1^n$ stand for? [duplicate]

I'm seeing this all over my Katz and Lindell book and I don't see where they introduced it.
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### How do these figures represent a boolean function?

In the Wikipedia article "Bent functions", there are some figures representing those Bent functions: How do these figures represent a boolean function ?
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### What is meant by $\tilde\Omega(\lambda^4)$?

I'm currently reading the paper (Leveled) fully homomorphic encryption without bootstrapping , and the following paragraph was near the start: What is meant by the symbol used? Is it merely to ...
I am reading my lecture and I found this definition: Let be $F$ be a family of hash functions, that is, a parameterized set $$F=\{g_k:\{0,1\}^{*}\rightarrow\{0,1\}^{n}|k\in K\},$$ where $n\in ... 1answer 107 views ### What is meant by this notation in the ElGamal key generation process? Alice chooses i) A large prime$p_A$(say 200 to 300 digits) ii) A primitive element$\alpha_A$modulo$p_A$, iii) A (possibly random) integer$d_A$with$2 \le d_A \le p_A-2$. Alice ... 1answer 320 views ### What does$(\mathbb{Z}_n^*)^2$mean? In a paper they write once,$(\mathbb{Z}_n^*)^2$. Is this the group of quadratic residues or is it something else? Here the theorem: Under the strong RSA assumption, given a modulus$n$, along with ... 2answers 317 views ### Why does key generation take an input$1^k$, and how do I represent it in practice? 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 ... 1answer 335 views ### What does the expression$1^n$mean as a function argument? In a paper about predicate encryption or attribute based encryption, the setup function is mentioned with the$setup(1^n)$or$setup(1^l)$. I want to know what is meant here. Is it multiples of ones ... 3answers 346 views ### What do$0^n$and$1^n$mean in cryptography? EDIT : I added more context. Let$f$= {$f_k$} be a pseudo random function family. Let$G(x)$be a pseudo-random generator such that:$G(x)$=$f_x$($0^k$)$f_x$($1^k$) where k=$|x|$. I don't ... 2answers 3k views ### What exactly is a negligible (and non-negligible) function? The mathematical definition of neglible and non-neglible functions is fairly clear-cut, but why they are important and how they are used in cryptography? 2answers 358 views ### Why is a non fixed-length encryption scheme worse than a fixed-length one? I have the following definition (highlights by me): An (efficient secret-key) encryption scheme$(Gen,Enc,Dec)$, where$Gen$and$Enc$are PPT algorithms and$Dec$is a Deterministic Polytime ... 2answers 133 views ### Standard symbol / notation for “x knows y”, or the inverse What's the standard way to express "$x$knows about$y$", or "$x$has no knowledge of$y$" in cryptographic notation? Example (PRNG predictor):$\exists f : P(f(G(k)|_{0..n}) = G(k)|_{n+1}) \geq 0.5 ...
I am studying elliptic curves problems, which also includes study of related protocols such as ECIES. A there is a problem I don't understand operation $||$. What this operation mean? Some stuff is ...