Authenticated Encryption in TLS
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- Christopher Hicks
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1 Authenticated Encryption in TLS
2 Same modelling & verification approach concrete security: each lossy step documented by a game and a reduction (or an assumption) on paper Standardized complications - multiple algorithms and constructions (crypto agility) - multiple keys - conditional security (crypto strength, compromise) - wire format, fragmentation, padding - stateful (stream encryption) Poor TLS track record - Many implementation flaws - Attacks on weak cryptography (MD5, SHA1, ) - Attacks on weak constructions (MAC-Encode-then-Encrypt) - Attacks on compression - Persistent side channels - Persistent truncation attacks
3 Handshake AppData Alert Plaintext Key 0 (1 sided) Key 1 Key 2 Key 3 Write channel Handshake AppData Alert Plaintext Key 1 Read channel Key 2 Key 3
4 TLS 1.3 gets rid of weak constructions, encrypts parts of the handshake, introduces plenty of auxiliary keys AppData ct = 0x17 Handshake ct = 0x16 plaintext Alert ct = 0x15 format parse plaintext ct 000 l + 1 App Data TLS cipherlen (l + 1) encrypt decrypt ciphertext tag
5 We model record-layer security using a game at every level of the construction. We make code-based security assumptions on the crypto primitives (PRF, MAC) We obtain security guarantees at the toplevel API for the TLS record layer Generic AES Handshake/Alert keys: k 0, k 1, PRF ChaCha20 Record LHSE StAE AEAD GHASH Application fragments: d 0, d 1, d 2 MAC Sequence of streams keyed by Handshake Length-Hiding (padded) Multiplexed Streams Stream Encryption with sequence numbers Generic AEAD construction Poly1305 Verified Crypto library
6 Symmetric Cryptography AES128 AES256 Chacha20 GHASH Poly1305 Cipher IND-PRF 1-Time MAC IND-1CMA AEAD AEAD.Encoding AEAD.Invariant Stream Encryption TLS record protection Record Layer Protection
7 Client Server encrypt #2 TLS record layer decrypt #1
8 Client Server ideal encryption log #0 #1 encrypt #2 random sampling table lookup decrypt #1
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10 We program & verify AEAD for TLS 1.2 and TLS 1.3. We do not consider here classic, time-battered TLS modes such as AES_CBC (Mac-Encode-then-Encrypt)
11 One-time Pad for the MAC IV 0 IV 1 IV n AEAD Key PRF PRF PRF lengths of plaintext and additional data Ciphertext (tag) T a g Authentication key
12 One-Time MACs (INT-CMA1) Ciphers (IND-PRF) For both GF128 or Poly1305, we get strong probabilistic security. Assumed for AES and Chacha20
13 One-Time MACs (INT-CMA1) Ciphers (IND-PRF) Construction: authenticated materials and their lengths are encoded as coefficients of a polynomial in a field (GF128 or 2^130-5) The MAC is the polynomial evaluated at a random point, then masked. We get strong probabilistic security. Modelling: we use a variant with specialized oracles for each usage of the resulting blocks - as one-time MAC key materials - as one-time pad for encryption - as one-time pad for decryption
14 many kinds of proofs not just code safety! Given a cipher, modelled as a pseudo-random function a field for computing one-time MACs injective message encodings We program and verify a generic authenticated stream encryption with associated data. We show safety functional correctness security (reduction to PRF assumption) concrete security bounds for the 3 main record ciphersuites of TLS functional correctness (low-level assembly) LHAE AES128 AES256 AES CBC TLS record protection TLS API TLS FFI Chacha20 Cipher IND-PRF AEAD Stream Encryption arithmetic correctness (field computations) GHASH 1-Time MAC IND-1CMA Poly1305 AEAD.Encoding AEAD.Invariant abstraction & agility security idealization injectivity loops & stateful invariants (reasoning on ideal logs) TLS-specific mechanisms fragmentation content multiplexing length-hiding, padding re-keying 0-RTT, 0.5-RTT
15 Theorem: the 3 main record ciphersuites for TLS 1.2 and 1.3 are secure, except with probabilities Standard crypto assumption Probabilistic proof (on paper) in abstract field + F* verification IND-PRF IND-1CMA AEAD AEAD.Encoding AEAD.Invariant Stream Encryption q e is the number of encrypted records; q d is the number of chosen-ciphertext decryptions; q b is the total number of blocks for the PRF F* type-based verification on code formalizing game-based reduction
16 We verified concrete security on low-level, standard-compliant code (not just a crypto proof on paper) Interop as client and server with 3 other implementations of TLS 1.2 and 1.3 Reasonable performance. AES128 AES256 AES CBC Chacha20 Cipher IND-PRF AEAD GHASH Poly Time MAC IND-1CMA AEAD.Encoding AEAD.Invariant Stream Encryption LHAE TLS record protection TLS API TLS FFI
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19 TLS 1.3 Handshake (Outline) TLS *** RSA SHA ECDH AES Crypto Algorithms
20 Client Server
21 Handshake Negotiation Messages syntax: parse/format Extensions Configuration Certificates Signing config & mode HMAC State machine Session Log flights keys digests shares Hash Key Schedule ODH PRF TLS API Application (HTTPS etc) Record Layer Protection Network (TCP)
22 Most of the RFC, most of the code. Correctness? Metaprogramming in F* Performance? Intermediate copies considered harmful. Security? Handshake digest computed on the fly Example: ClientHello message Example: HandshakeLog.recv
23 high-level parser val parsech: bytes -> option clienthello inverse properties val injch: clienthello -> Lemma high-level type type clienthello = ClientHello: pv: protocolversion -> id: vlbytes > cs: seq ciphersuite { } -> high-level formatter val formatch: clienthello -> bytes erased specification low-level validator val validatech: len: UInt32.t -> input: lbuffer len -> Stack (option (erased clienthello * UInt32.t)) (requires fun h0 -> live input) (ensures fun h0 result h1 -> h0 = h1 /\ match result with Some (ch, pos) -> pos <= len /\ format ch = buffer.read input h0 0..pos-1 None -> True) low-level in-place code extracted to C low-level serializer val serializech: output: buffer -> len: UInt32.t -> pv: -> -> Heap (option UInt32.t) (ensures fun h0 result h1 -> modifies h0 output.[0..len-1] h1 /\ match result with Some pos -> //idem
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25 pre-shared key Integrity early secret Export (QUIC) Diffie-Hellman shared secret (g xy ) handshake secret master secret Encryption Export (QUIC) Caption: two kinds of key derivation steps key materials Handshake Integrity prior secret Encryption Integrity Encryption pre-shared keys for future sessions Extract Expand new secret derived secret
26 pre-shared key Integrity early secret Export (QUIC) Diffie-Hellman shared secret (g xy ) handshake secret master secret Encryption Export (QUIC) Handshake Integrity Encryption pre-shared keys for future sessions Integrity Encryption Our (fresh) crypto model precisely reflects F* code modularity, involves a security definition for each color, supports agility and key compromise.
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