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4

You've mostly pieced it out. This is a DER encoding the the public key, and consists of a sequence of two integers (the first being the modulus, and the second being the exponent). Here is the breakdown of the encoding: 30 The value 30 is used to signify 'sequence'; this is a container that carries a list of DER-encoded objects. 82 01 0a Whenever we ...


3

The certificate makes sure that whoever you're talking to is who they claim they are. With TLS/SSL without certs you wouldn't notice if you're communicating with an impostor over an encrypted channel instead of whoever you're expecting to communicate with. This leads to so called man-in-the-middle attacks. You really should read this, if you're going to use ...


3

Okay, I came up with this, it's not a complete answer and the attack presented is pretty weak without a follow-up algorithm for breaking a somewhat unbalanced modulus but let me know if you spot any flaws or have any ideas to improve it... If $n = pq$ with $p, q$ prime and $\gcd(pq, (p - 1)(q - 1)) = r > 1$ then clearly $r = p$ or $r = q$. Now ...


3

A lot of modern cryptography is based on some mathematical assumptions and aims to achieve what is called Computational Security. That means that the adversary (Eve) could get some information about the plaintext with a negligible probability and the adversary is modeled as someone with bounded computational power, storage and bounded time. So all the ...


2

This is called the common modulus attack. Bezout's Identity says that there exists $x$ and $y$ such that $ax + by = gcd(a, b)$. In our case we have $gcd(e_a,e_b) = 1$, so we can find $x$ and $y$ such that $e_{a}x + e_{b}y = 1$ (you can use the extended euclidean algorithm for this). After solving for $x$ and $y$, you compute: $C^xC^y\mod N$ to get $M$. ...


1

Guess the catch in the video is in how the participants exchange details 'publicly'. If the Man-In-The-Middle can intercept and manipulate what is being 'publicly' shared, then the attempt to eavesdrop would still be successful.


1

An inner product is a map from a vector space crossed with itself to $\mathbb{R}$ or $\mathbb{C}$. Also an inner product must be positive definite: $\langle x, x\rangle\geq 0$. A bilinear map, to contrast, is simply a map $A\times B\to C$ for linear spaces $A,B,C$ which is bilinear. I think positive definiteness is the most important thing that inner ...


1

1) Yes. This is the common modulus attack and has actually been answered many times on this forum. 2) Assuming $r$ is prime, yes. $\phi(n)$, (the totient of $n$) can be computed by subtracting 1 from each of $n$'s prime factors and multiplying them together.


1

You actually don't trust the certificate by itself. A certificate is like a diploma that a company (or a domain, e.g. www.crypto.com) obtained from some trusted party, called CA, or Certificate Authority. This diploma states that www.crypto.com is allowed to communicate with you using the public key written in the diploma. But, as you mentioned, ...


1

Public-key cryptography is not sufficiently computationally burdensome to where other approaches must be used for authentication protocols. Note though that what you describe is not actually public-key based. The verification of the MAC requires Dave and Bob to both have a shared key. Also, note that a random component must be included in some manner in all ...



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