Pure-Python SPAKE2

• License: MIT
• Dependencies: "cryptography" (for hkdf)
• Compatible With: Python 3.9, 3.10, 3.11, 3.12, PyPy3
• 

This library implements the SPAKE2 password-authenticated key exchange ("PAKE") algorithm. This allows two parties, who share a weak password, to safely derive a strong shared secret (and therefore build an encrypted+authenticated channel).

A passive attacker who eavesdrops on the connection learns no information about the password or the generated secret. An active attacker (man-in-the-middle) gets exactly one guess at the password, and unless they get it right, they learn no information about the password or the generated secret. Each execution of the protocol enables one guess. The use of a weak password is made safer by the rate-limiting of guesses: no off-line dictionary attack is available to the network-level attacker, and the protocol does not depend upon having previously-established confidentiality of the network (unlike e.g. sending a plaintext password over TLS).

The protocol requires the exchange of one pair of messages, so only one round trip is necessary to establish the session key. If key-confirmation is necessary, that will require a second round trip.

All messages are bytestrings. For the default security level (using the Ed25519 elliptic curve, roughly equivalent to an 128-bit symmetric key), the message is 33 bytes long.

What Is It Good For?

PAKE can be used in a pairing protocol, like the initial version of Firefox Sync (the one with J-PAKE), to introduce one device to another and help them share secrets. In this mode, one device creates a random code, the user copies that code to the second device, then both devices use the code as a one-time password and run the PAKE protocol. Once both devices have a shared strong key, they can exchange other secrets safely.

PAKE can also be used (carefully) in a login protocol, where SRP is perhaps the best-known approach. Traditional non-PAKE login consists of sending a plaintext password through a TLS-encrypted channel, to a server which then checks it (by hashing/stretching and comparing against a stored verifier). In a PAKE login, both sides put the password into their PAKE protocol, and then confirm that their generated key is the same. This nominally does not require the initial TLS-protected channel. However note that it requires other, deeper design considerations (the PAKE protocol must be bound to whatever protected channel you end up using, else the attacker can wait for PAKE to complete normally and then steal the channel), and is not simply a drop-in replacement. In addition, the server cannot hash/stretch the password very much (see the note on "Augmented PAKE" below), so unless the client is willing to perform key-stretching before running PAKE, the server's stored verifier will be vulnerable to a low-cost dictionary attack.

Usage

Alice and Bob both initialize their SPAKE2 instances with the same (weak) password. They will exchange messages to (hopefully) derive a shared secret key. The protocol is symmetric: for each operation that Alice does, Bob will do the same.

However, there are two roles in the SPAKE2 protocol, "A" and "B". The two sides must agree ahead of time which one will play which role (the messages they generate depend upon which side they play). There are two separate classes, SPAKE2_A and SPAKE2_B, and a complete interaction will use one of each (one SPAKE2_A on one computer, and one SPAKE2_B on the other computer).

Each instance of a SPAKE2 protocol uses a set of shared parameters. These include a group, a generator, and a pair of arbitrary group elements. This library comes with several pre-generated parameter sets, with various security levels.

You start by creating an instance (either SPAKE2_A or SPAKE2_B) with the password. Then you ask the instance for the outbound message by calling msg_out=s.start(), and send it to your partner. Once you receive the corresponding inbound message, you pass it into the instance and extract the (shared) key bytestring with key=s.finish(msg_in). For example, the client-side might do:

from spake2 import SPAKE2_A
s = SPAKE2_A(b"our password")
msg_out = s.start()
send(msg_out) # this is message A->B
msg_in = receive()
key = s.finish(msg_in)

while the server-side might do:

from spake2 import SPAKE2_B
q = SPAKE2_B(b"our password")
msg_out = q.start()
send(msg_out)
msg_in = receive() # this is message A->B
key = q.finish(msg_in)

If both sides used the same password, and there is no man-in-the-middle, then both sides will obtain the same key. If not, the two sides will get different keys, so using "key" for data encryption will result in garbled data.

The shared "key" can be used as an HMAC key to provide data integrity on subsequent messages, or as an authenticated-encryption key (e.g. nacl.secretbox). It can also be fed into [HKDF] 1 to derive other session keys as necessary.

