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16

They are both linear, but in different algebraic Groups. Which is to say, xor is linear in any finite field of characteristic 2, while 'ordinary' addition is linear in the infinite field of the Real numbers. Addition modulo $n$ (which is more cryptologically significant than addition over the Reals) is also a linear operation, but in the ring of integers ...


8

What is the definition of linearity? Linearity is defined for maps between vector spaces. If you have a field $F$ and two vector spaces $U$ and $V$ over the field $F$, a map $$T:U\rightarrow V$$ is said to be linear if $$T(\gamma_1\odot u_1\oplus\gamma_2\odot u_2)=\gamma_1 \odot T(u_1)\oplus\gamma_2\odot T(u_2)$$ whenever $\gamma_1,\gamma_2\in F$ and ...


7

It is possible to turn a hash function into a stream cipher; there are several methods for that, and the simplest is to compute $h(K||IV||x)$ for hash function $h$, initialization vector $IV$, and successive values of a counter $x$. This yields an arbitrarily long sequence of pseudo-random blocks (32 bytes per invocation if $h$ is SHA-256). Then XOR that ...


6

Some brief thoughts: Shared secret Generation: $$s=E_a(B)=E_b(A)$$ The shared secret is generated by encrypting the other users public key with your private key. This is effectively an ECDH step, which is very reasonable, and one of the key aims of C25519$^{[1]}$. Key Generation: $$s_0=\mathrm{SHA256}(s); s_i=\mathrm{SHA256}(s_{i-1})$$ First, using the ...


5

What do you mean 'a one time pad with a password'? One time pads don't take passwords, they take samples of truly random data as long as the message. If what you're doing is taking the password, repeating it N times, and using that as if it were a random one-time pad, well, that can usually be broken even if you don't send a second message. If what you're ...


5

To answer your question: no this is not homomorphic encryption because one of the plaintexts is used unencrypted. There may be times when it is a useful property, but the only uses I know of it are to demonstrate the malleability of xor ciphers. To be a homomorphic encryption function, it should be possible to calculate the encryption of some function of ...


4

The two plaintexts are almost certainly identical. At the very least, any difference between them must be representable in 32 bytes, since that's as much information as the XOR of the encrypted files contains. Assuming that the plaintexts are indeed identical, we can also see that changing the encryption key has a very simple and predictable effect on the ...


4

For simple XOR-based encryption algorithms such as OTP, the key size must be the same as the message size. If you choose a smaller key and try to divide the message into chunks, you would not have a perfectly secure scheme anymore. Now, since you tagged java, I'm assuming that this increase in time for smaller key sizes is due to the code trying to divide ...


4

We typically refer to a homomorphic cipher if we can take two ciphertexts and combine them in a way that has a predictible result on the plaintexts. In your example you have taken one ciphertext and one plaintext. Using a stream cipher correctly you should never have 2 ciphertexts encrypted with the same portion of a keystream. So, combining two ciphertexts ...


3

Occasionally, for instance in very constrained environment, it can be useful to use only a few cryptographic primitives for all processing. (When you only have a hammer everything looks like a nail.) In such environments, it may be useful to use key derivation function to derive stream to be used as a stream cipher, or use hash function as cipher and so on. ...


3

What is the significance of the repetition? Does it mean that a 6 character key was used and repeated across the same characters within P1 and P2??? I'm assuming your assumption about this being an xor cipher with the pad used twice for two ciphertexts. It does not mean a 6 character key was used. A one time pad used twice could result in this ...


3

A better way to solve your problem is: on the server, encrypt the document under a document encryption key (a unique key that's specific to that document). The document remains encrypted in storage encrypted under this document key. When a client requests the document, send the client a copy of the encrypted document, as well as an encryption of the ...


3

This is called an Even-Mansour cipher. Actually, for the differential cryptanalysis it does not matter what sort of difference you use, you only need that it propagates deterministically through linear transformations (whatever linearity means). In this case you use a difference modulo $2^{32}$: $$ A \boxminus B \equiv (A-B)\pmod{2^{32}}. $$ You compute ...


2

You mention hardware complexity, but there definitely is more software complexity in using XNOR. Most programming languages have a XOR operator, but no XNOR. Likewise, assembly languages lack XNOR (at least x86 does). That means it would basically take twice the cycles to use XNOR in place of XOR, except where two XNORs would cancel and you'd be back to XOR. ...


2

So a fundamental property of multi-party anonymous systems is you are only anonymous out of the number of honest participants in the system. If the Stasi control everyone else at the dinner table and know they didn't send the message, then they know you did no matter what protocol you use. In your case with this ring topology, because only your two ...


2

The Hamming distance is more effective when you suspect that the plaintext has been XORed with some repeating keystream. That's because XOR works at a bit level, as does the Hamming distance. The Index of Coincidence is more effective when you suspect that the plaintext has been combined with some repeating keystream, where the combiner works ...


2

There are two possibilities here: AES is secure, in which case no one can open your encryption without knowing your keys, regardless of whether you layer anything else on top of AES. AES is not secure and someone knows how to break it. In that case the security of your encryption might only be as strong as the second layer of encryption. In neither case ...


2

Apart from the obvious security vulnerability from using a simple XOR operation to convert between plaintext and ciphertext you also run into the massive security-flaw of each identical plaintext generates identical ciphertext. In any given message, if a constant cipher operation is used along with a constant key, the resultant ciphertext will be same for ...


1

For CBC mode, the IV must be Never used twice with the same key Unpredictable So, in your example (filename$\oplus$key), if you ever encrypt two files that have the same filename with the same key, you will violate #1. Now, you may be tempted to say "but I always generate a new key for every file that I encrypt, so that example doesn't apply". Fine, ...


1

I don't really know what the point of this but I think that's already covered in the comments above. So, about your Vernam cipher resp. One-Time-Pad: The "trick" of the OTP - and we can prove mathematically that it is secure - is that the key has to have the same length as the cipher text and also we assume the key was send over a secure channel (what ever ...


1

There are a reasonable number of assumptions I'm going to have to make to try and answer this question. For perfect security, we require that the keystream is truely random, and never reused (OTP,shannon). I've decided to add in a short answer here: STOP! There's absolutely no need to use a reduced character set thing anyway - you can just use your random ...


1

Collusion is a concern but unlikely in very large ad-hoc ring networks where each ring is a one-shot random walk of a suitably large and mostly trustworthy membership pool. Collision and congestion are problems though; read below. If the opponent(s) can determine where the message or the key to decipher the message came from, the poster is done for. ...


1

The answer is almost definitely no for what I think you want (question is still unclear). I was hoping someone else could give a definite no, but since they haven't I figured I'd write this up. Your exact secret sharing method probably needs to be fully described in the question. I'm going to assume that $a=a_1\oplus a_2\oplus\dots\oplus a_n$ and similarly ...


1

There is an entire class of ciphers that do exactly this. They're called stream ciphers. At their most basic, they pretend to be a one-time pad. You give them a small key and they generate a stream of seemingly random bits. You then XOR these bits with your plain-text to make ciphertext. You can add bells and whistles to this basic behaviour but what I've ...



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