Tagged Questions

Questions concerning the mathematics of secure communication. Relevant topics include elliptic curve cryptography, secure key exchanges, and public-key cryptography (eg. the RSA cryptosystem).

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Are there any unitary matrices which satisfy the Yang-Baxter equation which are universal for quantum computation?

Let $H$ be a finite dimensional hilbert space. Let $L:H\otimes H\rightarrow H\otimes H$ be a unitary transformation. Then the equation (L\otimes I)(I\otimes L)(L\otimes I)=(I\otimes L)(L\otimes I)(I\...
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Do the normal forms for braid groups really conceal information about better than randomly applying the braid relations?

In braid based cryptography, one typically wants to conceal the way a certain braid $b$ has been obtained. One therefore puts $b$ into some normal form. Since every braid has a unique normal form, the ...
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Inverting a function

I posted this question on crypto.SE but got no answer: Let $w = a_0 \cdot a_1 \cdots a_{n-1}$ be a word from $\{0,1\}^n$, $|w| = n$ Let $m = \sum_{i=0}^{n-1}{ a_i \cdot 2 ^ {n-1-i} }$ be the ...
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Elliptic Curve Multiplication [closed]

What would happen if I performed Elliptic Curve multiplication on some random point within the FiniteField that wasn't actually on the curve? I assume that I would get a point in return but would that ...
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“The Two Sheriffs” puzzle -2: threshold for security

I've already asked a question “The Two Sheriffs” puzzle with wrong assumption. Yoav Kallus in his amazing answer using Fano plane showed that the problem has a solution in the case of seven suspects. ...
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Factorization when a factor is partially known

Let's say that I have a very large number of the order ($10^{250+}$) which is composite. I have been given one of its factor partially to a significant amount of digits (say 75+). Then, how can I ...
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Future-Proof Encrypt for Multiple Independent Parties

I have a secret message which I want to encrypt such that any of several different keys can open it independently. The keys can't know about each other and it has to be able to work completely ...
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Canonical lifts from $\mathbb F_q$ and CM-theory

One knows that (ordinary) Jacobians of hyperelliptic curves over a finite field $\mathbb F_q$ (mostly of genus 1 (elliptic curves) and 2) are extensively studied by cryptographers, as a platform for ...
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Genus 2 hyperelliptic cryptography : typical discriminant and class number

As far as I know, there is no standard yet for cryptography based on the DLP over Jacobians of genus 2 curves. Yet, what can we say about the class number, and the discriminant of the complex ...
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Encrypting the same message using different schemes

$E_1$ and $E_2$ are IND-CPA secure encryption schemes. $E$ is defined as: $k_1,k_2 \leftarrow K_1 \times K_2$ . $E_{k_1,k_2}(m) \leftarrow E_{1,k_1}(m)||E_{2,k_2}(m)$. Hope the notations are in an ...
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Connection between inf-entropy rate and min-entropy

I am reading the paper "Generating random bits from an arbitrary source: fundamental limits" by Vembu and Verdu. This paper is written in the language of information theory, however, I need to ...
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Anomalous elliptic curves over finite rings

I was wondering if it is possible to solve the discrete logarithm on an Elliptic Curve E(Z/nZ) (defined over the ring of integers modulo a composite n) with #E(Z/nZ)=n by applying a method analogous ...
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largest size for a randomness extractor

I am not so expert in theoretical computer science, so sorry if the question is trivial, i just could not find it in literature. Suppose we have a source $X$ with min-entropy $\ell$, the randomness ...
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Are there very strongly pseudorandom permutations?

A pseudorandom permutation can be defined formally as a function $\phi$ from $\{0,1\}^k\times\{0,1\}^n$ to $\{0,1\}^n$ such that for every $x\in\{0,1\}^k$ the function $\phi_x:y\mapsto\phi(x,y)$ is a ...
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Collision resistance of hash functions after permuting one hash digest

Given a hash function H and a fixed permutation pi of the digest set. Consider "collisions" of the form H(x) = pi(H(x')). How is resistance against this kind of ...
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Will quantum computing kill cryptography ? [closed]

I apologize as this question is not really mathematical, and therefore perhaps not well-suited for this site. Please feel free to close it if you think it is not. My reason for asking it here is that ...
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Which hard mathematical problems do you have to solve to earn bitcoins ?

A virtual currency called bitcoins has been in the news recently. It is said that in order to "mine" bitcoins, you have to solve hard mathematical problems. Now, there are two kinds of mathematical ...
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Let $E(\mathbb{F_q})$ - elliptic curve. $G_1 = E(\mathbb{F_q})[r]$. $|G_1| = r$. $k$ is minimal such $r | q^k - 1$. $\pi_q$ - $q$-power Frobenius endomorphism. $G_2 = E(\mathbb{F_{q^k}})[r] \cap ... 4answers 1k views The “interplay” between additive and multiplicative structure in a field A field is an ordered triple$(F, +,\cdot)$of a set$F$and binary operations$+,\times$on$F$such that$(F,+)$and$(F\backslash 0,\times)$are abelian groups satisfying the distributive laws$\...
First of all, the Guillou-Quisquater digital signature scheme is: Note everything is $\bmod n$. Message is denoted by $m$. Private key: $s$ Public key: Hash function $H$, $e$, \$L=s^e\...