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. ...

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59 views

PRNG output with truly random noise

I am considering a situation where an adversary does not have access to the $n$-bit output string of a PRNG, but instead receives a noisy version of it, where each bit of the string is flipped with ...
2
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3answers
202 views

What is the point of differential cryptanalysis when the amount of necessary plaintext is unrealistic?

As someone with a non-crypto background, I learned that differential cryptanalysis is mostly weak against ciphers like DES because, being a chosen plaintext attack, for a state of art complexity of $2^...
3
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0answers
35 views

Computing cost for a trillionaire to compute GNFS in RFC 3766

RFC 3766, Section 4.1 discusses picking $n$ to achieve some target cost for employing the GNFS, i.e., $T$ is known and $N$ is unknown in the below equation: $$T = \kappa \cdot \exp{\left(c \cdot (\ln{...
3
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2answers
104 views

Importance of round complexity in determining the efficiency of an MPC protocol

Literature has different ways of specifying complexity of an MPC protocol: computation complexity that measures the number of (assumed primitive) operations performed by all the parties; ...
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0answers
46 views

Quantum complexity of LWE

As per my understanding LWE is quantum secure because there is no known quantum algorithm to solve LWE in polynomial time. Due to the reductions given by Regev et al. If there is any algorithm that ...
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1answer
57 views

Carmichael's function in Cryptography

The Carmichael's function says that for $a\in \mathbb{Z}_n^*$, if $gcd(a,n)=1$, then \begin{equation} a^{\lambda(n)} \equiv 1 \;(mod\; n). \end{equation} My aim is to find $a$ if factorization of $n$ ...
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1answer
23 views

Time complexity of looking up in a rainbow table

It is mentioned in the famous paper Making a Faster Cryptanalytic Time-Memory Trade-Off (pdf) by Philippe Oechslin that: The total number of calculations we have to make is thus $\frac{t(t−1)}{2}...
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2answers
110 views

Practical differences between circuits and turing machines for cryptography

In formal cryptography, we model algorithms (mostly our adversaries) as (Probabilistic) Turing Machines or as boolean circuits. In our lecture on formal cryptography, we learned that circuits are more ...
3
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0answers
64 views

Majority encryption algorithm?

Assume that I want to leave an encrypted message to a group of $n$ people in a way that they can only decrypt it if they work together in the following sense: For some fixed $k < n$ every sub-...
3
votes
2answers
702 views

Is AES solvable by reducing to SAT?

Consider a known plaintext attack on AES — just so we have an actual system of equalities that we can feed to a SAT solver. Is AES solvable in this way? In other words, will the algorithm eventually ...
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0answers
45 views

Best/average/worst-case complexity for cryptography

I understand that the complexity of a problem can be measured by it's best-case, average-case, or worst-case complexity. Am I correct in thinking that, for cryptographic purposes, each of these is of ...
1
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1answer
70 views

Running time of Shamir's secret sharing scheme

Let $p>n$ be a prime number. The key steps in the $(t,n)$ Shamir's secret sharing is as follows: Steps of dealer: Choosing $s \in \mathbb{Z}_p^*$ Selecting $b_i \in \mathbb{Z}_p^*$ for ...
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1answer
62 views

Function with no fast path and with fast proof

When a function is iterated and each time a previous result is used as input to the next iteration (feedback), so that there is a limited benefit from parallel computing, is there such function that: ...
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1answer
74 views

Finding a secret cipher given the key and known plaintext?

Let $x,y,k$ be plain text, cipher text and key respectively. Also suppose $\operatorname{Enc}$ is the algorithm of encryption for block cipher with size $n$. So we have $$\operatorname{Enc}_k(x)=y$$ ...
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0answers
123 views

Complexity using RSA

You encrypt a message using the RSA encryption system as $t^e \pmod n$ , where $t, e < n$ and $t$ is the numerical equivalent of the message. The message is written in a $27$-letter alphabet and is ...
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1answer
72 views

Find a constant $C$ in $O(Cn^2)$?

