pynkode/docs/nkode_authentication_template.md

nKode Authentication

Play around with the code in this jupyter notebook.

Customer Creation

Before a user can be created, a customer with random attribute and set values is created. The customers manage user's. They define an nKode policy, keypad's dimensions, attributes/sets in the keypad, and the frequency of attribute renew.

nKode Policy and Keypad Size

An nKode policy defines:

• the maximum length of a user's nKode
• the minimum length of a user's nKode
• the number of unique set values in a user's nKode
• the number of unique values in a user's nKode
• the number of bytes an attribute or set value is

The keypad size defines:

• the number of keys in the keypad displayed to the user
• attributes per key

The number of attributes must be greater than the number of keys to be dispersion resistant.

api = NKodeAPI()

policy = NKodePolicy(
    max_nkode_len=10,
    min_nkode_len=4,
    distinct_sets=0,
    distinct_attributes=4,
    byte_len=2
)

keypad_size = KeypadSize(
    numb_of_keys = 5,
    attrs_per_key = 6 # aka number of sets
)

customer_id = api.create_new_customer(keypad_size, policy)
customer = api.customers[customer_id]

Customer Attributes and Sets

A customer has users and defines the attributes and set values for all its users. Since our customer has 5 keys and 6 attributes per key, this gives a customer interface of 30 distinct attributes and 6 distinct attribute sets. Each attribute belongs to one of the 6 sets. In this example, each attribute and set value is a unique 2 byte integer.

set_vals = customer.attributes.set_vals

Customer Sets: {{ customer_set_vals }}

attr_vals = customer.attributes.attr_vals
keypad_view(attr_vals, keypad_size.attrs_per_key)

Customer Attributes:
{% for attrs in customer_attr_view -%}
{{ attrs }}
{% endfor %}

Attributes organized by set:

attr_set_view = matrix_transpose(attr_keypad_view)
set_attribute_dict = dict(zip(set_vals, attr_set_view))

Set to Attribute Map:
{% for set_val, attrs in set_attribute_dict.items() -%}
{{ set_val }} : {{ attrs }}
{% endfor %}

User Signup

Now that we have a customer, we can create users. To create a new user:

1. Generate a random interface
2. User sets their nKode and sends their selection to the server
3. User confirms their nKode and the user is created if the nKode matches the nKode policy

Random Interface Generation

For the server to determine the users nkode, the user's interface must be dispersable. To make the interface dispersable, the server will randomly drop attribute sets to make the number of attributes equal to the number of keys. In our case, the server randomly drops 1 attribute set to give us a 5 X 5 keypad with possible index values ranging from 0-29. Each value in the interface is the index value of a customer attribute. The user never learns what their "real" attribute is. They don't see the index value that represents their nKode or the customer value it is associated with.

session_id, signup_interface = api.generate_index_interface(customer_id)
signup_interface_keypad = list_to_matrix(signup_interface, keypad_size.attrs_per_key)

Signup Keypad:
{% for key in signup_keypad -%}
Key {{ loop.index }}: {{ key }}
{% endfor %}

Set nKode

The user identifies attributes in the interface they want in their nkode. Each attribute has an index value. Below the user has selected {{ user_passcode }}. These index values can be represented by anything in the GUI. The only requirement is that the GUI attributes must be associated with the same index everytime the user goes to login. If the user wants to change anything about their interface, they must also change their nkode.

username = {{ username }}
user_passcode = {{ user_passcode }}
selected_keys_set = select_keys_with_passcode_values(user_passcode, signup_interface, keypad_size.attrs_per_key)

Selected Keys
{{ selected_keys_set }}

The user's passcode server side attributes are:

server_side_attr = [customer.attributes.attr_vals[idx] for idx in user_passcode]

User Passcode Server-side Attributes: {{ server_side_attr }}

Confirm nKode

The user submits the set interface to the sever and recieves the confirm interface as a response. The user finds their nKode again.

confirm_interface = api.set_nkode(username, customer_id, selected_keys_set, session_id)
keypad_view(confirm_interface, keypad_size.numb_of_keys)
selected_keys_confirm = select_keys_with_passcode_values(user_passcode, confirm_interface, keypad_size.numb_of_keys)

Confirm Keypad:
{% for key in confirm_keypad -%}
Key {{ loop.index }}: {{ key }}
{% endfor %}
Selected Keys:
{{ selected_keys_confirm }}

The user submits their confirm key selection and the user is created

success = api.confirm_nkode(username, customer_id, selected_keys_confirm, session_id)

Passcode Enciphering, Hashing, and Salting

When a new user creates an nKode, the server caches its set and confirm interface as well as the users key selection. The on the last api.confirm_nkode the server:

1. Deduces the users attributes
2. Validates the Passcode against the nKodePolicy
3. Creates new User Cipher Keys
4. Enciphers the user's mask
5. Enciphers, salts and hashes the user's passcode

