# Questions tagged [complexity]

Complexity describes - in simple words - how hard (complex) it is to reach a specific goal; and under which conditions. In cryptography, this mostly ends up in using the complexity theory to analyze things. One of the main goals of complexity theory is to prove lower bounds on the resources (e.g. time and/or space) needed to solve a certain computational problem. Cryptography can therefore be seen as the complexity theory's main field of use.

242 questions
Filter by
Sorted by
Tagged with
1 vote
43 views

### What is the Work Factor of the one time pad?

Work Factor is defined as the minimum amount of work (can be the length of the key) to determine the secret key of an cryptosystem (HAC, Menezes, Alfred J. et al). And One time pad have unconditional ...
151 views

### Cryptography based on #P-complete problems

Are there any examples of a cryptographic scheme based on (an average-case form of) a #P-complete problem?
42 views

### Which is the smallest, cyclic in 3 directions, consistent structure of random values which can be hidden at the adversaries machine? (some comparison)

Or more general each member can be part of up to three 2D locally euclidean planes of 2 different dimensions. (each of those planes is cyclic in two orthogonal directions, like a torus) Given just ...
422 views

### RSA decryption using CRT: How does it affect the complexity?

There is an efficient variant of the RSA using the CRT: \begin{align*} d_p &= d \pmod{p-1}\\ d_q &= d \pmod{p-1} \\ q_{\operatorname{inv}} &= q^{-1} \pmod{p} \end{align*} where the ...
1 vote
65 views

### Does generic group black box model prohibit MSB of discrete logarithm?

Black box generic models prohibit calculation of discrete logarithm in groups of order $q=2p+1$ where $p,q$ are random primes to $\Omega(\sqrt{p})$ steps (refer Discrete Logarithm in the generic group ...
488 views

### Notion of elementary operation when complexities in the form of $2^{128}$

In lots of cryptoanalytic papers I read, attack complexities are stated in the form of a constant. For example, this related key attack on of AES states: [...] For AES-256 we show the first key ...
67 views

### LWE with the matrix A repeated

Consider the following version of Learning With Errors. You are either given $(A, As_1 + e_1, As_2 + e_2, \ldots, As_k + e_k)$ or $(A, u_1, u_2, \ldots, u_k)$, where $A$ is an $m \times n$ matrix ...
1 vote
37 views

### How secure is a projection to a subspace with much lower member size for $x\mapsto x^a$ mod $N = PQ$, $P=2p+1$, $Q=2qr+1$, to target space $r=2abc+1$?

A cyclic sequence can be produced with $$s_{i+1} = s_i^a \mod N$$ with $N = P \cdot Q$ and $P = 2\cdot p+1$ and $Q = 2\cdot q\cdot r+1$ and $r = 2\cdot u \cdot v \cdot w +1$ with $P,Q,p,q,r,u,v,w$ ...
40 views

### How difficult is finding $i$ for sequence $s_{i} = g^{s_{i-1}} \mod P$ with $s_0 = g$ for given value $v\in [1,P-1]$

Assuming we found a constant $g$ and a prime $P$ which is able to produce all values from $1$ to $P-1$ with it's sequence $$s_{i} = g^{s_{i-1}} \mod P$$ $$s_0 = g$$ How many steps are needed to ...
66 views

140 views

### Provable Lower Bounds for some Algorithmic Problems?

Are there any problems for which we have known lower bounds? For example, for comparison based sorting, we know you need $\Omega(n \log n)$ comparisons. Edit: I'm aware that this requires restricting ...
118 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 ...
612 views

### Complexity of Gaussian Elimination over a Finite Field

I read somewhere that the complexity of solving a Linear $n\times n$ system over a Finite Field $\Bbb F_q$ using Gaussian Elimination is $\mathcal{O}(n^3)$ operations in $\Bbb F_q$. What's the role of ...
1 vote
81 views

### Digital Signature Complexity [duplicate]

I'm not familiar with algorithm complexity so I'm asking here. I need help determining degital signature complexity, I did some research and all I found is complexity for the D.S.A only: 𝑂(𝐷𝑆𝐴 𝑆𝑖...
145 views

### If OWF were to exist, do we know for sure that one of the candidate OWF would indeed be a OWF?

We have several candidates for OWF, like multiplication/factoring and discrete exponencial/logarithm. What I am asking is: Does the existence of one way functions imply that our candidate functions ...