Questions tagged [cryptography]
Questions on the mathematics behind cryptography, cryptanalysis, encryption and decryption, and the making and breaking of codes and ciphers.
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How to attack universal hash function based on finite-field arithmetic?
As per the Recursive n-gram hashing is pairwise independent, at best paper, I want to use the algorithm described in chapter 6 and 7 (page 7 - 10). The hash works as follows:
Define a random function ...
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Frey-Rück Attack - Tate-Lichtenbaum Pairing
I am trying to understand the Frey-Rück attack and found different ways of a possible implementation. Since I am not yet very familiar with the Tate-Lichtenbaum pairing and the theory of divisors I ...
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Cryptocurrency Math
I'm looking for any relevant books/articles on the maths of cryptocurrency transactions. Also open to any resources that may have some cryptocurrency transactions but not it may not be the main bite.
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What's the function poly() ??
In cryptographic context, we often observe the function $\mathsf{poly}$.
For example , let $n$ be an integer, this function is called in a manner such as $\mathsf{poly}$(n).
What's the exact ...
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Proof help: RSA Encryption
I am trying to fill in the middle of this proof:
$$ \begin{align}
m_1 ^e \mod N \cdot \left( m_2 ^e \mod N\right)^{-1}\mod N & = \\
& \quad \vdots \\
& = \left( \frac {m_1}{m_2}\right)^e\...
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The Miller-Rabin Test clarification
I'm teaching myself cryptography but have realised that it has a lot of number theory as a part of it, one area which I'm a bit confused over is the Miller-Rabin test and how to use it in questions. A ...
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A special case of zero-knowledge computation
This question is inspired by the disappearance of Malaysian Air 370.
Let's suppose the plane crashed into the ocean. These are hotly contested waters where various countries (US, China, India, others) ...
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Shortest vector problem as hidden subgroup problem
I posted this question on the cryptography stack exchange with a bounty, but I haven’t gotten much attention. I think part of the reason might be that I’m really interested in the use of group theory ...
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Shortcut to compute $2^{(p+1)/4}\bmod p$, where $p$ is prime and $p\equiv3\pmod4$?
It's given a prime $p$ with $p\equiv3\pmod4$.
What shortcut (if any) is there to compute $x=2^{(p+1)/4}\bmod p$, compared to a general algorithm to compute $x=2^k\bmod p$ applied for $k=(p+1)/4$ ?
I'...
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Canonical lift of Elliptic curve in Smart attack
Smart attack details
Given some curve $E/\mathbb F_p$ with order $p$, lift it to $E_0=E/\mathbb Q_p$ and define the subgroups of $E/\mathbb Q_p$: $E_r=\{(x,y)\in E/\mathbb Q_p|v_p(x)\leq-2r,v_p(y)\...
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Relationship between remainders of shifted polynomials in polynomial divisions.
I'm trying to understand a digital communication protocol that is deployed in the European high-speed train balize systems (link). The goal is to implement such a system in digital hardware.
In this ...
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Analyzing an Obfuscation Algorithm
I'm a software developer, not a mathematician. I saw a question about decoding ciphertext so I'm assuming this is not off-topic in this forum.
I have a legacy database that seems to be obfuscated, ...
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Rank of Elliptic Curve over Finite Field
In the paper titled: "The Elliptic Curve Digital Signature Algorithm" by Don Johnson and Alfred Menezes, there is a statement in section 4.3 "Basic Facts":
$ E(F_q) $ is an abelian group of rank 1 ...
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Prove that combinatorial (n,t) secret sharing has one efficient solution.
One method for threshold secret sharing involves splitting a secret into multiple parts and distributing it amongst $n$ people such that any subset of threshold $t$ members can reconstruct the secret, ...
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Where do hash functions come from?
I have some basic understanding of how hash functions work, however, I have no idea of how mathematicians created them.
Were them a byproduct of a non cryptografics related research or were them a ...
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