Joseph Jaeger Igors Stepanovs Alice and Bob want E2E secure - - PowerPoint PPT Presentation
Joseph Jaeger Igors Stepanovs Alice and Bob want E2E secure - - PowerPoint PPT Presentation
Optimal Channel Security Against Fine-Grained State Compromise: The Safety of Messaging Joseph Jaeger Igors Stepanovs Alice and Bob want E2E secure communication But what about E2E Tools? Plenty of Theory Symmetric encryption Asymmetric
Alice and Bob want E2E secure communication
Plenty of Theory … Symmetric encryption Asymmetric encryption Session key exchange Signatures …
But what about E2E Tools?
2
PGP is a pain! TLS is for web servers!
≠
Messaging Apps Emerging as most convenient & usable.
E2E Messaging Apps
3 WhatsApp Facebook Messenger
(Secret Conversations)
iMessage Telegram (Secret Chats) Many more… Skype
(Private Conversations)
Signal Viber Apps Targeting E2E Security:
Understanding their security is important! We aim to better understand its goal: Security against state compromise
Whatsapp alone encrypts ~55 billion messages/day.
These are all based on Open Whisper System’s Double Ratchet Algorithm. (i.e. the techniques of Signal)
~700 million iPhones in use.
Traditional Encryption Key Updating Encryption
m2 m3
k
c
Enc Dec
k k
c
Enc Dec
k k
c
Enc Dec
k
m1 m1 m2 m3
4
Enc
k m
c
Yoink! later
Enc
m
c
k2
k1
? ??
Enc
m
c
Yoink!
k1
now How does attacker access secrets?
- Steals physical device
- Malware
- Border searches
- Unpatched vulnerabilities
- …
Addressed in practice: Messaging app designers in practice are trying to protect against this threat by updating the secret key using ratcheting.
c
Enc Dec
m1 m1 k1 k1 m2
c
Enc Dec
m2 k2 k2 m3
c
Enc Dec
m3 k3 k3
update keys update keys
k ∈ ~ KA ∩ ~ KB
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∈ ~ KA ∩ ~ KB
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Informal goals:
- Forward security: prior keys or communications remain secure
- Backward security: future keys or communications remain secure
Exactly what threat these goals prevent in practice needs careful consideration …
- Less useful when threat is persistent malware than can directly exfiltrate messages.
- More useful when users delete old messages, malware exfiltrates keys instead of messages,
malware’s presence limited by software security. Forward and backward security are of particular interest for secure messaging because conversations can be very long lived … a chat session can stay open for a year … Traditional Encryption Key Updating Encryption
m2 m3
k
c
Enc Dec
k k
c
Enc Dec
k k
c
Enc Dec
k
m1 m1 m2 m3
c
Enc Dec
m1 m1 k1 k1 m2
c
Enc Dec
m2 k2 k2 m3
c
Enc Dec
m3 k3 k3
update keys update keys
k ∈ ~ KA ∩ ~ KB
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sha1_base64="BDPMi9hInOgx3u7dcs9rhajoz4=">AJUXic5VZLb9w2EFbcR2ylD6c95kLUcNFDvCsZBZLCMB7bTRIi3r2kAyzAoaqRlLJECSe16I+gP5dcU6Cn9Hz301qHEfcRJXRFgQIlsKvhzHzDmeEnkXGZc2C4PWtlfe/+D26tr/p2Pv7k0/W7nz3VslIMTpnMpXoeUw05F3BquMnheamAFnEOz+LgbU/G4PSXIoTMy3hvKCZ4Cln1KDqYv0gyhSAqC+biAsnR2NgdVRQM4rT+rumudhrIkbLP7PuNxfrG0EvaAd5WwidsOG5Mby4e/u3KJGsKkAYlOtz8KgNOc1VYazHBo/qjSUlF3SDM5QFLQAfV635TZkEzUJSaXCnzCk1S4jalpoPS1i9LRp6us2q3yX7awy6cPzmouyMiBYt1Ba5cRIYntHEq6AmXyKAmWKY6EjaizGCHfX/zpvEX1kjAhKcRT/VIKhPz2I9mUkpzDf7CAzPKCfEj+zSqAkI2iQZjs2xd287kuWCaLKEoK/wI/65HM/zy5aGgyJfEj5YmNrKPNQ1GVGSwCB4Dhgeiq7jgxnCRLUIlEFc4bR8dHGU0CGlA1wH2k4Rkl2BdE1JMcd8Ku/+a0FhWhoyp4rLSRJtpDv0ENM8EtldyBrnQtmSHZvrsCHElh4s6vUxCVEVy267Yds7TaHbnSZVBrzn0Gtl01NIjLN5eRawjO1JpMRiA40C17SEpRlSLeAzWmX5GCQFjtBPr1TudJhRTAstc9kTd1tzgALNpByumlumav4S27A5mX5nOwytFBuk6PGbT6SV7tlkR4FVRl3XevwicSVjaVOFwUF503HoPGdeKOcmTfaSGt0oPncFZgkRjK3OTMsXLG8SoCcHA06FBdzhYNVZtTRZCnBuZLINHV9WahEh8zsp4ELWpauNdZtws2IWMuW/TYmB31l6WSMtW4NkFnEAm/2nHtb1nFLDE1i3DgmaxQ6qgOXGcpXPHWd6PwL7bi3xLfx7fPsP0i34Z3R7B4H+DboF/0+6pfyGU+UmE34o7SFX9081xuq/0C8oZKD6B+5M1v2hknFDB9DP+Omf7x3Mnh8eHJ4sHX4w6D/5MnW8PhoePT3vf9EdAEVM/AVdNWhPeQ9kCuk6ypj7/db+rt4H74TXB/O2h8vCiE168FbwtPt3th0At/DYe7bsrw6p3z/vC+8oLvQfeI+xN/ROPea98n72Xnu/rv6y+vuat7bSua7cpjPvTfG2p0/AHsX9EQ=</latexit>k ∈ ~ KA ∩ ~ KB
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Prior Work Analyzed entirety of Signal key exchange and ratcheting Does not model encryption Introduced ratcheted key exchange and ratcheted encryption. One-directional communication Only sender’s state vulnerable Extended ratcheted key exchange to be bidirectional Does not model encryption What security goal does ratcheting achieve? Formalize it Show that ratcheting achieves it.
7
Prior Work What security goal does ratcheting achieve? Formalize it Show that ratcheting achieves it. Our Work What is the BEST POSSIBLE messaging security we can achieve in the face of fine-grained state compromise? Formalize it Show how to achieve it. NOT ratcheting!
Define strongest possible security of a channel against fine-grained state compromise.
Our Contributions
Define Key-Updatable Digital Signatures (KUDS) Key-Updatable Public-Key Encryption (KUPKE) Constructions of KUDS and KUPKE. Proofs that our constructions achieve our strong definitions of security.
1. 2. 3. 5. 4.
Construction
KUDS scheme KUPKE scheme Secure Channel Hash function
8
Changed from proceedings version due to bugs in security proofs.
Our Threat Model
Our Adversary has: Complete control of communication. Ability to arbitrarily and repeatedly expose secrets. We want the best achievable integrity and privacy.
Does the Double Ratchet Algorithm (Signal) achieve this?
Answer: No. For example an attacker can,
forge messages to an exposed user read ciphertexts from an exposed user and more One exposure allows perfect MITM
An Implication: Does this matter in practice?
Hard to say - requires better knowledge of attacks occurring in practice
Can we just tweak Signal?
all preventable attacks should be prevented
Probably not - seems to require fundamentally different techniques
This part is preventable.
Init
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sha1_base64="PU9au/QiK2YFDVJgVmoN6QUWuQM=">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</latexit><latexit sha1_base64="PU9au/QiK2YFDVJgVmoN6QUWuQM=">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</latexit><latexit sha1_base64="hGFsLX2aV8Xej8VlWJ6v98gS/v0=">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</latexit>(Bidirectional) Channel Syntax
10
From
Allows messages to cross “on the wire”, But preserves message order in either direction. Stateful encryption… Allowing bidirectional communication.