Steps 1-2 are straight forward. For a better idea of how they work, see pyNKode

User Cipher Keys

User Cipher Keys Data Structure

set_key = generate_random_nonrepeating_list(keypad_size.attrs_per_key, max_numb=2**(8*numb_of_bytes))
set_key = xor_lists(set_key, customer_attr.set_vals)

UserCipherKeys(
    alpha_key=generate_random_nonrepeating_list(keypad_size.attrs_per_key * keypad_size.numb_of_keys, max_numb=2**(8*numb_of_bytes)),
    pass_key=generate_random_nonrepeating_list(max_nkode_len, max_numb=2**(8*numb_of_bytes)),
    mask_key=generate_random_nonrepeating_list(max_nkode_len, max_numb=2**(8*numb_of_bytes)),
    set_key=set_key,
    salt=bcrypt.gensalt(),
    max_nkode_len=max_nkode_len
)

User Cipher Keys Values

user_keys = UserCipherKeys(
    alpha_key = {{ user_keys.alpha_key }},
    pass_key = {{ user_keys.pass_key }},
    mask_key = {{ user_keys.mask_key }},
    set_key =  {{ user_keys.set_key }},
    salt = {{ user_keys.salt }},
    max_nkode_len = {{ user_keys.max_nkode_len }}
)

The method UserCipherKeys.encipher_nkode secures a users nKode in the database. This method is called in api.confirm_nkode

class EncipheredNKode(BaseModel):
    code: str
    mask: str

Mask Enciphering

Recall:

• set_key_i = (set_rand_numb_i ^ set_val_i)

• mask_key_i = mask_rand_numb_i

• padded_passcode_server_set_i = set_val_i

• len(set_key) == len(mask_key) == (padded_passcode_server_set) == max_nkode_len == 10 where i is the index

• mask_i = mask_key_i ^ padded_passcode_server_set_i ^ set_key_i

• mask_i = mask_rand_num_i ^ set_val_i ^ set_rand_numb_i ^ set_val_i

• mask_i = mask_rand_num_i ^ set_rand_numb_i # set_val_i is cancelled out

# the passcode is deduced in confirm_nkode. These values are the index values of the customer attribute values
passcode = {{ user_passcode }}
passcode_server_attr = [customer.attributes.attr_vals[idx] for idx in passcode]
passcode_server_set = [customer.attributes.get_attr_set_val(attr) for attr in passcode_server_attr]

Passcode Set Vals: {{ passcode_server_attr }}
Passcode Attr Vals: {{ passcode_server_set }}

# pad passcode set list with random set values so the list is equal to the max nkode value. This hids the nKode's length
padded_passcode_server_set = user_keys.pad_user_mask(passcode_server_set, customer.nkode_policy.max_nkode_len)

# get the index of each set value
set_idx = [customer.attributes.get_set_index(set_val) for set_val in padded_passcode_server_set]

# find the set values matching set key to cancel out the set value
mask_set_keys = [user_keys.set_key[idx] for idx in set_idx]

# xor the set key, passocode set value and the mask key
ciphered_mask = xor_lists(mask_set_keys, padded_passcode_server_set)
ciphered_mask = xor_lists(ciphered_mask, user_keys.mask_key)

# encode ciphered mask in base64
mask = user_keys.encode_base64_str(ciphered_mask)
Mask: {{ enciphered_nkode.mask }}

Passcode Enciphering and Hashing

• ciphered_customer_attr = alpha_key ^ customer_attr
• ciphered_passcode_i = pass_key_i ^ ciphered_customer_attr_i
• code = hash(ciphered_passcode, salt)

ciphered_customer_attrs = xor_lists(customer.attributes.attr_vals, user_keys.alpha_key)
passcode_ciphered_attrs = [ciphered_customer_attrs[idx] for idx in passcode]
pad_len = customer.nkode_policy.max_nkode_len - passcode_len

passcode_ciphered_attrs.extend([0 for _ in range(pad_len)])

ciphered_code = xor_lists(passcode_ciphered_attrs, user_keys.pass_key)

passcode_bytes = int_array_to_bytes(ciphered_code)
passcode_digest = base64.b64encode(hashlib.sha256(passcode_bytes).digest())
hashed_data = bcrypt.hashpw(passcode_digest, user_keys.salt)
code = hashed_data.decode("utf-8")

Code: {{ enciphered_nkode.code }}

User Login

1. Get login interface
2. Login

Get Login Interface

The client requests the user's login interface.

login_interface = api.get_login_interface(username, customer_id)
keypad_view(login_interface, keypad_size.attrs_per_key)

The server returns a randomly shuffled interface. Learn more about how the User Interface Shuffle works

Login Interface Keypad View:
{% for key in login_keypad -%}
Key {{ loop.index }}: {{ key }}
{% endfor %}

Recall the user's passcode is user_passcode = {{ user_passcode }} so the user selects keys selected_keys_login = {{ selected_login_keys }}

success = api.login(customer_id, username, selected_keys_login)