The SPAKE2 instances, and the messages they create, are single-use. Create a new one for each new session.

Key Confirmation

To safely test for identical keys before use, you can perform a second message exchange at the end of the protocol, before actually using the key (be careful to not simply send the shared key over the wire: this would allow a MitM to learn the key that they could otherwise not guess).

Alice does this:

...
key = s.finish(msg_in)
confirm_A = HKDF(key, info="confirm_A", length=32)
expected_confirm_B = HKDF(key, info="confirm_B", length=32)
send(confirm_A)
confirm_B = receive()
assert confirm_B == expected_confirm_B

And Bob does this:

...
key = q.finish(msg_in)
expected_confirm_A = HKDF(key, info="confirm_A", length=32)
confirm_B = HKDF(key, info="confirm_B", length=32)
send(confirm_B)
confirm_A = receive()
assert confirm_A == expected_confirm_A

Symmetric Usage

A single SPAKE2 instance must be used asymmetrically: the two sides must somehow decide (ahead of time) which role they will each play. The implementation includes the side identifier in the exchanged message to guard against an SPAKE2_A talking to another SPAKE2_A. Typically a "client" will take on the A role, and the "server" will be B.

This is a nuisance for more egalitarian protocols, where there's no clear way to assign these roles ahead of time. In this case, use SPAKE2_Symmetric on both sides. This uses a different set of parameters (so it is not interoperable with SPAKE2_A or SPAKE2_B, but should otherwise behave the same way.

Carol does:

s1 = SPAKE2_Symmetric(pw)
outmsg1 = s1.start()
send(outmsg1)

Dave does the same:

s2 = SPAKE2_Symmetric(pw)
outmsg2 = s2.start()
send(outmsg2)

Carol then processes Dave's incoming message:

inmsg2 = receive() # this is outmsg1
key = s1.finish(inmsg2)

And Dave does the same:

inmsg1 = receive() # this is outmsg2
key = s2.finish(inmsg1)

Identifier Strings

The SPAKE2 protocol includes a pair of "identity strings" idA and idB that are included in the final key-derivation hash. This binds the key to a single pair of parties, or for some specific purpose.

For example, when user "alice" logs into "example.com", both sides should set idA = b"alice" and idB = b"example.com". This prevents an attacker from substituting messages from unrelated login sessions (other users on the same server, or other servers for the same user).

This also makes sure the session is established with the correct service. If Alice has one password for "example.com" but uses it for both login and file-transfer services, idB should be different for the two services. Otherwise if Alice is simultaneously connecting to both services, and attacker could rearrange the messages and cause her login client to connect to the file-transfer server, and vice versa.

If provided, idA and idB must be bytestrings. They default to an empty string.

SPAKE2_Symmetric uses a single idSymmetric= string, instead of idA and idB. Both sides must provide the same idSymmetric=, or leave it empty.

Serialization

Sometimes, you can't hold the SPAKE2 instance in memory for the whole negotiation: perhaps all your program state is stored in a database, and nothing lives in RAM for more than a few moments. You can persist the data from a SPAKE2 instance with data = p.serialize(), after the call to start. Then later, when the inbound message is received, you can reconstruct the instance with p = SPAKE2_A.from_serialized(data) before calling p.finish(msg).

def first():
    p = SPAKE2_A(password)
    send(p.start())
    open('saved','w').write(p.serialize())
 
def second(inbound_message):
    p = SPAKE2_A.from_serialized(open('saved').read())
    key = p.finish(inbound_message)
    return key

The instance data is highly sensitive and includes the password: protect it carefully. An eavesdropper who learns the instance state from just one side will be able to reconstruct the shared key. data is a printable ASCII bytestring (the JSON-encoding of a small dictionary). For ParamsEd25519, the serialized data requires 221 bytes.

Note that you must restore the instance with the same side (SPAKE2_A vs SPAKE2_B) and params= (if overridden) as you used when first creating it. Otherwise from_serialized() will throw an exception. If you use non-default parameters, you might want to store an indicator along with the serialized state.

