The cryptography tag has no usage guidance.

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### Optimal covering and CSPNG

Consider a function $f: \{0,1\}^n \to \{0,1\}^{cn}$, where $c>1$.
A random $f$ with high probability generates optimal covering of $\{0,1\}^{cn}$,
i. e.:
$\forall x \in \{0,1\}^{cn}$ $\exists y ...

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118 views

### What should I read to prepare for research in Number Theoretic Cryptography? [closed]

I am not sure if this is the correct place to ask this, and if it is not the correct place, I would appreciate if you could direct me to where I could get this problem answered.
I have just begun my ...

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36 views

### How much p-adic logarithm with precision 2 speeds discrete logarithm modulo $p^2$?

Let $p$ be large prime and $g$ generator of the multiplicative
group modulo $p^2$.
The discrete logarithm (DL) modulo $p^2$ asks : given $g,A,p$, find $x$
satisfying $g^x \equiv A \pmod{p^2}$.
...

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**1**answer

99 views

### Mestre-type algorithm for higher-genus curves?

Is there an analogous algorithm for genus $g>2$ curves that, given a complete set of invariants, outputs a curve with those invariants?
(I'm interested in particular in $g=3$.)
Any references ...

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**3**answers

319 views

### “Most Similar Vector Problem” on an Integer Lattice?

I am currently working on problem that I think could be expressed as an integer lattice problem.
Given $u \in \mathbb{R}^n$ and a bounded integer lattice $L = \mathbb{Z}^n \cap [-M,M]^n$ I would like ...

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**1**answer

114 views

### 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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463 views

### “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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619 views

### 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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352 views

### A balls and urns model for a hashing problem

Fix $N \in \mathbb{N}$. Suppose we throw $N$ numbered balls into $N$ numbered urns, so that for each $b \in \{1,\ldots,N\}$, ball $b$ lands in urn $j$ with equal probability $1/N$. Choose a number $c ...

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163 views

### PRNG and coding theory

Let $k, n \in \mathbb{N}$, $k = (1 - \epsilon)n$ where $1 >\epsilon > 0$.
I want to find $f: \{0,1\}^k \to \{0, 1\}^n$
such that:
1) $f(a) \not= f(b)$ if $a \not=b $
2) for any $x \in ...

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**1**answer

82 views

### 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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1k views

### Bitcoin Research

I have recently been assigned to advise a student on a senior thesis. She has taken linear algebra, introductory real analysis, and abstract algebra. Her interest is in cryptography. And she has a ...

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61 views

### Showing that a crypto hash function is not permutation, possibly conditionally?

Let $f$ be some crypto hash function, say MD5 with output $n$ bits. Restrict the input to $n$ bits.
Cryptographer told me it is open problem if such restricted collision
exists, i.e. $f(x)=f(y),x \ne ...

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3k views

### Encrypting a message for multiple recipients

Let $m$ be a secret message that needs to be sent to $n >1$ recipients. Let each recipient $r_i$ have a public key $p_i$ and private key $s_i$. Is there a scheme such that we can encrypt the ...

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### Is there a security analysis of the GQ digital signature scheme?

I'm doing summer cryptography research and I am have been looking for a security analysis of the Guillou-Quisquater (GQ) digital signature scheme, but I have been unable to find one.
Since this is ...

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1k views

### Securing privacy of “who communicates with whom” under Orwell-like conditions

Assume that there is a big and powerful country with an
information-greedy secret service which has backdoors to all internet nodes
throughout the world which permit him to observe all exchanged data ...

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594 views

### Mathematics of privacy?

I wonder to which extent the current public debate on privacy issues (not only by state sniffing, but e.g. by microtargetting ads too an issue) offers interesting questions in mathematics?
Can we ...

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2k views

### Zero-knowledge proof of positivity

If I have committed to a number x by revealing g^x mod p, can I prove that 0 < x mod (p-1) < (p-1)/2, i.e. that x is positive, without leaking any more information about x?
My bounty is ending ...

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**1**answer

135 views

### DL-problem on abelian variety

Let $A$ be an abelian variety over $\mathbb{F_q}$ with dimension $n$. Let $q$ be a constant.
Is there polynomial algorithm of finding discrete logarithm in $A$?
UPD: really I don't undestend: can we ...

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241 views

### Modular polynomials for elliptic curves point counting

The Schoof-Elkies-Atkin (SEA) algorithm (for counting points on elliptic curves over a finite field) performs computations over polynomials modulo some modular polynomials. Originally the "classical" ...