. . . . . .
Send
<latexit 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<latexit 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security
Send(u, m0, m1, ad)
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Tell which message is encrypted or
- Forge a new ciphertext
party u encrypts one of two messages Attacker Goals: party u receives a ciphertext party u exposes secret state
Step 1: specify interface
Adversary has: Complete control of communication. Ability to expose secrets.
11
Exp(u, rand)
<latexit 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sha1_base64="Y0A7U9w9AjeBLaY6bZ79lAFWFE=">AJnic5VZfa9xGEFfStLmq/5z2qeRlqXFJwb6TCEpxpDkcjQNpb6dhKwjFmtRrqNpV2xu/L5Io58mkKf2m/St1L61i/R985Kq7uLE1xKRS6cKfRzPxmZ2Z/2t24zLk2QfDblatvXHvzreu9t/13n3v/Q/Wbnz4WMtKMThkMpfqaUw15FzAoeEmh6elAlrEOTyJT4fW/uQMlOZSHJhZCcFzQRPOaMGVSdrH0elkmx0Xt6qNqOCmolOa0VFMv/sZG096AfNIK8KoRPWPTfGJzeu/xElklUFCMNyqvVRGJTmuKbKcJbD3I8qDSVlpzSDIxQFLUAf10Nc7KBmoSkUuFPGNJoVxE1LbSeFTF6NmletFnl62xHlUnvHNdclJUBwdqJ0ionRhLbEJwBczkMxQoUxzJWxCFWUG2+b7G5eNv7BGAqY8jXiqJ1KZmMd+1EkpzTX4Sw/MKCfEj+zTqAoI2SAajM2ycW06k+eCabKCoqzwI/y7GM3w0+cjQZEiR+tvNjIPtY0nFCRwTJ4DBgeiK7ighvDRbYMlUBc4WvzaOEo0FIA7oOsJ8kJLsE65qSYobrVtj14TGsjLkjCouK020meUwSEDzTGB7JWeg+y6ULdlRtA7nhNjSg2W9PiYhqmLVbTdskY3d5tCONpNKY/4d1HrZ1CQi01xOLyTcqTWZTkC0oC54SUtQliHtBDanXZKDQVrsNBHo5zutJxVSzAosc9UTdVsLgwN0ry2smFma/4cmrJbmP1kWu8wtFJAuE2OGrf4SF7tpkV6FRl3HWtxScSZzaWOm0UFJw3PQON38RL5XTeaCON0YEW767AJDGSucXpsHDO8ioBcrA3bFcLBQOVplJS5OVBdKItPU9WpEi0ys1sDF7QsXWus25SbCbGWLbvhJQd9ae4e8lU49wEnUEk/HzHtb9x7Shgia0bhgXz5QqpgubEcpVvnDs9H4E9ta4Vv49/j2H6Rb8M/o9hoC/Rt0C/6fdEv5JafKZSbcKO0hVw8ONcYaPNPKGSgBg/cmawHYyWTihl+BoOMm8H+vYPhw9HB6MHW6Jvh4NGjrfH+3njvu3tfDyZAE1B9A+fzpiK8XDQHcp1k83r/y/vzejvYDL8INreDuY8XhfDiteBV4fF2Pwz64bfB+t2v3JWh5930PvFueaF327vrPfTG3qHvBfe96P3k+9H3o/937p/dq6Xr3iMB95L43e738CS4DjYQ=</latexit>Game INTERD
Ch
b $ {0, 1} sI rI sR rR 0 (σI, σR) $ Ch.Init (zI, zR) $ (Ch.SendRS)2 (ηI, ηR) $ (Ch.RecvRS)2 b0 $ DSend,Recv,Exp Return (b0 = b) Send(u, m0, m1, ad) If nextop 6= (u, “send”) and nextop 6= ? then return ? If |m0| 6= |m1| then return ? (σu, c) Ch.Send(σu, ad, mb; zu) nextop ? su su + 1 ; zu $ Ch.SendRS ctableu[su] (c, ad) Return c Recv(u, c, ad) If nextop 6= (u, “recv”) and nextop 6= ? then return ? (σu, m) Ch.Recv(σu, ad, c; ηu) nextop ? ; ηu $ Ch.RecvRS If m 6= ? then ru ru + 1 If b = 0 and (c, ad) 6= ctableu[ru] then Return m Return ? Exp(u, rand) If nextop 6= ? then return ? (z, η) (ε, ε) If rand = “send” then nextop (u, “send”) ; z zu Else if rand = “recv” then nextop (u, “recv”) ; η ηu Return (σu, z, η)
<latexit 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security Step 2: generic attacks
We specified eight attacks that would break security of any channel.
