On 2 January 2017 at 05:51, Jason Resch <[email protected]> wrote:
> Fully Homomorphic Encryption ( https://en.wikipedia.org/wiki/ > Homomorphic_encryption ) is a recently discovered concept in the field of > cryptography (the science of hiding information). > > Basic encryption primer, skip if you are familiar with this already: > > > With conventional encryption, some message M is encrypted using some > secret key K, to yield a ciphertext C. We can view the encryption operation > as a function that takes two parameters: > > *C = Encrypt(M, K)* > > The ciphertext appears as complete gibberish to anyone who sees it, and > absent knowledge of the key K, will be unable to make sense of it. *A > simple example of an encryption function is to assume M is a number between > 0 and 999. K could be a randomly chosen number on the same range (0, 999), > and the encryption function computes the remainder of (M + K) / 1000.* > > With knowledge of the key, however, there is a corresponding decryption > function, that takes the ciphertext and the key and returns the original > message: > > *M = Decrypt(C, K)* > > However, absent knowledge of the key, C could represent any possible > message, in a sense it is only determined when K is provided. *An example > decryption example, based on the previous encryption example, is to compute > the remainder of (1000 + C - K) / 1000.* > > > > Now to Fully Homomorphic Encryption (FHE), FHE enables any sequence of > multiplications and additions to be performed on a cipher text by an entity > who *has no knowledge* of the key. For example: > > M = 10 > C = Encrypt(M, K) > > C_1 = FHE_MUL(C, 2) > C_2 = FHE_ADD(C_1, 5) > > 20 = M*2 = Decrypt(C_1, K) > 25 = M*2+5 = Decrypt(C_2, K) > > The magic here is that FHE_MUL and FHE_ADD are functions that operate on > encrypted data--data that is meaningless without knowledge of the key. And > when we decrypt the modified encrypted data we get the result we would > expect. > > The ability to perform multiplication and addition may seem trivial, but > actually any logic circuit can be made from stringing together additions > and multiplications in the proper sequence. Therefore, any computable > function can be implemented and applied to encrypted data. > > > Now on to the philosophy, what if we create a FHE circuit that computes > the state of a brain at time t2, given the state of the brain at time t1. > Perhaps it does a molecular simulation of all the particles in a person's > brain, and runs the physical simulation to advance it some period of time. > For example: > > *BrainState_Time-(n+1) = BrainSim(BrainState_Time-n)* > > We then create the proper circuit of logic gates to implement the function > BrainSim, and convert it to a series of multiply and add operations. > Applied to any input. Finally, we replace all the adds and multiplies with > FHE_ADD's and FHE_MUL's. > > I can now provide an encrypted brain state to another entity, who can > compute as many time cycles on the brain state as desired. Let's say I > provide you my encrypted brain state file, and you compute one year's worth > of time sequences of the brain state, and return this encrypted result to > me. > > When I decrypt the result, I will have a brain state file representing the > state of my brain one as it will have evolved over one year's worth of time. > > > Many questions arise from such a thought experiment considering FHE brain > simulation on encrypted brain state files: > > > 1. Is the consciousness recovered by running the FHE emulation? > a) If yes, we are faced with the difficulty of how this mind can access > itself and its own mental states without knowledge of the encryption key. > b) If no, we are faced wit the difficulty that this mind emulation is a > philosophical zombie, at least until we decrypt it? > > 2. Is the decryption step at the end necessary or irrelevant to recovering > consciousness? > > 3. If we perform the decryption at each step of the way, does that recover > consciousness along the way? > > 4. Does skipping steps along the way without performing the decryption of > the intermediate steps impact what the simulated mind experiences (if it > experiences anything ay all) > > 5. What if the key is deleted before the FHE computations are performed? > > 6. Is FHE emulation the ultimate key to information privacy when we say > yes to the doctor, or is it the ultimate disaster when we accidentally > zombiefy ourselves by uploading our encrypted brain states to be processed > in the cloud? > > 7. Would you say yes to the FHE doctor? > > > I am interested in hearing everyone's thoughts on the matter. > I can't "decrypt" my own brain, in the sense that I'm not aware of the neural processes happening in it and even if I were I would not be able to correlate them to thoughts, so I don't see why encryption with FHE should make a diffference. -- Stathis Papaioannou -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