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**1**answer

95 views

### Functional Encryption for Inner Product Predicates

I want to try to implement a functional encryption scheme proposed in http://eprint.iacr.org/2011/410. The first problem I faced with is a TrapGen algorithm. In the paper theorem 3.1 states that:
...

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233 views

### Polynomial dynamical systems

The question is somewhat related to the theory of permutation polynomials. Let $\mathbb{F}_p$ be a finite field of $p$ elements ($p$ is prime) and $\mathcal{V} = \mathbb{F}_p^2 = \{ (t_1,t_2)\::\: ...

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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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**1**answer

217 views

### 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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193 views

### 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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### Private Randomness extractor

Suppose we are given two random variables $X$ and $Y$ with fixed marginal and joint distribution. What is the maximum randomness that we can extract from $Y$ that is independent from $X$, that is, if ...

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### Is this obfuscation scheme unbreakable?

I've just come across this popular article about a breakthrough (which can be purchased here), published in Foundations of Computer Science (FOCS), 2013 IEEE 54th Annual Symposium by a team of ...

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### Whitening a random bit sequence

Given an (infinite) stream of uncorrelated random bit with a known "reasonable" bias (say 15-85% 1's) I want to whiten it, e.i. produce a shorter stream of bits that has no bias. The restriction is ...

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### Pairing on elliptic curve

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 ...

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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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### Predicting if something is a code

I'm trying to help a non-mathematical friend by posting a question of his here. He studies literature and has come across a book which is written in a made-up language. The book is hundreds of ...

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### Oracle separating FIP for bounded-depth Frege from FIP for Frege (and hardness conditions on DDH)

Is there an oracle such that in the relativized world, bd-Frege (bounded depth Frege propositional proof system) has FIP (feasible interpolation property) but Frege does not have FIP?
Such an ...

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### Is there a two-party multiplicative and additive secret sharing scheme ?

A secret sharing scheme such as Shamir's secret sharing allow to perform addition and multiplication for secret values so far as there is at least 3 participants. Addition of two secret values is done ...

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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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152 views

### Lattice basis reductions and finding minimal values

While reading several articles about lattice basis reduction I am left with a few questions.
For one, I came across this piece of text
Let $\alpha$ and $\beta \in \mathbb{R}$. Also let $X>0$ and ...

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13k views

### Example of a good Zero Knowledge Proof.

I am working on my zero knowledge proofs and I am looking for a good example of a real world proof of this type. An even better answer would be a Zero Knowledge Proof that shows the statement isn't ...

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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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350 views

### cryptographic primitive process

Is there a cryptographic primitive process/method for creating cryptographic tools like symmetric encryption/decryption, Hash code generator, MAC generator and Random number generator?
...

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973 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
...

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### Is Guillou-Quisquater existentially unforgeable against adaptive message attack under a random oracle model?

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 $H$, $e$, ...

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### Attack on CRT-RSA

The survey paper of Prof. Dan Boneh entitled
"Twenty years of attacks on the RSA cryptosystem" mentioned that (Page 5)
one can attack CRT-RSA in square root of decryption exponent. However no
...

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### Knowing md5(c+x), is it possible to find md5(x)?

Suppose:
md5(c1 + x) = c2
md5(x) = y
Is it possible to find y, if c1 and c2 are known and x is uknown? Basically, I know md5(salt + key) and I want to find md5(key).

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### Diophantine approximation

Say absolute values of $a,b,c$ is $O(log^{k}{n})$ for some positive constant $k$.
Given positive integer $n$ that is reasonably large, we cannot always find integers $a,b,c$ such that $|a{b^{c}} - n|$ ...

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### Cryptography and Availability

Hi,
Here is a question in cryptography which is probably naive, and a reference request.
Suppose I have 3 matrices(I1, I2, and I3 -same size) that I want to combine them some how(? do not know yet) ...

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341 views

### Computing the correlation between two vectors without divulging them

Alice and Bob respectively know a vector of $N$ real numbers $u$ and $v$. They would both like to know $\rho = \langle u,v \rangle/N$ but Alice does not want Bob to gain anymore information about $u$ ...

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1k views

### Question on randomness extractors

Person A has a source $W$ with min-entropy($W$) = $k$. He also has an extra piece of information about the random source, denoted with $y$, such that min-entropy($W|y$) = $k/3$.
The adversary doesn't ...