Paranoia secure UUID generation

I need to generate many unique identifier on a distributed system.

In paranoia mode, I wan't to be sure to :

never have collision

prevent the determination of the computer's location used to generate the identifier (Mac adresse and date time)

I think generate UUID.

If I use UUID1 (based on MAC address, timestamp, etc...) :

I'm sure to never have collision

It's possible to find the location

If I use UUID4 (based on random generator) :

It's possible to have collision (The chance of a collision is really, really, really small, but exist ! )

I'm sure it's not possible to dermine the location (date and computer)

Do you have a solution to satisfy both constraints ?

---

May be we can combine UUID1 with a "static permutation" function determine by a "secret" key? The function must be bijective.

inspired by : http://code.activestate.com/recipes/126037-getting-nth-permutation-of-a-sequence/

def getPerm(seq, index):
    "Returns the <index>th permutation of <seq>"
    seqc= list(seq[:])
    seqn= [seqc.pop()]
    divider= 2 # divider is meant to be len(seqn)+1, just a bit faster
    while seqc:
        index, new_index= index//divider, index%divider
        seqn.insert(new_index, seqc.pop())
        divider+= 1
    return "".join(seqn)


secret=123456**123456 # a big secret integer

secure_id=getPerm("af5f2a30-aa9e-11e7-abc4-cec278b6b50a",secret)
# "1-a-faa4cba8c5b0ae372a72-ec-1fb9560e" ==> Same character, just change order

secure_id=getPerm("aaaaaaa0-bbbb-cccc-xxxx-yyyyyyyyyy0y",secret)
# "c-b-axaxxybyyyx0ybacyaya-cy-caybay0y" ==> Same secret => Same permutation  (check position of caracter '0' and '-')

We can improve the permutation "obfuscation" by preserving the position of '-' caracter

---

May be we can be simply encode the UUID, using Base64 to easy transfert/store the ID. Encode is also a bijective function.

import base64

def encode(string,key):
    encoded_chars = []
    for i in xrange(len(string)):
        key_c = key[i % len(key)]
        encoded_c = chr((256 + ord(string[i]) + ord(key_c)) % 256)
        encoded_chars.append(encoded_c)
    encoded_string = "".join(encoded_chars)
    return base64.urlsafe_b64encode(encoded_string)

def decode(encoded_string,key):
    decoded_chars = []
    string=base64.urlsafe_b64decode(encoded_string)
    for i in xrange(len(string)):
        key_c = key[i % len(key)]
        decoded_c = chr((256 + ord(string[i]) - ord(key_c)) % 256)
        decoded_chars.append(decoded_c)
    encoded_string = "".join(decoded_chars)
    return "".join(decoded_chars)

secure_id=encode("af5f2a30-aa9e-11e7-abc4-cec278b6b50a","secret")
# "1MuY2JfVppWQ08at2JKUo8qroMbF1Zmh1srGpJys1ZvFp5XV"

uuid=decode(secure_id,"secret")
# "af5f2a30-aa9e-11e7-abc4-cec278b6b50a"

By this way, I'have always the secret probleme.

(note : we don't need decode function)

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