I am writing a paper on RSA, and I am calculating some encryption running times. I have been told that the encryption running time is $O(n^2)$ where $n$ is the modulus. I have also been told that ...
0
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1answer
157 views

Performance of Fully homomorphic encryption VS Paillier encryption in Practice

Consider two schemes both have computation complexity linear to the input size (i.e. number of inputs). One scheme is based on Paillier encryption and the other one is based on fully homomorphic ...
4
votes
1answer
197 views

Usage of Zero-knowledge proofs for NP-complete languages

It is well known that if OWFs/PRGs exist, then there is a zero knowledge proof for any NP-complete language, say G3C (graph coloring in 3 colors). The zero-knowledge notion maintains that any ...
2
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0answers
37 views

DSSP reduction to DSSI

In “Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies" by DeFeo, Jao and Plut, a reduction from the Decisional Supersingular Product (DSSP) problem to Decisional ...
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3answers
113 views

How can complexity be increased or decreased in AES?

I have been studying data compression for a while. For educational purposes, after a lot of reading, I managed to create a software that performs encryption and authentication using AES256-GCM. ...
0
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1answer
148 views

computational complexity class of decryption of AES [closed]

I haven't really seen what computational complexity class of decryption of AES is. Can anyone provide reference papers or answers here?
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1answer
80 views

What is meant by - computational complexity $2^x$?

Recently Bi-clique Cryptanalysis allowed to obtain following results on full AES ES that claim to have The first key recovery attack on the full AES-128 with computational complexity $2^{126.1}$ The ...
5
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1answer
866 views

Why does applying 56-bit DES twice only give 57 bits of security? [duplicate]

Given two 56-bit keys, $k_1$ and $k_2$, why does $E_{k_1}(E_{k_2}(M))$ only give 57 bits of security? So basically I'm unsure why it only gives 57 bits of security; I understand that one key will ...
0
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1answer
370 views

uniform vs. non-uniform PPT

I'm trying to understand PPT and in particular what the differences are in uniform and non-uniform PPT's. First, this is how I see it: A Probabilistic Polynomial-Time algorithm A is an algorithm that ...
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1answer
652 views

Why is AES unbreakable?

Why is it said that AES is unbreakable? Brute force attacks would take years to crack it, so is it possible to crack it if the computational speed of machines increase in the following decade?
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1answer
87 views

One-one correspondance complete function

I am reading the paper by John B. Kam and Georges I. Davida (1979) titled Structured Design of Substitution-Permutation Encryption Networks. On page 749 it reads ...
2
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1answer
684 views

Differences between Work Factor and Time Complexity

I am interested to know if work factor means the same thing as time complexity. Quoting Work Factor : Uncovering keys in cryptosystems The Work Factor of a cryptosystem is related to its key-...
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2answers
289 views

Is the complexity of Caesar (shift) ciphers “n * n!”?

Can we say that any shift cipher to be decrypted needs an algorithm of complexity “n * n!”? (where n is number of possible ...
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2answers
337 views

How fast would a polynomial time factoring algorithm compute?

I know factoring is the chief means of breaking RSA keys. I know an algorithm that runs in polynomial time would be able to break an RSA key pair "quickly". But how quickly is "quickly"? Note, I'm not ...
0
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1answer
153 views

How much (home PC) CPU time is required to generate a prime number of a given size?

How much CPU time is required on a typical home computer to generate a prime number of size 100 bit, 200 bit , 512 bit and 1024 bit using given random bits of the respective sizes? Please note that ...
3
votes
1answer
124 views

Is xgcd faster than Fermat for calculating $d$ in RSA?

I want to calculate $d$ from $e$ when generating RSA keys. What is faster? Calculating $\operatorname{xgcd}(e,p)$ and $\operatorname{xgcd}(e,q)$ and CRT. Or calculating $e^{p-2}\bmod p$ and $e^{q-2}...
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0answers
52 views

Asymmetric encryptions' computational complexity [duplicate]

I need to know the computational complexity of the public key encryption (e.g. Paillier), please. (i.e.Paillier in his paper mentions that the computational complexity of most of public key ...
4
votes
1answer
237 views

Are post-quantum cryptographic ciphers *also* secure if the P=NP conjecture holds true?

