Multi-Instance Security and its Application to Password- Based Cryptography
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1 Multi-Instance Security and its Application to Password- Based Cryptography Stefano Tessaro MIT Joint work with Mihir Bellare (UC San Diego) Thomas Ristenpart (Univ. of Wisconsin)
2 Scenario: File encryption Want to store data in encrypted form using symmetric encryption.
3 Scenario: File encryption Want to store data in encrypted form using symmetric encryption. Keys need to be securely stored for later decryption
4 Scenario: File encryption Want to store data in encrypted form using symmetric encryption. Keys need to be securely stored for later decryption Alternative solution: Password-based cryptography.
5 Password-based encryption
6 Password-based encryption Used widely: Winzip, OpenOffice, Mac OS X FileVault,TrueCrypt, WiFi WPA (PBKDF),
7 Password-based encryption Used widely: Winzip, OpenOffice, Mac OS X FileVault,TrueCrypt, WiFi WPA (PBKDF), K = Key-derivation function KDF q1w2e3
8 Password-based encryption Used widely: Winzip, OpenOffice, Mac OS X FileVault,TrueCrypt, WiFi WPA (PBKDF), K = Key-derivation function KDF q1w2e3 PB-Encrypt(pw, M) K KDF(pw) C ENC(K, M) Return C
9 Password-based encryption Used widely: Winzip, OpenOffice, Mac OS X FileVault,TrueCrypt, WiFi WPA (PBKDF), ENC(K, M) K = Key-derivation function KDF q1w2e3 PB-Encrypt(pw, M) K KDF(pw) C ENC(K, M) Return C
10 Problem: Weak passwords are unavoidable
11 Problem: Weak passwords are unavoidable
12 Problem: Weak passwords are unavoidable
13 Mitigating dictionary attacks via iteration KDF = H c
14 Mitigating dictionary attacks via iteration KDF = H c pw H H H K c times
15 Mitigating dictionary attacks via iteration KDF = H c pw H H H K c times H {0,1} {0,1} n is cryptographic hash function (e.g., SHA-256)
16 Mitigating dictionary attacks via iteration KDF = H c pw H H H K c times H {0,1} {0,1} n is cryptographic hash function (e.g., SHA-256) PB-Encrypt(pw, M) K H c (pw) C ENC(K, M) Return C
17 Mitigating dictionary attacks via iteration KDF = H c pw H H H K c times H {0,1} {0,1} n is cryptographic hash function (e.g., SHA-256) PB-Encrypt(pw, M) K H c (pw) C ENC(K, M) Return C Expectation: Work N to guess pw Work c N to break PB-Encrypt
18 Mitigating dictionary attacks via iteration KDF = H c pw H H H K c times H {0,1} {0,1} n is cryptographic hash function (e.g., SHA-256) PB-Encrypt(pw, M) K H c (pw) C ENC(K, M) Return C Expectation: Work N to guess pw Work c N to break PB-Encrypt N = 2 32
19 Mitigating dictionary attacks via iteration KDF = H c pw H H H K c times H {0,1} {0,1} n is cryptographic hash function (e.g., SHA-256) PB-Encrypt(pw, M) K H c (pw) C ENC(K, M) Return C Expectation: Work N to guess pw Work c N to break PB-Encrypt N = 2 32 N c = = 2 52
20 Mitigating dictionary attacks via iteration KDF = H c pw H H H K c times H {0,1} {0,1} n is cryptographic hash function (e.g., SHA-256) PB-Encrypt(pw, M) K H c (pw) C ENC(K, M) Return C Expectation: Work N to guess pw Work c N to break PB-Encrypt N = 2 32 N c = = 2 52
21 Mitigating dictionary attacks via iteration KDF = H c pw H H H K c times H {0,1} {0,1} n is cryptographic hash function (e.g., SHA-256) PB-Encrypt(pw, M) K H c (pw) C ENC(K, M) Return C Expectation: Work N to guess pw Work c N to break PB-Encrypt N = 2 32 N c = = 2 52
22 PB-Encryption in the multi-user setting Real world has multiple users:
23 PB-Encryption in the multi-user setting Real world has multiple users: C 1 PB Encrypt(pw 1, M 1 ) C 2 PB Encrypt(pw 2, M 2 ) C 3 PB Encrypt(pw 3, M 3 )
