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. Jason -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