Also remember that you must never re-use a SPAKE2 instance for multiple key agreements: that would reveal the key and/or password. Never use .from_serialized() more than once on the same saved state, and delete the state as soon as the incoming message is processed. SPAKE2 has internal checks to throw exceptions when instances are used multiple times, but the serialize/restore process can bypass those checks, so use with care.

Database-backed applications should store the outbound message (p.start()) in the DB next to the serialized SPAKE2 state, so they can re-send the same message if the application crashes before it has been successfully delivered. p.start() cannot be called on the instance that .from_serialized() produces.

Security

SPAKE2's strength against cryptographic attacks depends upon the parameters you use, which also influence the execution speed. Use the strongest parameters your time budget can afford.

The library defaults to the fast and secure Ed25519 elliptic-curve group through the ParamsEd25519 parameter set. This offers a 128-bit security level, small messages, and fairly fast execution speed.

If for some reason you don't care for elliptic curves, the spake2.params module includes three integer-group parameter sets: Params1024, Params2048, Params3072, offering 80-bit, 112-bit, and 128-bit security levels respectively.

To override the default parameters, include a params= value when you create the SPAKE2 instance. Both sides must use the same parameters.

from spake2 import SPAKE2_A
from spake2.parameters.i3072 import Params3072
s = SPAKE2_A(b"password", params=Params3072)

Note that if you serialize an instance with non-default params=, you must restore it with the same parameters, otherwise you will get an exception:

s = SPAKE2_A.from_serialized(data, params=Params3072)

This library is very much not constant-time, and does not protect against timing attacks. Do not allow attackers to measure how long it takes you to create or respond to a message.

This library depends upon a strong source of random numbers. Do not use it on a system where os.urandom() is weak.

Speed

To run the built-in speed tests, just run python setup.py speed.

SPAKE2 consists of two phases, separated by a single message exchange. The time these phases take is split roughly 40/60. On my 2012 Mac Mini (2.6GHz Core-i7), the default ParamsEd25519 security level takes about 14ms to complete both phases. For the integer groups, larger groups are slower and require larger messages (and their serialized state is larger), but are more secure. The complete output of python setup.py speed is:

ParamsEd25519: msglen= 33, statelen=221, full=13.9ms, start= 5.5ms
Params1024   : msglen=129, statelen=197, full= 4.3ms, start= 1.8ms
Params2048   : msglen=257, statelen=213, full=20.8ms, start= 8.5ms
Params3072   : msglen=385, statelen=221, full=41.5ms, start=16.5ms

A slower CPU (1.8GHz Intel Atom) takes about 8x as long (76/32/157/322ms).

This library uses only Python. A version which used C speedups for the large modular multiplication operations would probably be an order of magnitude faster.

Testing

To run the built-in test suite from a source directory, for all supported python versions, do:

tox

On my computer, the tests take approximately two seconds (per version).

History

The protocol was described as "PAKE2" in ["cryptobook"] 2 from Dan Boneh and Victor Shoup. This is a form of "SPAKE2", defined by Abdalla and Pointcheval at [RSA 2005] 3. Additional recommendations for groups and distinguished elements were published in [Ladd's IETF draft] 4.

The Ed25519 implementation uses code adapted from Daniel Bernstein (djb), Matthew Dempsky, Daniel Holth, Ron Garret, with further optimizations by Brian Warner5. The "arbitrary element" computation, which must be the same for both participants, is from python-pure25519 version 0.5.

The Boneh/Shoup chapter that defines PAKE2 also defines an augmented variant named "PAKE2+", which changes one side (typically a server) to record a derivative of the password instead of the actual password. In PAKE2+, a server compromise does not immediately give access to the passwords: instead, the attacker must perform an offline dictionary attack against the stolen data before they can learn the passwords. PAKE2+ support is planned, but not yet implemented.

The security of the symmetric case was proved by Kobara/Imai6 in 2003, and uses different (slightly weaker?) reductions than that of the asymmetric form. See also Mike Hamburg's analysis7 from 2015.

Brian Warner first wrote this Python version in July 2010.

footnotes