24 PB-Encryption in the multi-user setting Real world has multiple users: C 1 PB Encrypt(pw 1, M 1 ) C 2 PB Encrypt(pw 2, M 2 ) C 3 PB Encrypt(pw 3, M 3 )
25 PB-Encryption in the multi-user setting Real world has multiple users: C 1 PB Encrypt(pw 1, M 1 ) C 2 PB Encrypt(pw 2, M 2 ) C 3 PB Encrypt(pw 3, M 3 )
26 PB-Encryption in the multi-user setting Real world has multiple users: C 1 PB Encrypt(pw 1, M 1 ) C 2 PB Encrypt(pw 2, M 2 ) M 1 Work c N to retrieve M 1 C 3 PB Encrypt(pw 3, M 3 )
27 PB-Encryption in the multi-user setting Real world has multiple users: C 1 PB Encrypt(pw 1, M 1 ) C 2 PB Encrypt(pw 2, M 2 ) M 1 Work c N to retrieve M 1 C 3 PB Encrypt(pw 3, M 3 )
28 PB-Encryption in the multi-user setting Real world has multiple users: C 1 PB Encrypt(pw 1, M 1 ) C 2 PB Encrypt(pw 2, M 2 ) Additional work to retrieve M 2? M 1 M 2 Work c N to retrieve M 1 C 3 PB Encrypt(pw 3, M 3 )
29 PB-Encryption in the multi-user setting Real world has multiple users: C 1 PB Encrypt(pw 1, M 1 ) C 2 PB Encrypt(pw 2, M 2 ) Additional work to retrieve M 2? M 1 M 2 Work c N to retrieve M 1 C 3 PB Encrypt(pw 3, M 3 ) Ideally: Work m c N to retrieve m plaintexts!
30 Multi-instance security amplification Not true in general:
31 Multi-instance security amplification Not true in general:
32 Multi-instance security amplification Not true in general: c times pw 1 H H H K 1
33 Multi-instance security amplification Not true in general: c times pw 1 H H H K 1 pw N H H H K N
34 Multi-instance security amplification Not true in general: c times pw 1 H H H K 1 pw N H H H K N Work N c + Work N / ciphertext = N c + m vs N c m
35 Multi-instance security amplification Not true in general: New design goal: Multi-instance c times security amplification Hardness of breaking multiple instances must increase linearly in the number of instances. pw 1 H H H K 1 pw N H H H K N Work N c + Work N / ciphertext = N c + m vs N c m
36 PKCS#5 Password-based cryptography standard Salting as suggested in PKCS#5 prevents attack
37 PKCS#5 Password-based cryptography standard Salting as suggested in PKCS#5 prevents attack KDF1: pw salt H H H K
38 PKCS#5 Password-based cryptography standard Salting as suggested in PKCS#5 prevents attack KDF1: pw salt H H H K Randomly chosen per KDF evaluation
39 PKCS#5 Password-based cryptography standard Salting as suggested in PKCS#5 prevents attack KDF1: pw salt H H H K PB-Encrypt(pw, M) salt {0,1} s K H c (pw salt) C ENC(K, M) Return C salt Randomly chosen per KDF evaluation
40 PKCS#5 Password-based cryptography standard Salting as suggested in PKCS#5 prevents attack KDF1: pw salt H H H K PB-Encrypt(pw, M) salt {0,1} s K H c (pw salt) C ENC(K, M) Return C salt Randomly chosen per KDF evaluation
41 PKCS#5 Password-based cryptography standard Salting as suggested in PKCS#5 prevents attack KDF1: pw salt H H H K PB-Encrypt(pw, M) salt {0,1} s K H c (pw salt) C ENC(K, M) Return C salt Randomly chosen per KDF evaluation
42 PKCS#5 Password-based cryptography standard Salting as suggested in PKCS#5 prevents attack KDF1: pw salt H H H K PB-Encrypt(pw, M) salt {0,1} s K H c (pw salt) C ENC(K, M) Return C salt Randomly chosen per KDF evaluation Allows decryption
43 PKCS#5 Password-based cryptography standard Salting as suggested in PKCS#5 prevents attack KDF1: pw salt H H H K PB-Encrypt(pw, M) salt {0,1} s K H c (pw salt) C ENC(K, M) Return C salt Randomly chosen per KDF evaluation Allows decryption Question: Does salting provably ensure multiinstance security amplification?