Validate Login Key Entry

• decipher user mask and recover nkode set values
• get presumed attribute from key selection and set values
• encipher, salt and hash presumed attribute values and compare it to the users hashed code

Decipher Mask

Recall:

• set_key_i = (set_key_rand_numb_i ^ set_val_i)
• mask_i = mask_key_rand_num_i ^ set_key_rand_numb_i

Recover nKode set values:

• decode mask from base64 to int
• deciphered_mask = mask ^ mask_key
• deciphered_mask_i = set_key_rand_numb # mask_key_rand_num_i is cancelled out
• set_key_rand_component = set_key ^ set_values
• deduce the set value

user = customer.users[username]
user_keys = user.user_keys
user_mask = user.enciphered_passcode.mask
decoded_mask = user_keys.decode_base64_str(user_mask)
deciphered_mask = xor_lists(decoded_mask, user_keys.mask_key)
set_key_rand_component = xor_lists(set_vals, user_keys.set_key)
passcode_sets = []
for set_cipher in deciphered_mask[:passcode_len]:
    set_idx = set_key_rand_component.index(set_cipher)
    passcode_sets.append(set_vals[set_idx])

Passcode Sets: {{ login_passcode_sets }}

Get Presumed Attributes

set_vals_idx = [customer.attributes.get_set_index(set_val) for set_val in passcode_sets]

presumed_selected_attributes_idx = []
for idx in range(passcode_len):
    key_numb = selected_keys_login[idx]
    set_idx = set_vals_idx[idx]
    selected_attr_idx = customer.users[username].user_interface.get_attr_idx_by_keynumb_setidx(key_numb, set_idx)
    presumed_selected_attributes_idx.append(selected_attr_idx)

Presumped Passcode: {{ presumed_selected_attributes_idx }}
Recall User Passcode: {{ user_passcode }}

Compare Enciphered Passcodes

enciphered_nkode = user_keys.encipher_salt_hash_code(presumed_selected_attributes_idx, customer.attributes)

If enciphered_nkode == user.enciphered_passcode.code, the user's key selection is valid and the login is successful.

Renew Attributes

Attributes renew is invoked with the renew_attributes method: api.renew_attributes(customer_id) The renew attributes processes has three steps:

1. Renew Customer Attributes
2. Renew User Keys
3. Refresh User on Login

When the renew_attributes method is called, the customer attributes are renewed and all it's users go through an intermediate renew step. The user if fully renewed after their first successful login. This first login refreshes their keys, salt, and hash.

Customer Renew

Old Customer attributes and set values are cached copied to variables before they are renewed.

old_sets = customer.attributes.set_vals

Customer Sets: {{ customer_set_vals }}

old_attr = customer.attributes.attr_vals

Customer Attributes:
{% for attrs in customer_attr_view -%}
{{ attrs }}
{% endfor %}

After the renew, the customer attributes and sets are new randomly generated values.

api.renew_attributes(customer_id)

set_vals = customer.attributes.set_vals

Customer Sets: {{ customer_new_set_vals }}

attr_vals = customer.attributes.attr_vals

Customer Attributes:
{% for attrs in customer_new_attr_view -%}
{{ attrs }}
{% endfor %}

Renew User

During the renew, each user goes through a temporary transition period.

attrs_xor = xor_lists(new_attrs, old_attrs)
sets_xor = xor_lists(new_sets, old_sets)
for user in customer.users.values():
    user.renew = True
    user.user_keys.set_key = xor_lists(user.user_keys.set_key, sets_xor)
    user.user_keys.alpha_key = xor_lists(user.user_keys.alpha_key, attrs_xor)

User Alpha Key

The user's alpha key was a randomly generated list of length numb_of_keys * attr_per_key. Now each value in the alpha key is alpha_key_i = old_alpha_key_i ^ new_attr_i ^ old_attr_i. Recall in the login process, ciphered_customer_attrs = alpha_key ^ customer_attr. Since the customer_attr is now the new value, it gets cancelled out leaving:

new_alpha_key = old_alpha_key ^ old_attr ^ new_attr
ciphered_customer_attrs = new_alpha_key ^ new_attr
ciphered_customer_attrs = old_alpha_key ^ old_attr # since new_attr cancel out

We can valid the user's login attempt with the same hash using the new customer attributes

User Set Key

The user's set key was a randomly generated list of length attr_per_key xor customer_set_vals. Now the old_set_vals have been replaced with the new new_set_vals. The deciphering process described above remains the same.

User Refresh

Once the user has a successful login, they get a new salt and cipher keys, and their enciphered_passcode is recomputed with the new values.

user.user_keys = UserCipherKeys.new(
    customer.attributes.keypad_size,
    customer.attributes.set_vals,
    user.user_keys.max_nkode_len
)
user.enciphered_passcode = user.user_keys.encipher_nkode(presumed_selected_attributes_idx, customer.attributes)
user.renew = False