On 01 Jan 2017, at 19:51, Jason Resch 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?
Nothing would change from the first person view of the encrypted brain
state, except that he would have a low probability to be able to
manifest itself relatively to the the person who can no more decrypt it.
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?
There is no problem, except the relative one mentionned above. The
encrypted data would only change the destination (in the arithmetical
reality).
7. Would you say yes to the FHE doctor?
I would say NO, not because I would fear to die in that process, but I
would fail to arrive where I intend to access to, I think.
Of course the computable functions used in the FHE needs to not
destroy information, like a constant function for example, but I guess
that is part of the FHE protocol. I would say no for a simple
teleportation also if I learn that they did lose the key of the
reconstitution box.
Bruno
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 [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.
http://iridia.ulb.ac.be/~marchal/
--
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.
