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"Invertibility of the cryptographic primitive" is just a fancy way of saying "you can decrypt things encrypted with that key." All the first sentence means is "if you can recover the key, you can decrypt anything encrypted with that key." As the second sentence points out, there are conceivably attacks where you can decrypt things encrypted with a key but ...


1

Issues: It is going to be extremely easy to find $y$ as the GCD of every number of the ciphertext. The only way to avoid this is to make all the letters' associated numbers have a common factor, but then you can just divide out by said common factor (it'll mess with the successive letters, but we'll get to that later). Once you have a candidate value for ...


0

Maybe you can create a hash function like that, but it will have a major security weakness, because in order to achieve your goal, you need some correlated manipulations in the input and output. And that can be exploited by an attacker for cryptanalysis. Assume you have a given input and know its according hash value. If you flip a single bit in the input, ...


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I think what you're missing here is that a cryptographic hash by itself is not actually sufficient to verify the integrity of a message. Consider this: I want to send a message over the Internet (on an insecure connection, e.g. UDP), but have it be protected from tampering. I take the message and attach at the end a cryptographic hash of the message (e.g. ...


5

First, it's not said that AES is unbreakable, merely that none of the currently known attacks reduce the computational cost to a point where it's feasible. The current best attack on AES-128 takes 2^126.1 operations, if we had a computer (or cluster) several million times more efficient than any current computer and could operate at the thermodynamic ...


2

If you are looking for something that is faster than AES, there are several options. HOWEVER (and this is a big one) if AES-NI instructions (hardware acceleration) are available to you, there is nothing that can come close. My computer is a few years old, and I get 3100MiB/s in CTR mode. That is 3 gigabytes every second. That is faster than the network ...



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