For Example
Expose state of one user and create forgery to other Expose state of one user and decrypt ciphertext from other Expose sending randomness of user to know which message is encrypted Expose state of user and decrypt ciphertext from same Expose state of user and create forgery to same
NOT generic attacks (i.e. attacks we require security against)
12
Adversary DSend,Recv,Exp
1
(σ, z, η) ← Exp(I, ε) n ← maxc2[Ch.Send(σ,ε,1)] |c| m ←$ {0, 1}n+2 c ← Send(I, m, 1, ε) If |c| ≤ n then return 1 Return 0 Adversary DSend,Recv,Exp
2
c ← Send(I, 1, 1, ε) m ← Recv(R, c, ε) If m = ⊥ then return 1 Return 0 Adversary DSend,Recv,Exp
3
(σ, z, η) ← Exp(I, ε) (σ, c) ←$ Ch.Send(σ, ε, 1) m ← Recv(R, c, ε) If m = ⊥ then return 1 Return 0 Adversary DSend,Recv,Exp
3.1
(σ, z, η) ← Exp(I, ε) (σ, c) ←$ Ch.Send(σ, ε, 1) m ← Recv(R, c, ε) (σ, c) ←$ Ch.Send(σ, ε, 1) m ← Recv(R, c, ε) If m = ⊥ then return 1 Return 0 Adversary DSend,Recv,Exp
3.2
(σ, z, η) ← Exp(I, ε) (σ, c) ←$ Ch.Send(σ, ε, 1) m ← Recv(R, c, ε) c ← Send(R, 0, 1, ε) (σ, m) ←$ Ch.Recv(σ, ε, c) If m = 1 then return 1 Return 0 Adversary DSend,Recv,Exp
4
c ← Send(I, 0, 1, ε) (σ, z, η) ← Exp(R, ε) (σ, m) ←$ Ch.Recv(σ, ε, c) If m = 1 then return 1 Return 0 Adversary DSend,Recv,Exp
5
(σ, z, η) ← Exp(R, ε) c ← Send(I, 0, 1, ε) (σ, m) ←$ Ch.Recv(σ, ε, c) If m = 1 then return 1 Return 0 Adversary DSend,Recv,Exp
6
(σ, z, η) ← Exp(I, “send”) (σ, c) ← Ch.Send(σ, ε, 1; z) c0 ← Send(I, 0, 1, ε) If c0 = c then return 1 Return 0
<latexit 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security Step 3: augment interface
Added minimal restrictions to disallow generic attacks
Our security definition AEAC: (Authenticated encryption against compromise) Some implications
Users can’t forge to self Users can’t read own ciphertexts After decrypting a ciphertext lose ability to decrypt it After sending ciphertext lose ability to authenticate it
We achieve with new forms of
PKE DS
After decrypting a forged ciphertext unable to encrypt to / decrypt from valid partner.
13
Key-Updatable Digital Signature Schemes From a forward-secure DS scheme. Augment DS scheme with algorithms to update keys with respect to arbitrary strings.
14
Syntax Security Construction
New Public Key Primitives
Variant of (one-time) strong unforgeability.
Sign(m)
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to a sequence of updates disallowed if exposed key for ~
∆2 v ~ ∆1
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∆1
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update key, sign update string then evolve to future key.
