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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 $Y$.

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### How to design a reversible shifted XOR with an S-box?

According to this post, S-boxes are invertible. Inverting S-boxes can be very easy: you simply create a lookup table that reverse all the possible substitutions of the S-box. E.g. if the S-box maps ...
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### Is there any bijective obfuscation scheme which maintains a byte order (e.g. sorted) or does so after not too many trials? (for 128bit = 16 byte)

We have given 16 bytes and apply some order to them. For example sorting them by their absolute value. We want to obfuscate them as best as possible while maintaining their order. That means if we ...
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### Public one-way bijection [duplicate]

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 ...
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146 views

### 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 ...
1 vote
204 views

### Does an binary elliptic curve like sect571r1 support a bijective asymmetric operation pair on bytes? If so, is there a self-contained example?

I'm wondering if a binary elliptic curve (such as sect571r1 aka B-571) supports pairs of asymmetric operations (for example, either sign/verify or encrypt/decrypt) on a fixed bit or byte input size in ...
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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 ...
• 123
255 views

### 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 ...
710 views

### 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 ...
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1 vote
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### Why $f(x)=x^e$ is a bijection i.f.f $e\in{\mathbf{Z^*_{\phi(N)}}}$?

I understand that if $e\in{\mathbf{Z^*_{\phi(N)}}}$ then $\gcd(e,\phi(N))=1$ and if $e\not\in{\mathbf{Z^*_{\phi(N)}}}$ than $\gcd(e,\phi(N))\neq{}1$. But I couldn't figure out why this implies ...
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