44 Iteration and salting in the real world No salting! No iteration!
45 Our results
46 Our results Question: Does salting provably ensure multi-instance security amplification?
47 Our results Question: Does salting provably ensure multi-instance security amplification? Answer: We do not really know!
48 Our results Question: Does salting provably ensure multi-instance security amplification? Answer: We do not really know! 1) No formal proof!
49 Our results Question: Does salting provably ensure multi-instance security amplification? Answer: We do not really know! 1) No formal proof! 2) No formal model!
50 Our results Question: Does salting provably ensure multi-instance security amplification? Answer: We do not really know! 1) No formal proof! 2) No formal model! Our contributions: 1) General definitional framework for multi-instance security of arbitrary cryptographic primitives. 2) Case study: Security analysis of PKCS#5 within our framework.
51 Outline 1. Multi-instance security 2. Security of PKCS#5 A case study
52 Outline 1. Multi-instance security 2. Security of PKCS#5 A case study
53 Single-instance security PB-Encryption LOR-Security b 0,1 pw PWD
54 Single-instance security PB-Encryption LOR-Security m 0, m 1 m 0 = m 1 b 0,1 pw PWD ENC(pw, m b )
55 Single-instance security PB-Encryption LOR-Security m 0, m 1 m 0 = m 1 b 0,1 pw PWD ENC(pw, m b ) b
56 Single-instance security PB-Encryption LOR-Security m 0, m 1 m 0 = m 1 b 0,1 pw PWD ENC(pw, m b ) b Adv lor A = 2 [Pr b = b 1 2]
57 Single-instance security PB-Encryption LOR-Security m 0, m 1 m 0 = m 1 b 0,1 pw PWD ENC(pw, m b ) b Adv lor A = 2 [Pr b = b 1 2]
58 Single-instance security PB-Encryption LOR-Security m 0, m 1 m 0 = m 1 b 0,1 pw PWD ENC(pw, m b ) b Adv lor A = 2 [Pr b = b 1 2] PWR-Security pw PWD
59 Single-instance security PB-Encryption LOR-Security m 0, m 1 m 0 = m 1 b 0,1 pw PWD ENC(pw, m b ) b Adv lor A = 2 [Pr b = b 1 2] m PWR-Security pw PWD ENC(pw, m)
60 Single-instance security PB-Encryption LOR-Security m 0, m 1 m 0 = m 1 b 0,1 pw PWD ENC(pw, m b ) b Adv lor A = 2 [Pr b = b 1 2] m PWR-Security pw PWD pw ENC(pw, m)
61 Single-instance security PB-Encryption LOR-Security m 0, m 1 m 0 = m 1 b 0,1 pw PWD ENC(pw, m b ) b Adv lor A = 2 [Pr b = b 1 2] m PWR-Security pw PWD pw ENC(pw, m) Adv pwr A = Pr[pw = pw]
62 The multi-instance (mi) security vista Our goal: Define security metric for scheme S wrt property P to measure success of an adversary that: instances of the scheme concurrently. Corrupts up to t < m instances of the scheme (e.g., learns passwords). Wins if it breaks P for all uncorrupted instances.
63 The multi-instance (mi) security vista Our goal: Define security metric for scheme S wrt property P to measure success of an adversary that: Attacks m instances of the scheme concurrently. Corrupts up to t < m instances of the scheme (e.g., learns passwords). Wins if it breaks P for all uncorrupted instances.
64 The multi-instance (mi) security vista < mm instances of the scheme (e.g., learns passwords). Our goal: Define security metric for scheme S wrt property P to measure success of an adversary that: Attacks m instances of the scheme concurrently. Corrupts up to t < m instances of the scheme (e.g., learns passwords). Wins if it breaks P for all uncorrupted instances.
65 The multi-instance (mi) security vista < mm instances of the scheme (e.g., learns passwords). Our goal: Define security metric for scheme S wrt property P to measure success of an adversary that: Attacks m instances of the scheme concurrently. Wins if it breaks P for all uncorrupted instances. Wins if it breaks P for all uncorrupted instances.
