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The immediately obvious way to do this is to use RSA in a large-public-exponent format. That is, the server selects an RSA modulus, and a large public exponent (say, $e = 2^{2^{30}}+1$) [1]; if the RSA primes are safe primes, this practically eliminates the possibility that $e$ is not relative prime to either $p-1$ or $q-1$. The server would internally ...


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How is asymmetric cryptography safe under these conditions? Well, you sort of outlined (but see kelalaka's corrections) how you would use asymmetric crypto to do authentication; that is, to make sure that the message was actually sent from $A$. You ask "how does that provide privacy?". The answer, of course, is "if that's all you do, it doesn't". If we ...


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Firstly, you misunderstood what is a signature and encryption with the public key. A signature requires a hash then sign paradigm with the senders private key so that any receiver can verify the signature. The RSA paper gave the first idea to digital signatures that were insecure and the Rabin Signature released in 1979 is the fist secure signature that ...


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Since antiquity (and, for ceremonial purposes, up to the present day) physical document have had seals affixed to them. In principle, these seals allow anyone, if he knows what he's looking for, to judge the authenticity of a document without consulting the authority that issued it. (In practice, there are obviously ways of producing convincing forgeries, ...


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Is there a way, then, of doing something like the above, but without the need for a central authority? Why, yes, we do have a way to solve that problem - we refer to it as a 'digital signature' Here's how it works: Select a signature algorithm, and come up with a public/private key pair for a signature algorithm With the private key, generate a signature ...


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I'm unaware of any proof of impossibility (although it wouldn't surprise me if one existed), but the fundamental issue here is there's no fundamental way that "physical identity" and "digital identity" are bound together. In short, given any algorithm $\mathcal{A}$ which generates some "seal" (or some private information used to generate seals in the future),...


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Why we don't use additive groups? Is it a security thing? Yes, it's a security consideration. If we used the additive group $(\Bbb Z_N,+)$ rather than $(\Bbb Z_N^*,*)$ for RSA, public encryption would go $M\mapsto C=e\,M\bmod N$ rather than $M\mapsto C=M^e\bmod N$. Problem is, decryption would be trivial since anyone with the public key $(N,e)$ could ...


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Your question is not clear. Which additive group would you like to use? RSA is hard because the group ${\mathbb Z}_N^*$ has unknown order (assuming the factorization of $N$ is unknown). Which additive group has that property?


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Cycles (not necessarily Hamiltonian) in the Cayley graph correspond to relations among generators of the group. The RSA assumption can be written as "It is computationally difficult to find a non-trivial relation in the RSA group $(\mathbb{Z}/pq\mathbb{Z})^*$", which is a property of $(\mathbb{Z}/pq\mathbb{Z})^*$ known as being "pseudo-free" (see The RSA ...


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Disclaimer: I'm not familiar with NTRU, and not in my comfort zon. Hence the many edits. The problem asked can be summarized as: given $n$, $q$ coprime to prime $p$, and for $0\le i<n$ the coefficients $f_i\in\{-1,0,1\}$ of $F=\displaystyle\sum_{0\le i<n}f_i$, find the $n$ coefficients $q_i$ of $F_q$ and $p_i$ of $F_p$ such that, with polynomial ...


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How much Unsafe is using secp256k1 for ECIES and what dangers/weakness it exposes /what attack it makes possible? Let's have a look through the "failures" that secp256k1 achieves according to SafeCurves. ECDLP: "disc": This means that the curve has a specific value to be small. As the website indicates this is not inherently bad or exploitable, it just ...


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The correct place to store public key on the web is the certificate you request from a CA (Certificate Authority. Many are paid, but there are ones that are free). You generate your key-pair and creates a "Certificate Signing Request" and the CA issues a certificate to you once they've done some verification. Also, the public key for encryption is nowadays ...


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You're describing methods of solving LWE via reduction to SVP. In particular: Sieving and Enumeration are methods of solving exact SVP Basis reduction is a method of solving approximate SVP There are additionally ways of solving LWE directly (the classic example is the Arora-Ge attack, which works when the noise distribution is too concentrated). Daniele ...


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RSA is based on some mathematical theorems. The first theorem that you need to learn is the Euler's Theorem; if $n$ and $a$ are coprime positive integers, then $$a^{{\varphi (n)}}\equiv 1\bmod n.$$ when $n$ is a prime it is the Little Fermat Theorem. This theorem tell us that in the power we use modulo $\varphi(n)$, i,e, $$a^{x} \equiv a^{x \bmod\varphi(n)...


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The RSA cryptosystem's parametrization depends on parameters $(p,q,e)$, where $p,q \in \mathbb{P}$ (primes) and being $e$ coprime with $N$ then $\gcd(N,e)=1$. Think this way, as $(N,e)$ is public, imagine if $\gcd(N,e)\neq 1$, then we've found either $p$ or $q$. A simple way to proceed for RSA key generation is the following one: Select two primes numbers $...


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Your finding is correct. From your links; In cryptography, signcryption is a public-key primitive that simultaneously performs the functions of both digital signature and encryption. Authenticated encryption (AE) and authenticated encryption with associated data (AEAD) are forms of encryption which simultaneously assure the confidentiality and ...


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