First of all, I only understand the P versus NP debate on a rather shallow level as I am not a computer scientist. So perhaps the answer to the question is straightforward but if not, I would be ...
3
votes
2answers
463 views

Proving that a function is not invert-able (one way function)

I am having problems with proving if the one-way function (http://crypto.stackexchange.com/tags/one-way-function/info) is hard to invert or not. $2^\sqrt {m} $ one-way function $ f: \{0, 1\}^{2m} \...
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1answer
143 views

DES-X , computation load and storage

The passage said that the computational load to attack DES-X can be reduced to approximately $2^{(56+64)}=2^{120}$ steps,and the storage of data sets should be $2^{64}$. But I can't figure why it is ...
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0answers
166 views

Complexity of verifying OTP secret

What is the minimum number of unique pairs of digests and inputs to a one-time pass needed to verify that a secret is equal to a ...
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257 views

Solution with high decryption cost and low encryption cost

I am looking for any cryptographic solution that will meet those requirements : Only known method to get the encrypted string need to be brute force. Decrypting on modern computer not more than ...
4
votes
2answers
241 views

Computational Complexity - When is it really exponential time?

I'm currently working on the discrete logarithm problem and the relevant attacks. I'm fine on the mathematical side of things, but when it comes to estimation of running times I run into problems. ...
2
votes
1answer
331 views

How to calculate complexity of ElGamal cryptosystem?

How to calculate time and space complexity of ElGamal encryption and decryption as there are two exponentiation operation during encryption and one during decryption? Here is my code for encryption: <...
3
votes
1answer
190 views

Is it a good idea to use Lagrange/Newtonian interpolation for encryption?

I see that Lagrange interpolation is commonly used for secret sharing, but could it be used for encryption? The goal is to reduce database I/O and compute new values on the fly. Suppose the use case ...
3
votes
1answer
386 views

What does it mean for an adversary to run in PPT?

I've been reading this question where a detailed description of mine is given, I've understood that a polynomial-time adversary is an adversary for which the only feasible strategy are those that take ...
1
vote
1answer
270 views

How to calculate bit strength of Integer Factorization Cryptography (IFC) such as RSA using Python

I would like to know how to calculate the bit-strength of Integer Factorization Cryptography (IFC) such as RSA by using Python. I gathered it is based off the complexity of factorizing the modulus (...
1
vote
1answer
247 views

PRG existance and P versus NP

how can we prove that if there is a secure PRG then P!=NP or in reverse order?(is there any reduction?) a secure PRG is a pseudo random generator that for every eficient (running in probabilistic ...
2
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1answer
520 views

ECC Complexity order of point addition, scalar point multiplication and selecting random point

I am facing this problem in calculating the order of a process which involves ECC point addition: $P+Q$ , scalar multiplication: $aP$, and selecting random points in the group. The group is of prime ...
2
votes
1answer
177 views

Explanations for the complexity values for second preimage attack on GOST?

I've been reading the article "A (second) preimage attack on the GOST hash function" by F. Mendel et al (link) and I'm having some difficulty to grasp some of the values of complexities/probabilities ...
3
votes
1answer
264 views

Will non-ECC algorithms like RSA eventually become too inefficient?

The strength of symmetric and asymmetric encryption schemes scales with the key length, but there is a difference between symmetric algorithms like AES and asymmetric algorithms like RSA. For example,...
4
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2answers
346 views

Can we say that if $P=NP$ there is no CPA secure public key encryption?

I've learned that public key encryption is based on the problem of Discrete Log (as regard to group theory) which believed to be hard. But, can we say that it doesn't matter on which problem our ...
4
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1answer
273 views

Solve a Modular Exponentiation

It might be common, but if we had to solve an equation like this $m=s^{e}$ mod $n$ where $m,e,n$ are known. How can we find $s$. What optimisations could be applied? And what would the complexity of ...
2
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1answer
337 views

Brute force attack expected running time

I am a bit confused about the expected running times of brute force attacks on different cryptosystems. So let's assume a key size of $2^n$ bits. Symmetric key cryptography: $E(brute)$ = $2^{n-1}\...
4
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1answer
442 views

Fully Homomorphic Encryption over the Integers - Runtime Question

I have a question regarding the paper "Fully Homomorphic Encryption over the Integers" (http://eprint.iacr.org/2009/616.pdf): On page 6 after they set their parameters, it says "This setting results ...