# Tag Info

7

He [Ed: Eve] then sends his half to Alice signed and establishes a connection. Now Alice is communicating with Eve and Eve is decrypting the message and sending to Bob. Eve can only sign with her own private key. So your attack only works if Alice accepts the signature from Eve. That means that: Eve's public verification key needs to be trusted and that ...

6

The web article states ..a key generation program (produces) two keys. It is arbitrary which of these is made public and which is kept private. This second sentence is wrong, especially since it appears in a general discussion about "Asymmetrical-key algorithms" (sic: the closer usual adjective in the cryptographic literature is asymmetric, and the ...

5

we can arbitrarily choose an exponent $e$ as long as $\gcd(e,\phi(n))=1$. No. If we want any security, we further : Must NOT choose $e=1$, because that makes $x\to x^e\bmod n$ the identity function over $[0,n)$. Must NOT choose $e$ in a way revealing information about of $\phi(n)$ or the factors of $n$ beyond that $\gcd(e,\phi(n))=1$. For example we can ...

4

Mathematically. It is only true that the public and private sides are arbitrary in the very specific case where you're using textbook RSA with keys that were generated starting with a large, random exponent as in the original RSA paper. This is absolutely not the case for other asymmetric cryptosystems, or even for most implementations of RSA where the ...

2

But what is the most appropriate choice for it? For public exponent $e$, small values are preferred like $\{3, 5, 17, 257, \text{ or } 65537\}$. With this, we can guarantee that the number of operations is low. We can control this with our choice. Of course, for the choice of $e$, we must have $\gcd(e,p)=1$ for any prime $p$ divides the modulus $n$. This ...

2

Shouldn't the other parameters have exactly the same requirements? Certainly not all other parameters. The vendor could set requirements for $e$, but they would be different. For the other key parameters, extra requirements would be unusual, and there could be a valid technical reason for them only if you are using gear (software or hardware) that the ...

1

No this is not generally true, it must be a misunderstanding. The private key could entirely contain the public key and the scheme still be secure, but clearly reversing the roles of the public and private keys in such a scheme would be trivially broken (as now the public key would reveal the private key). Apart from that it would often not even be clear ...

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