Cryptography Are there "dual plain text" crypto systems? |
| Are there "dual plain text" crypto systems? Posted: 25 Mar 2018 05:53 AM PDT Are there crypto systems that take two plain texts A and B along with two keys k_a and k_b and merge them into a single cipher text in such a way that when decrypting under key_a or key_b yields A or B respectively, but does not ease decryption of the other plain text? My imagined situation is that you encrypt your secret text with a "dummy text". Then if the need arises, you can comply with a demand for the encryption key by handing over the dummy key, which unlocks the dummy plain text while keeping the real secret text hidden. Now, I imagine this wouldn't be too useful in practice because the attacker would recognize that you're using this strategy and demand both keys. I'm still interested in the theory behind such a scheme though (if it exists!) [link] [comments]  | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Encrypting/decrypting numbers with modular multiplicative inverses Posted: 25 Mar 2018 02:43 AM PDT Let's say I have 2048 random numbers, from 1 to 2048, and I need 24 of them (repeats are allowed) to generate a private key hash that only I can know. I want to write these numbers on a piece of paper and put it in a safe. But before I do that, I want to encrypt them, so if anyone cracks open my safe, he won't be able to generate the private key with those 24 numbers, unless he decrypts them first. So let's say these are my 24 numbers n: To encrypt each one, I would use a modulo m larger than 2048 to prevent collisions, and a number x relatively prime (coprime) to m which I would multiply n with, for example, m=90000 and x=19921117, so that: For the 24 numbers above, this would yield:
Now to decrypt this, I would first calculate the modular multiplicative inverse (mpi) of m and x, 90000 and 19921117, which is 22453, so that: Now, this is obviously easy for me to decrypt because I know both the modulo (90000) and the coprime (19921117) I used, but what if someone does not know them - how long would it take to bruteforce with modern computers (assuming they know they can decrypt with a modular multiplicative inverse) all possible combinations of 1: moduli between 89976 (largest n_encrypted value) and 90000 and 2: all their coprime numbers >90000 up to let's say, 1000000 (1 million)? What about up to 1000000000 (1 billion)? What if the modulo range goes up to 9000000? Would something like this take days or years to decrypt, in other words, is such encryption relatively secure today? If so, up from which modulo/coprime range: millions, billions, less, more? [link] [comments]  |
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