# Questions tagged [hardness-assumptions]

Mathematical problems that are thought to be difficult to solve for all cases in polynomial time

122 questions
Filter by
Sorted by
Tagged with
62 views

### Boneh DDH Paper - Sampling Integers in Random Reduction

I've been reading Dan Boneh's DDH paper, in particular section 3.1 which covers DDH randomized reduction. The first two sentences of theorem 3.1 state: Let $\Bbb G = \{G_p\}$ be a family of finite ...
320 views

### Decrypting small integers under RSA

Let $(n,e)$ be an RSA public key. Suppose $c = m^e \pmod n$, where $c>1$ is a very small integer. For concreteness, say $c=2$ or $c=4$. Is it hard to find $m$ under the RSA assumption (or any of ...
56 views

### Group of quadratic residue over Blum integer

Let $x$ be a random element from $QR_n$, the quadratic residue group over Blum integer n (where $n=p*q$ and $p$ and $q$ are safe primes), and $g$ a generator of $QR_n$. Are the following ...
1k views

53 views

### Hard instances of matrix factorization

Are there any hard problems related to matrix factorization? Suppose $E$ is hermitian with public eigenvectors such that $U^T\Lambda U = E$ with $U$ public but $E,\Lambda$ secret. Given $X$ secret, we ...
48 views

39 views

### How hard will it be to solve an equation in elliptic curve group/ cyclic group where Discrete Logarithm is hard?

Given an Elliptic curve group $E(\mathbb{F}_q)$ where the Discrete Logarithm Problem (DLP) is hard and a base point $G \in E(\mathbb{F}_q)$ with large prime order $n$, what will be the advantage of a ...
335 views

### Where does the meaning of reduction to a hard problem lie?

Given a protocol, if we can reduce breaking the protocol to a hard problem, such as DLP or CDH, we can say that this protocol is secure. Theoretically speaking, reduction is a good method to prove the ...
67 views

### Algebraic Variants of NTRU

There are a large number of algebraic NTRU variants: for example, in some (such as ETRU), the underlying ring has been changed to the ring of integers of a certain number field; there is GR-NTRU, ...
199 views

66 views

70 views

110 views

### $P \ne NP$: a proof relating complexity theory to block ciphers

I started thinking about P vs NP after reading another question on this stack exchange. Here I propose a proof that relates P vs NP to the existence of a secure block cipher in the elf model. Let's ...
271 views

### MLWE (and RLWE) to LWE reductions proof

In crypto papers, cryptanalysis of MLWE/RLWE/etc. is often reduced to LWE. Why can we do this? Is there strict proof of such reductions?
276 views

### How is the matrix A related to the lattice space L in SIS?

Is the matrix $A= (b_1|,...,|b_m)$ where B=$(b_1,...,b_m)$ is the basis of the lattice space, $L$(B)? Not sure if the answer is trivial however I'm having trouble seeing how SIS is a lattice hard ...
133 views

### Is phi-hiding assumption as hard as integer factorization?

Phi-hiding assumption can be simply stated as (wrt hardness) It is difficult to find small factors of $\varphi(m)$ where $m$ is a number whose factorization is unknown and $\varphi$ is Euler's ...