# Tag Info

6

That's because the public key in DER format (which is a way of expressing X.509 objects as a sequence of bytes) includes more than just the modulus. Specifically, it consists of: This is a collection of the following objects; that takes up 4 bytes The first object is an integer (which happens to be the public modulus); the integer itself is 257 bytes (not ...

4

It appears that based on your description, the server has a 2048 bit key pair and the clients logging in have 4096 bit key pairs. In this case, do I have the brute force protection of 2048 or 4096 bits? For someone to impersonate one of your users, they would have to break the 4096 bit key. For someone to impersonate the server, they would have to ...

4

I had a similar problem, and it took me a long time to figure out all the math, as some of the proofs can be rather terse. So, I took it upon myself to write a full explanation of how to factor N, without all the symbols and relying on a bit less prior knowledge. Anyway, such a system is not safe. If you know a valid $e$ and $d$, you can factor $N$. ...

4

If I right understood your question, you think that from N it is easy to compute $p$ and $q$. But it is not true. For computing $p$ and $q$ from $N$, you need to solve factorization problem. And this is very difficult. If $N$ small number, then you can use brute force. But when it comes to RSA, $N$ is a very big number. And it will take many hundreds years ...

2

Of course you can use Elliptic Curve cryptography to do public key encryption, that is, a method with a public key and a private key; anyone with the public key can encrypt, but only someone with the private key can decrypt. One way would be to use the Integrated Encryption System. It's does most everything for you (allowing the encryption of arbitrary ...

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If you know even a single key pair $(e,d)$, then you can factor $N$, so that's pretty much the ultimate attack — efficient, total key recovery. For a short, digestible proof of this, see the last fact on page three of Dan Boneh's Twenty Years of Attacks on the RSA Cryptosystem.

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I happened to see some similar question like this. The question mentioned about sending fake signature message. The method is like this: Find some random string R. Use the public key to encrypt the random string R, let the result be X. (R,X) is your signature pair.(Think backwards) When someone verifies the signature, he'll compare {R} with X which are ...

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Disclaimer: I am not familiar with Identity-Based Key Exchange, know only the most basic Identity-Based Encryption setup, and restrict to that. For other than trivialities, I refer to Ricky Demer's answer. The defining property of Identity-Based Encryption is: a user's ID and the KGC's public key is all it takes to encipher; and a user gets from a Key ...

2

There are plenty of papers on forward-secure IBE, one could just google that term. Here, I will focus on IBE with a property that I would call "key forgetting", and work toward a candidate construction for depth-O(1) HIBE with that property. One could apply either of the sections "Random Oracles, depth-O(1) adaptive-ID security, and (lack of) ...

1

What you describe is a digital signature, which works using methods very similar to the one you suggest. Examples include elgamal-signature and RSA signature schemes (the second of which I would recommend you read). Digital signatures allow you to provide a public signature that 'proves' you provided the message. As the author, you would produce database ...

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While there are some obvious checks you can do, you can't cover everything: You can check that the modulus is a composite odd number of the appropriate size If you want to put in the effort, you can do a quick check if the modulus has any small factors You can check if the public exponent is an odd number > 1 However, you can't check beyond that; you ...

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For ordinary key exchange, leaking Alice's private key obviously allows the adversary to impersonate Alice to other people, but should not allow the adversary to (e.g.) impersonate Bob to Alice, or compromise sessions from the past. I am not familiar with identity-based key exchange, but I would expect something similar to apply. After the key has leaked, ...

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I think the very first question before diving into designing the protocol would be to ask yourself what kind of secure communication do you want? Namely, there are two options to consider when it comes to communication between the IM users: For the client-server secure communication, there are two directions to consider: From “sender to server”, you ...

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There's a much simpler way to factor $n$ when you know $d$ at least when $e$ is small (like when it is usually 65537). You know that $ed = 1 \, (\textrm{mod} \,\phi)$. Since you know $e$ and $d$ you can calculate $S = ed - 1$ and this number must be divisible by $\phi$ due to the first equation. Note that the magnitiude of this value is around 65537 times ...

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