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Are there any cryptographic primitives/protocols allowing the sender to signal to the recipient faster that the message is intended for them, yet not reveal the true recipient to everyone else and allow them to quickly skip trying to decrypt the message? It doesn't appear that the problem of recognizing the message (without leaking who the message is for) ...


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How this general kind of thing is handled today is with hybrid encryption. A symmetric key is generated and the message is encrypted with that. Then the symmetric key is key wrapped (encrypted) using the public key of each intended recipient. (Keep in mind that RSA can only encrypt small amounts of data.) This only encrypts the data once. You can make it ...


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I'm going to treat this question as a strict one time pad one. With a key k of sufficient length, say 128 bits, is it possible to use kth multiple of π as a one-time pad? That's 107 characters of description plus 128 bits of secrecy (plus $\pi$ which is a known constant). Your Kolmogorov complexity cannot exceed 200 characters if you consider that:- $$\pi =...


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That is not practical since either you keep a sequence of the bits of the $\pi$ or regenerate them every time. You may need to store 64GB sequence if you want to encrypt such files. Then you need to multiply it with the 128-bit number. That is not practical, consider multiplication of 64GB number with a random 128-bit number. OTP needs true random bit ...


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Note that $$\frac{7(p-5)}8+3=\frac{7p-11}8\equiv \frac{7p-11}8-p-1\equiv -\frac{(p+3)}8\pmod{p-1}.$$ Similarly $$\frac{p-5}8+1=\frac{p+3}8$$ And so $v^3(v^7)^{\frac{p-5}8}\equiv v^{-\frac{(p+3)}8}\pmod p$. Likewise $u(u)^{\frac{p-5}8}\equiv u^{\frac{p+3}8}$ as required. The reason is to save a modular division which is quite a pricey operation.


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