66 PWR security
67 PWR security pw 1 PWD pw 2 PWD pw 3 PWD
68 PWR security pw 1 PWD pw 2 PWD pw 3 PWD
69 PWR security pw 1 PWD pw 2 PWD pw 3 PWD
70 PWR security pw 1 PWD pw 2 PWD pw 3 PWD
71 PWR security (pw 1, pw 2, pw 3 ) pw 1 PWD pw 2 PWD pw 3 PWD
72 PWR security (pw 1, pw 2, pw 3 ) pw 1 PWD pw 2 PWD pw 3 PWD Adv m pwr A = Pr[pw 1 = pw 1,, pw m = pw m ]
73 LOR security b 1 0,1 pw 1 PWD b 3 0,1 pw 3 PWD b 2 0,1 pw 2 PWD
74 LOR security b 1 0,1 pw 1 PWD b 3 0,1 pw 3 PWD b 2 0,1 pw 2 PWD
75 LOR security b 1 0,1 pw 1 PWD b 3 0,1 pw 3 PWD b 2 0,1 pw 2 PWD
76 LOR security b 1 0,1 pw 1 PWD b 3 0,1 pw 3 PWD Adv m lor A =? b 2 0,1 pw 2 PWD
77 Defining mi security for encryption Attempt #1: AND-advantage
78 Defining mi security for encryption Attempt #1: AND-advantage LORA-security: Output: b 1,, b m Advantage: Adv m lora A = Pr[ b 1,, b m = b 1,, b m ]
79 Defining mi security for encryption Attempt #1: AND-advantage LORA-security: Output: b 1,, b m Advantage: Adv m lora A = Pr[ b 1,, b m = b 1,, b m ] Problem: Does not measure hardness of winning all uncorrupted instances.
80 Defining mi security for encryption Attempt #1: AND-advantage LORA-security: Output: b 1,, b m Advantage: Adv m lora A = Pr[ b 1,, b m = b 1,, b m ] Problem: Does not measure hardness of winning all uncorrupted instances. Reason: If adversary with Pr[b 1 = b 1 ] > 3/4 Then adversary guessing second bit at random, with Pr b 1, b 2 = b 1, b 2 > = 3/8
81 Defining mi security for encryption Attempt #1: AND-advantage LORA-security: Output: b 1,, b m Advantage: Adv m lora A = Pr[ b 1,, b m = b 1,, b m ] Problem: Does not measure hardness of winning all uncorrupted instances. Reason: If adversary with Pr[b 1 = b 1 ] > 3/4 Then adversary guessing second bit at random, with Pr b 1, b 2 = b 1, b 2 > = 3/8
82 Defining mi security for encryption Attempt #2: XOR-advantage
83 Defining mi security for encryption Attempt #2: XOR-advantage LORX-security: Output: b Advantage: Adv m lorx A = 2 Pr b = b 1 b m 1/2
84 Defining mi security for encryption Attempt #2: XOR-advantage LORX-security: Output: b Advantage: Adv m lorx A = 2 Pr b = b 1 b m 1/2 Reason: If adversary with Pr b = b 1 > 1 + ε 2 Then: Adversary guessing second bit has no advantage Pr b = b 1 b 2 = 1 2
85 Mi security notions Relations m-lorx m-lora m-pwr
86 Mi security notions Relations m-lorx (1) m-lora m-pwr
87 Mi security notions Relations m-lorx (1) m-lora m-pwr
88 Mi security notions Relations m-lorx (1) m-lora m-pwr 1) Holds in most cases proof relies on probabilistic lemma from [U09].
89 Mi security notions Relations m-lorx (1) m-lora (2) m-pwr 1) Holds in most cases proof relies on probabilistic lemma from [U09].
