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.

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What are the theoretical memory requirements for these factoring algotihms?

Given an $n$ bit integer quadratic sieve takes $L(\frac12,1+o(1))$ time and number field sieve takes $L(\frac13,1.922)$ time where $L$ notation is given in https://en.wikipedia.org/wiki/L-notation. ...
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P-Complete hashes, hashing to a larger set

Historically hashes have been from a large set (say 256 characters) to a smaller set (256 bits). Also, hash functions that are P-complete have no known parallel algorithm; they must be computed ...
97 views

Is $g(x_1||x_2) = f(x_1 \wedge x_2)$ a one way function assuming f is a one way function

Intuitively I think not because assuming the bit string $x_1,x_2 \sim \{0,1\}^{n/2}$, $x_1 \wedge x_2$ is not uniformly random so if $g$ were still a one-way function then the fact that the definition ...
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Cryptomania and NP $\cap$ co-NP

Cryptomania is usually presented as the Impagliazzo's world, which gives us public-key cryptography under the assumption that trapdoor OWFs exist. For purposes of constructing public-key cryptography ...
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If trapdoor OWF exists then f is a trapdoor OWF, is there such a construction?

Is there a known construction of f, such that given that a trapdoor OWF exists then f is a trapdoor OWF, so we can construct inefficient cryptomania, ala Levin's construction for minicrypt in "The ...
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How many reversible gates would DES require?

How many reversible gates (said counting Toffoli and Controlled NOT, with free NOT) would be required to reversibly implement $(K,P)\mapsto(G,C)$ for the block cipher DES? $P$ is the plaintext, $C$ ...
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1 vote
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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 ...
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1 vote
397 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 ...
67 views

Difficulty of factoring large semiprime N if given a second value y = (p-1)*r, where r is a random large prime?

Lets say we have 2 public values: N and y $$N = pq$$ $$y = r(p-1)$$ Where p, q, and r are large primes, are different, have a large distance between them and are kept secret. I have three ...
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What do we mean when we say we need more than polynomial time many cipher texts

What does it mean when we say something like „we need more than polynomial time many cipher texts“? I understand it as „an adversarial can run for polynomial time and try as many messages as possible ...
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Speed comparison of encryption algorithms

I am trying to compare various encryption algorithms in terms of encryption duration, decryption duration, information entropy, NPCR, UACI, and correlation coefficients. I used a Lena 256x256 ...
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Which contemporary programming language is apt for implementation of algorithms in cryptography?

I am a researcher in cryptography. Most of the time I generally do theoretical/Mathematical work only and not doing the implementation part. I am not able to get the feel about the time complexity of ...
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Number of bit operations required for encryption in a Block cipher

I want to find out how many bit operations are performed for encryption in AES-128 with messages size $128$ bits. For public key encryptions such as RSA and ElGamal, I know that number of bit ...
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Composing subexponential L-function

Suppose $y=f(x)$ and $z=g(y)$ such that $y\in L_x[a,b]$ and $z\in L_y[c,d]$, where $L$ is the usual sub-exponential asymptotic notation L_x[a,b] = \exp\left((b+o(1))(\log x)^a(\log\log x)^{1-a}\...
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How to Solve Discret Log Computation Problem

Given $g^a$ in $Z_p$, it is hard to get the solution $a$. Everyone says yes, I wonder why it is hard. Could anyone give a specific mathematical way to show it is indeed hard?
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If finding a private key from a public key is [co-]NP-complete, does NP=co-NP?

In a given public key cryptosystem, if the problem of determining the private key from the public key is NP-complete or co-NP-complete, does that imply that NP = co-NP? Complexity theory is ...
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