OTR AKE in Verifpal
Mon 15 May 2023 — download

I recently attended a talk at work about formal verification of cryptographic protocol, and was horrified by the nested amount of complexity to do basic reasoning. Which reminded me about Verifpal:

Verifpal® is new software for verifying the security of cryptographic protocols. Building upon contemporary research in symbolic formal verification, Verifpal’s main aim is to appeal more to real-world practitioners, students and engineers without sacrificing comprehensive formal verification features.

So I modelled OTRv3's Authenticate Key Exchange in it, and here is the result (it'll look prettier once this gets merged.):

// OTRv3 Authenticated Key Exchange (AKE)
// https://otr.cypherpunks.ca/Protocol-v3-4.1.1.html

attacker[passive]

// Setup
principal Bob [
    knows private priv_b
    pub_b = G^priv_b
]
Bob  Alice: [pub_b]
principal Alice[
    knows private priv_a
    pub_a = G^priv_a
]
Alice  Bob: [pub_a]

// Go!
principal Bob [
    generates r, x
    g_x = G^x
    enc_gx = ENC(r, g_x)
    hash_gx = HASH(g_x)
]

Bob  Alice: enc_gx, hash_gx

principal Alice [
    generates y
    g_y = G^y
]

Alice  Bob: g_y

principal Bob [
    s = g_y^x
    c, c_ = HKDF(s, nil, nil)
    m1, m2, m1_, m2_ = HKDF(nil, s, nil)
    generates keyid_b
    Mb = MAC(m1, CONCAT(g_x, g_y, pub_b, keyid_b))
    Xb = CONCAT(pub_b, keyid_b, SIGN(priv_b, Mb))
    enc_c_x_b = ENC(c, Xb)
    mac_mc2_enc_c_x_b  = MAC(m2, ENC(c, Xb))
]

Bob  Alice: r, enc_c_x_b, mac_mc2_enc_c_x_b

principal Alice [
    dec_gx = DEC(r, enc_gx)
    _ = ASSERT(HASH(dec_gx), hash_gx)?
    s_ = dec_gx^y
    c_alice, c__alice = HKDF(s_, nil, nil)
    m1_alice, m2_alice, m1__alice, m2__alice = HKDF(nil, s_, nil)
    _ = ASSERT(mac_mc2_enc_c_x_b, MAC(m2_alice, enc_c_x_b))?
    xb_alice = DEC(c_alice, enc_c_x_b)
    pub_b_alice, keyd_b_alice, sig_b_mb_alice = SPLIT(xb_alice)
    mb_alice = MAC(m1_alice, CONCAT(dec_gx, g_y, pub_b_alice, keyd_b_alice))
    _ = SIGNVERIF(pub_b_alice, mb_alice, sig_b_mb_alice)?
    generates keyid_a
    ma = MAC(m1__alice, CONCAT(g_y, dec_gx, pub_a, keyid_a))
    xa = CONCAT(pub_a, keyid_a, SIGN(priv_a, ma))
    enc_c__x_a = ENC(c__alice, xa)
    mac_m2_enc_c__xa = MAC(m2__alice, ENC(c__alice, xa))
]

Alice  Bob: enc_c__x_a, mac_m2_enc_c__xa

principal Bob [
    _ = ASSERT(mac_m2_enc_c__xa, MAC(m2_, enc_c__x_a))?
    xa_bob = DEC(c_, enc_c__x_a)
    pub_a_bob, keyid_a_bob, sig_a_ma_bob = SPLIT(xa_bob)
    ma_bob = MAC(m1_, CONCAT(g_y, g_x, pub_a_bob, keyid_a_bob))
    _ = SIGNVERIF(pub_a_bob, ma_bob, sig_a_ma_bob)?
    _ = ASSERT(pub_a_bob, pub_a)?
]

queries [
    equivalence? s, s_
    confidentiality? s
    freshness? s

    equivalence? pub_b, pub_b_alice
    equivalence? pub_a, pub_a_bob
]
$ verifpal verify ./otr_ake.vp | tail -n 5

 Verifpal • Verification completed for 'otr_ake.vp' at 11:11:52 PM. 
 Verifpal • All queries pass. 

 Verifpal • Thank you for using Verifpal. 
$

The model was sent to VerifHub for everyone to enjoy.

Unfortunately, while being a breeze to use compared to the domain heavyweight contenders like CryptoVerif, Tamarin, Proverif, … Verifpal has some shortcomings:

  • It isn't maintained anymore.
  • Nadim Kobeissi, the author of Verifpal, who did his Phd on "Formal verification for real-world cryptographic protocols and implementations", to put it mildly, doesn't seem to be a great human being. Moreover, his stupid dunks on Citizen Lab ended up being cited in José Javier Olivas-Osuna's completely phony Pegasus report.
  • Only constants can be sent between principal, meaning that there are a ton of intermediary variables.
  • There is no way to add constrains on variables, like Alice verifies that Bob's gˣ is a legal value (2 ≤ gˣ ≤ modulus-2). One could use guarded constants like [g_x] to prevent an active attacker from messing with , but this can't be done on function results, like asserting that g_x obtained from DEC(…) is a legal value.
  • Some errors are silently ignored, like SPLIT(SPLIT(CONCAT(…))) instead of SPLIT(CONCAT(…)).
  • Multiplications aren't implemented: gˣ·gʸ isn't a thing, making it impossible to model OTR's SMP.