schastsp/PROTOCOL.md

Stateless Time-Scrambled Cyclic Hash Protocol

SaTS CHiP

Vocabulary

• A hash or digest is a fixed-length string that is the output of a hash function.
• A token is a fixed-length string sent by a client to a server to authenticate.
• A private key is a fairly unique and hardly guessable data that is generated by a machine and never shared.
• A request is sent from a client to a server, the server sends back a response.

Abstract

After designing some APIs, I found out that you must have at some point a token system to authenticate to your server. For the simplest design, the server attributes a unique token for each client, this token will then be sent over each request to authenticate.

The server may also regenerate the token at some time to avoid token theft.

An easy MITM attack could be to repeat a previously sent request while the token is still valid or even catch the client token and build a malicious request with its authentication.

In this document we will assume that what travels through the network is public, so any MITM can store it. Obviously I highly recommend using TLS for communicating, but we look here for a consistent token system, it only can be better through TLS.

A good alternative could be to use a one-time token where each request features a unique token. This design implies that the token is sent from the server to the client before being used ; so any MITM can catch it. To overcome this flaw we could have a system where one key is used to generate all the tokens in a consistent manner. If so, the tokens do not have to be sent and can be guessed from the key. But this also implies that the key is shared at some point between the client and the server.

A better solution would be to generate a private key on each client and use it to generate a token for each request. Also, to avoid to share the key and allow the server to easily check tokens, we would like a system where each token can be checked from the previous token without having to know the private key (because it is private...). It would avoid attackers to repeat requests (because each token is unique) or guess the private key because it never travels over the network. In addition short-lived one-time passwords have a mechanism that we could use to build a time-dependent system.

What we need

1. Generate a unique token for each request from a fixed private key
2. The token never to be the same
3. The token to be easily checked directly from the previous one
4. Each token to be only valid a few seconds after sending it
5. Each token to give no clue that could help guessing the next token.
6. A system where no key is shared ; only clients do the key processing and the server only to process a simple checking algorithm

Technology requirements

1. Mixing 2 hashes in a way that without one of them, the other is cryptographically impossible to guess (i.e. one-time pad).
2. Having a time-dependent unique feature, that could be found only a few seconds after sending it (as for TOTP).
3. A cryptographic hash function that, from an input of any length, outputs a fixed-length digest in a way that is impossible to guess the input back from it.

Protocols to define

This document will define and bundle 2 distinct protocols to make up a token system that implements the previous statements.

1. a Stateless Time Scrambling Protocol to take care of the request's invalidation over time.
2. a Stateless Cyclic Hash Algorithm to use a private key as a one-time token generator in a way that no clue is given over published tokens (i.e. one-way function).
3. A key renewal mechanism in a way that no clue is given over neither the old nor the new key.
4. A rescue protocol to resynchronise the client with a new key in a way that no clue is given over the network and the client has to process a "proof of work".

General knowledge & Notations

Notations

Symbols	Description
\parallel a\parallel	The absolute value of a ; e.g. \parallel -12 \parallel = 12
\mid a \mid	The integer value of a ; e.g. \mid 12.34 \mid = 12
a \oplus b	The bitwise operation XOR between binary words a and b
a \And b	The bitwise operation AND between binary words a and b
h(m)	The digest of the message m by a (consistent) secure cryptographic hash function h() ; e.g. sha512
h^n(m)	The digest of the n-recursive hash function h() with the input data m ; h^2(m) \equiv h(h(m)), h^1(m) \equiv h(m), and h^0(m) \equiv m.
a \ \mathbb{Z}_{(b)}	The result of a modulo b ; i.e. the remainder of the Euclidean division of a by b
t_{now}	The current Unix Timestamp in seconds

Variables

The whole system share a common context, each client holds a private keyset, and the server stores the last valid token of each client.

1. Common context

These variables are both on the server and clients. They are specific to the server so each client must match its values. These variables shape the system's context (W, min, belt, max).

Variable	Name	Description
W	time window	A number of seconds that is typically the maximum transmission time from end to end. It will be used by the time-scrambling protocol. The lower the number, the less time an attacker has to try to brute-force the tokens.
min	resynchonization range	A number that is used to resynchronize the client if there is a communication issue (e.g. lost request, lost response, attack). The higher the value, the higher the challenge for the client to recover the authentication, thus the harder for an attacker to guess it.
belt	security range	A number that is used to resynchronize the client if there is a communication shift (e.g. lost request, lost response, attack). It corresponds of the number of desynchronizations the client can handle before never being able to gain the authentication again.
max	maximum nonce	A number that is used to cap the value of client's nonces. A too high value will result on keys that will never be replaced, thus making them open to long-processing attacks (e.g. brute-force).

2. Client keyset

Every client holds a keyset (K, n, s). It represents its private key and is used to generate the tokens. The secure hash function is extended to a one-way function to generate all the tokens from the keyset. Note that the client may hold a secondary keyset between the generation of a new keyset and the server's validation of it.

