Cryptography Stack Exchange
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Questions tagged [bijection]

A bijection (or a bijective function) is a function $f$ from a set $X$ to a set $Y$ with the property that, for every $y$ in $Y$, there is exactly one $x$ in $X$ such that $f(x) = y$. It follows from this definition that no unmapped element exists in either $X$ or $Y$.

A bijection (or a bijective function) is a function $f$ from a set $X$ to a set $Y$ with the property that, for every $y$ in $Y$, there is exactly one $x$ in $X$ such that $f(x) = y$. It follows from this definition that no unmapped element exists in either $X$ or $Y$.

A bijective function from a set to itself is also called a .

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A bijective hash function

Suppose: $H: \{0,1\}^{n} \rightarrow \{0,1\}^{n}$. $H$ is bijective. It is difficult to derive $x$ from $H(x)$. Is this type of function possible? What would the strength of it be? I realize that RSA and discrete logarithms can fulfill this, but I…
Melab
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Public one-way bijection

What methods do we know to construct a function $f:D\to D$ with domain $D=[0,n)\cap\mathbb N$ (thus $n\in\mathbb N$ elements); demonstrably surjective (thus bijective since $D$ is finite); with definition requiring no trusted party for setup (e.g.…
fgrieu
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Are non bijective sboxes weaker (on feistel networks)?

I have heard it anecdotically that non-bijective sboxes are potentially weaker to be used in designs like feistel networks. (since by design, it is allowed for the sbox to be non-reversible) Is that a fact? The first thought I had on this was that…
Anton Paragas
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Need 32-bit mixing function that has perfect avalanche between octets

for my hobby tinkering project, I need a mixing function that takes 32-bit input and has 32-bit output (and will, most likely, run in a 32-bit C environment) and the following property (independent of endianness, i.e. it’s enough to only look at…
mirabilos
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Are there any bijective one-way functions not based on number-theoretic hardness assumptions?

I'm trying to find a bijective function $y=F(x)$ which should be easy to compute in one direction but hard to compute in the other, where the one-way property is not based on a number theoretic assumption. The hard direction should be preferably as…
SDL
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Proving that RSA encryption function with non-square free modulus is not a permutation

Here is a backgroung for the question on hand. While studying RSA I came up to the question about what happens if $p$ and $q$ involved in modulus computation are not actually primes? There is already a related topic on this (Why does RSA need p and…
Henadzi Matuts
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Find two hard to reverse functions f and h such that f ∘ h ∘ g = h (f and h injective, no constraints on g)

I am looking from 3 functions $f,g,h$ from $\mathbb N \to \mathbb N$ (they can be bijections, they need to be injective at least), such that: $$f \circ h \circ g = h $$ and $f$ is hard to reverse programmatically, and $h$ is hard to reverse…
Mathematical_Noob
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Hash functions, bijectiveness, and entropy

For those who don't know, a bijective function is one for which each input yields one and only one output. A block cipher, for example, is guaranteed to be bijective or you could not decrypt. When a hash function like SHA256 or SHA3 is used with an…
Adam Ierymenko
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Selecting bijective functions for permutations

How would one go about selecting an appropriate bijective function for introducing permutations into a cipher or hash? For example, $f(x) = x+1 \space mod \space n$ is a bijective function, but isn't particularly good as a permutation, in that the…
Polynomial
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How is the 'Algebraic Degree' calculated in the paper about analysing the white-box AES(Chow et al. 2002) by exploiting internal collisions?

This paper proposed a new attack on the initial white-box AES implementation of Chow et al. In order to determine the good solution, we use the particular structure of the function $S_{0}$. $S^{-1} \circ S_{0} \left( \cdot \right) = P_{0}\left(…
leet
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Bijective function with unknown reciprocal function

I have a use case where I need to build a unique identifier for my users with the email address and the "family member number". However, the two personal informations used to build the identifier must be hidden. I thought using a hash function for…
Guerric P
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Is it reasonable to consider that an encryption scheme must be invertible?

I am in a dispute regarding a test question in an exam. The question is something like that: What would happen if one were to use RSA with $n=100$ and $e=13$ to encrypt a message $m$? a) You would be able to encrypt the message but not decrypt…
user2891462
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Explain mixing bijection with an example

I am reading whitebox AES. "Mixing Bijection" is one of the important definition. For example, I copy one paragraph here: The look-up tables that incorporate bytes of round keys can be considered miniature block ciphers. The application of…
TJCLK
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Symmetric property of DDT of inverse function

Given a bijective function $F: \mathbb{F}_2^n \rightarrow \mathbb{F}_2^n$. The entry of the Difference Distribution Table (DDT) at row $\alpha$ and column $\beta$ is defined as $$DDT_{F}(\alpha,\beta) = \delta_F(\alpha, \beta) = |\{ x \in…
Florian
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I read ECB is bad because the same plaintext outputs the same ciphertext. Isn't that a requirement of a cipher?

In the Wikipedia article on Block Ciphers, it says about the Electronic Code Block mode: The disadvantage of this method is that identical plaintext blocks are encrypted into identical ciphertext blocks; thus, it does not hide data patterns…
CodyBugstein
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