σ
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sha1_base64="Kn9HOxAjmlhcNkcHjDp2APdeQB0=">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</latexit>Algorithm DSKU.UpdSk(sk, ∆) (skKE, i, Σ) sk Σ[i] $ DSKE.Sign(skKE, 0 k ∆) skKE $ DSKE.Up(skKE) sk (skKE, i + 1, Σ) Return sk
<latexit 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Immediate from a hierarchical identity-based encryption scheme. (Update strings correspond to HIBE identities.) Augment PKE scheme with algorithms to update keys with respect to arbitrary strings.
New Public Key Primitives
Key-Updatable Public Key Encryption
Enc(m0, m1, `)
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Security Construction Variant of CCA-security with labels
UpdDk()
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sha1_base64="xPlUKJZB6sHxrOKZRC7fS0vu0aE=">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</latexit>Challenge query to sequence of updates disallowed if exposed key for ~
∆2 v ~ ∆1
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∆1
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sha1_base64="NbQJvP7ocaMkdow8r3o1y9BDs3k=">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</latexit>Algorithm SCh.Send(, ad, m) (s, r, rack, sk, vk, ek, dk, hk, ⌧r,~ ⌧s) ← ; s ← s + 1 (sk0, vk0) ←$ DS.Kg ; (ek0, dk[s]) ←$ PKE.Kg ` ← (s, r, ad, vk0, ek0, ⌧r,~ ⌧s[s − 1]) (ek0, c0) ←$ PKE.Enc(ek, `, m,~ ⌧s[rack + 1, . . . , s − 1]) v ← (c0, `) ; ←$ DS.Sign(sk, v) c ← (, v) ; ~ ⌧s[s] ← H.Ev(hk, c) ← (s, r, rack, sk0, vk, ek, dk, hk, ⌧r,~ ⌧s) Return (, c)
<latexit 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Construction
Sent/Received Counters Signing/Encryption Keys Verification/Decryption Keys Sent/Received “Transcripts” Hash Function Key State stored by each party
16
Privacy from PKE. Integrity from DS Counter prevents reordering New keys with every message (Forward/Backward security) Key-updates (Forward security)
- ek/vk updated with sent transcripts
- dk/sk update with received transcripts
Channel KUPKE scheme Hash function KUDS scheme
PKE
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PKE, H]
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has 9 attacks against variants
sk/ek
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of our Bidirectional Channel
Theorem: Suppose
- is collision-resistant.
- is a UFEXP-secure and UNIQ-secure KUDS scheme.
- is an INDEXP-secure KUPKE scheme.
Then our channel, is AEAC-secure. Concretely:
D
Given adversary (making q queries) we build adversaries such that
Advaeac
SCh,D ≤ 2(q2−µ + Advcr H,AH + Advufexp DS,ADS + Advuniq DS,BDS) + Advindexp PKE,APKE
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sha1_base64="/VnOzeOWoxnlxHRxlNtPFcJWtpg=">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</latexit><latexit 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ADS, BDS, APKE
<latexit 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sha1_base64="z6aSzhFjV4+X5qB2upb9Vk5x1h8=">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</latexit><latexit sha1_base64="z6aSzhFjV4+X5qB2upb9Vk5x1h8=">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</latexit>Where
H
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= SCH[DS, PKE, H]
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sha1_base64="mEPEq9wv654sbyq6oI5wodHFv0I=">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</latexit>µ = H∞(DS.Kg) + H∞(PKE.Kg) + H∞(PKE.Enc)
<latexit 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sha1_base64="IRKCrprJTXtMznUFNo4QxXjtn1k=">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</latexit>Step 1: Integrity. Proof Step 2: Privacy. Substep 1.1: Cannot predict future ciphertext. (Min-entropy) Substep 1.2: Cannot cause transcript collision. (HF security) Substep 1.3: Cannot forge signatures. (DS security) Substep 2.1: Cannot send ciphertext with new signature. (DS uniqueness) Substep 2.2: Encryption is secure. (PKE security)
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Subtle proof step missed by some related papers Tight reduction to multi-user security of underlying primitives.
Thanks! Any questions?
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