Variable	Name	Description
K	private key	A secret binary data that must be large and random enough not to be brute forced.
n	key nonce	A number that is decremented at each token generation. Before n reaches 0, a new keyset must be generated.
s	key state	A number that reflects the state of the keyset. It is used to know what to do on the next request : - 0 : normal request - 1 : will switch to the new key - 2 : rescue proof of work sent, waiting for the server's acknowledgement

3. Server variables

Variable	Name	Description
T	last valid token	The server stores the last valid token from the client to check the next one.

Protocol

1. Client request generation

In each request, the client will send a pair of time-scrambled hashes (x_1, x_2) :

• x1 will hold the current one-time token
• x2 will hold the necessary data to check the next token

The client implements 3 protocols according to the keyset state :

• 0 : NORMAL - default authentication protocol.
• 1 : SWITCH - default protocol variation to switch to a new keyset when the current one is consumed (i.e. when n \leq min+belt).
• 2 : RESCUE - process the proof of work after receiving the server's challenge when there is a desynchronisation and generate a new keyset.

When the client switches to a new key, it has to store the new keyset along the current one, in order not to lose its authentication if the network fails.

• (K,n,s) - the current keyset
• (K',n',s') - the new keyset

A. NORMAL protocol (state 0)

Step	Calculation
1	Decrement n
2	t\_c = \mid \frac{t\_{now}}{W}\mid, m\_c = t\_c \ \mathbb{Z}\_{(2)}
3	x\_1 = h^{n}(K) \oplus h(t\_c)
4	x\_2 = x\_1 \oplus m\_c
5	if i <= min+belt \Rightarrow s = 1

Send x_1 and x_2.

B. SWITCH protocol (state 1)

Step	Calculation
1	t\_c = \mid \frac{t\_{now}}{W}\mid, m\_c = t\_c \ \mathbb{Z}\_{(2)}
2	x\_1 = h^{n}(K) \oplus h(t\_c)
3	Generate (K',n',s') until [(h^n(K) \oplus h^{n'}(K')) \And 0x1] \ \mathbb{Z}\_{(2)} = m\_c [(h^N(K) \oplus h^{n'}(K')) \And 0xf0] \ \mathbb{Z}\_{(3)} = s
4	x\_2 = h^{n'}(K') \oplus h(t\_c)

Send x_1 and x_2.

If the response succeeds, replace the key with the new one : K = K', n = n', s = 0

C. RESCUE protocol (state 2)

This protocol is processed when the server sends the 2 hashes (y_1, y_2) to the client (instead of the standard response). It means that the server has received a wrong hash, so it sends the rescue challenge to the client.

Step	Calculation
1	t\_c = \mid \frac{t\_{now}}{W} \mid , m\_c = t\_c \ \mathbb{Z}\_{(2)}
2	t'\_s = t\_c - \parallel m\_c - (y_1 \oplus y_2)\parallel
3	T = x\_1 \oplus h(t'\_s)
4	Find N \in [min ; n-min[,\ h^{N}(K) = T.
5	x\_1 = h^N(K) \oplus h(t\_c)
6	Generate (K',n',s') until : [(h^N(K) \oplus h^{n'}(K')) \And 1] \ \mathbb{Z}\_{(2)} = m\_c [(h^N(K) \oplus h^{n'}(K')) \And 11110000] \ \mathbb{Z}\_{(3)} = s
7	x\_2 = h^{n'}(K') \oplus h(t\_c)

Send x_1 and x_2.

If the response succeeds, replace the key with the new one : K = K', n = n', s = 0

2. Server management

When receiving a pair of hashes (x_1, x_2), the server has to :

1. Unscramble the request using the time-scrambling algorithm
2. Check the token t_1 held into x_1 :
   • VALID \rightarrow authenticated : store the token t_2 held into x_2, forward request to the logic unit
   • INVALID \rightarrow not authenticated : send the challenge hashes (y_1, y_2).

1. Unscramble the request

Step	Calculation
1	t\_s = \mid \frac{t\_{now}}{W}\mid, m\_s = t\_s \ \mathbb{Z}\_{(2)}
2	m\_c = x\_1 \oplus x\_2
3	t'\_c = t\_s - \parallel m_c - m_s \parallel
4	t\_1 = x\_1 \oplus h(t'\_c)
5	t\_2 = x\_2 \oplus h(t'\_c)

If h(t_1) = T :

• t_1 is valid
• store the next token T=t_2

Else, go to the invalid request management.

2. Invalid request management

When receiving an invalid token, the server may send back to the client a challenge to get the authentication back. This challenge is formed by 2 hashes (y_1, y_2).

Step	Calculation
1	t\_s = \mid \frac{t\_{now}}{W}\mid
2	y\_1 = T \oplus h(t\_c)
3	y\_2 = y\_1 \oplus (t\_c \ \mathbb{Z}\_{(2)})

Send y_1 and y_2.