AES non-bijective SBox
What effect does non-bijective SBox has on the Security provided by the AES?Is it possible to recover the key or decrypt the ciphertext?If it is possible, what are the specific requirements and...
View ArticleIs AES A Bijective Function
I wanted to ask whether AES is a bijective function, if I'm only observing it in the context of encrypting a single block.Suppose, I'm working with keys of size 256, and I've fixed a key...
View ArticleIn GPV08 lattice signature, why the fact that the bijective from quotient...
I was recently reading the lattice-based signature scheme GPV08 (full paper), and the following statement confuses me alot (which is in the section 5.1, page 17&18):Throughout the paper, we use two...
View ArticleHow 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 0xA5...
View ArticleIs there any bijective obfuscation scheme which maintains a byte order (e.g....
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...
View ArticlePublic 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...
View ArticleFind two hard to reverse functions f and h such that f ∘ h ∘ g = h (f and h...
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...
View ArticleHow are the cipher, the key and the initial message (that is not encrypted)...
Suppose that $m$ is a message that someone player $i$ wants to send to a network of other players $j\neq -i$. The player to prevent his message from cheating by others uses an encyrpstion scheme. Say...
View ArticleDoes an binary elliptic curve like sect571r1 support a bijective asymmetric...
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...
View ArticleExplain 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...
View ArticleHash 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...
View ArticleHow to prove that permutation and substitution ciphers satisfy H(X) = H(Y) in...
I was not able to mathematically prove that all permutation and substitution ciphers satisfy H(X)=H(Y) if we say that Y is the set of ciphertexts while X is the corresponding set of plaintexts in...
View ArticleHow is it possible to prove that Shanon entropy does not change applying any...
I was wondering how is it possible to mathematically prove that Shannon entropy does not change when applying any bijective function to X? For instance H(X) = H(f(X)) assuming that f is invertible and...
View ArticleHow is the 'Algebraic Degree' calculated in the paper about analysing the...
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 theparticular structure of the function $S_{0}$.$S^{-1} \circ...
View ArticleBijective 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...
View ArticleProving that RSA encryption function with non-square free modulus is not a...
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...
View ArticleIs 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 $e=13$ toencrypt a message $m$?a) You would be able...
View ArticleWhy $f(x)=x^e$ 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 bijection...
View ArticleAre bijective polynomials of degree $2 \bmod 2^m$ efficiently inverted?
Take a bijective polynomial of degree $2 \bmod 2^{64}$ like:$m = (n(n+1)/2)\ \bmod 2^{64}$It is bijective and can trivially be inverted for numbers up to $2^{32}$ by calculating...
View ArticleA 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...
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