90 Mi security notions Relations m-lorx (1) m-lora (2) m-pwr 1) Holds in most cases proof relies on probabilistic lemma from [U09]. 2) Very loose asymptotic implication based on Goldreich- Levin Theorem [GL89]
91 Relations LOR vs ROR m 0, m 1 b 0,1 pw PWD LOR-Security ENC(pw, m b ) b m 0 b 0,1 m 1 M pw PWD ROR-Security ENC(pw, m b ) b
92 Relations LOR vs ROR
93 Relations LOR vs ROR Classical textbook theorem. Adv ror t Adv lor t 2 Adv ror t
94 Relations LOR vs ROR Hybrid argument Classical textbook theorem. Adv ror t Adv lor t 2 Adv ror t
95 Relations LOR vs ROR Hybrid argument Classical textbook theorem. Adv ror t Adv lor t 2 Adv ror t L R L $ + $ R
96 Relations LOR vs ROR Hybrid argument Classical textbook theorem. Adv ror t Adv lor t 2 Adv ror t L R L $ + $ R Mi setting with m instances: Adv m rorx t Adv m lorx t 2 m Adv m rorx t
97 Relations LOR vs ROR Hybrid argument Classical textbook theorem. Adv ror t Adv lor t 2 Adv ror t L R L $ + $ R Mi setting with m instances: Adv m rorx t Adv m lorx t 2 m Adv m rorx t L R L $ $ R + L R L $ L $ + $ R $ R + L $ $ R
98 Relations LOR vs ROR Hybrid argument Classical textbook theorem. Adv ror t Adv lor t 2 Adv ror t L R L $ + $ R Tight! Mi setting with m instances: Adv m rorx t Adv m lorx t 2 m Adv m rorx t L R L $ $ R + L R L $ L $ + $ R $ R + L $ $ R
99 Outline 1. Multi-instance security 2. Security of PKCS#5 A case study
100 Outline 1. Multi-instance security 2. Security of PKCS#5 A case study
101 PKCS#5 Defining KDF Security
102 PKCS#5 Defining KDF Security Question: Does salting provably ensures multiinstance security amplification? YES!
103 PKCS#5 Defining KDF Security Question: Does salting provably ensures multiinstance security amplification? YES! pw salt H H H K
104 PKCS#5 Defining KDF Security Question: Does salting provably ensures multiinstance security amplification? YES! pw salt H H H K Main step: Security analysis of KDF1 for case H = RO.
105 KDF Security in the ROM KDF satisfies indifferentiability-like poperty [MRH04] Sim password distributions: Left Right pw 1 sa 1,, pw m sa m pw 1 sa 1,, pw m sa m KDF1 RO Test Sim K 1,, K m K 1,, K m 0/1 0/1
106 KDF Security in the ROM KDF satisfies indifferentiability-like poperty [MRH04] Sim password distributions: Left Right pw 1 sa 1,, pw m sa m pw 1 sa 1,, pw m sa m KDF1 RO Test Sim K 1,, K m q queries K 1,, K m q queries 0/1 0/1
107 KDF Security in the ROM KDF satisfies indifferentiability-like poperty [MRH04] Sim password distributions: Left Right pw 1 sa 1,, pw m sa m pw 1 sa 1,, pw m sa m KDF1 RO Test Sim K 1,, K m q queries K 1,, K m q queries 0/1 0/1
108 Final result: Security of PB-Encrypt Question: Does salting deliver multi-instance security amplification for PKCS#5? PB-Encrypt(pw, M) salt {0,1} s K H c (pw salt) C ENC(K, M) Return C salt Theorem: A making q RO queries, B such that m rorx q Adv PB Encrypt A < mcn + m Adv ror ENC B + q 2 2 n + q 2 2 s
109 Final result: Security of PB-Encrypt Question: Does salting deliver multi-instance security amplification for PKCS#5? PB-Encrypt(pw, M) salt {0,1} s K H c (pw salt) C ENC(K, M) Return C salt Theorem: A making q RO queries, B such that m rorx q Adv PB Encrypt A < mcn + m Adv ror ENC B + q 2 2 n + q 2 2 s Work m c N to break encryption (RO queries)
110 Concluding Remarks Summary:
111 Concluding Remarks Summary: The world has multiple users
112 Concluding Remarks Summary: The world has multiple users Weak individual instances sometimes unavoidable
113 Concluding Remarks Summary: The world has multiple users Weak individual instances sometimes unavoidable Mi security as a second line of defense
114 Concluding Remarks Summary: The world has multiple users Weak individual instances sometimes unavoidable Mi security as a second line of defense Interesting technical questions
115 Concluding Remarks Summary: The world has multiple users Weak individual instances sometimes unavoidable Mi security as a second line of defense Interesting technical questions First security analysis of PKCS#5 in the mi setting
116 Concluding Remarks Summary: The world has multiple users Weak individual instances sometimes unavoidable Mi security as a second line of defense Interesting technical questions First security analysis of PKCS#5 in the mi setting Thank you!
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