An Oblivious Password Cracking Server
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1 An Oblivious Password Cracking Server Aureliano Calvo - [email protected] Ariel Futoransky - [email protected] Carlos Sarraute - [email protected] Corelabs Core Security Technologies An Oblivious Password Cracking Server / 26
2 Agenda 1 Intro And Motivation 2 Standing On The Shoulders of Giants Hash-Reversing Tables Private Information Retrieval 3 Our Work 4 Future Work An Oblivious Password Cracking Server / 26
3 Intro Reversing cryptographically-strong hashes is really resource intensive. What if a resource constrained hacker wants to crack a password? Hash reversing tables to the rescue! An Oblivious Password Cracking Server / 26
4 Intro Reversing cryptographically-strong hashes is really resource intensive. What if a resource constrained hacker wants to crack a password? Hash reversing tables to the rescue! An Oblivious Password Cracking Server / 26
5 Intro Reversing cryptographically-strong hashes is really resource intensive. What if a resource constrained hacker wants to crack a password? Hash reversing tables to the rescue! An Oblivious Password Cracking Server / 26
6 Space-Time trade-off Rainbow tables allow to use O(N 2/3 ) space and O(N 2/3 ) time to invert a hash where N is the size of the pre-image. For instance a rainbow table used to break LM takes 34GBytes. What if the password cracker cannot store the tables? An Oblivious Password Cracking Server / 26
7 Space-Time trade-off Rainbow tables allow to use O(N 2/3 ) space and O(N 2/3 ) time to invert a hash where N is the size of the pre-image. For instance a rainbow table used to break LM takes 34GBytes. What if the password cracker cannot store the tables? An Oblivious Password Cracking Server / 26
8 Space-Time trade-off Rainbow tables allow to use O(N 2/3 ) space and O(N 2/3 ) time to invert a hash where N is the size of the pre-image. For instance a rainbow table used to break LM takes 34GBytes. What if the password cracker cannot store the tables? An Oblivious Password Cracking Server / 26
9 Privacy implications A server serves the tables. But... Now the server can know the passwords being cracked :(. An Oblivious Password Cracking Server / 26
10 Privacy implications A server serves the tables. But... Now the server can know the passwords being cracked :(. An Oblivious Password Cracking Server / 26
11 Privacy implications A server serves the tables. But... Now the server can know the passwords being cracked :(. An Oblivious Password Cracking Server / 26
12 Agenda 1 Intro And Motivation 2 Standing On The Shoulders of Giants Hash-Reversing Tables Private Information Retrieval 3 Our Work 4 Future Work An Oblivious Password Cracking Server / 26
13 Agenda 1 Intro And Motivation 2 Standing On The Shoulders of Giants Hash-Reversing Tables Private Information Retrieval 3 Our Work 4 Future Work An Oblivious Password Cracking Server / 26
14 Hellman Tables Store initial password and ending hash for each chain (length M). Each table stores M chains. M tables. Each one uses its own reduction function. An Oblivious Password Cracking Server / 26
15 Hellman Tables Store initial password and ending hash for each chain (length M). Each table stores M chains. M tables. Each one uses its own reduction function. An Oblivious Password Cracking Server / 26
16 Hellman Tables Store initial password and ending hash for each chain (length M). Each table stores M chains. M tables. Each one uses its own reduction function. An Oblivious Password Cracking Server / 26
17 Hellman Tables with Distinguished End-Points Differences with Hellman Tables End-points have a property that distinguishes them Such as number of leading 0s The expected length of chains is M. Minimizes number of queries made to the tables (just M). An Oblivious Password Cracking Server / 26
18 Hellman Tables with Distinguished End-Points Differences with Hellman Tables End-points have a property that distinguishes them Such as number of leading 0s The expected length of chains is M. Minimizes number of queries made to the tables (just M). An Oblivious Password Cracking Server / 26
19 Hellman Tables with Distinguished End-Points Differences with Hellman Tables End-points have a property that distinguishes them Such as number of leading 0s The expected length of chains is M. Minimizes number of queries made to the tables (just M). An Oblivious Password Cracking Server / 26
20 Hellman Tables with Distinguished End-Points Differences with Hellman Tables End-points have a property that distinguishes them Such as number of leading 0s The expected length of chains is M. Minimizes number of queries made to the tables (just M). An Oblivious Password Cracking Server / 26
21 Rainbow Tables Just one table with M 2 entries. Collisions are avoided by using a different reduction function for each step. This is the most popular kind of hash reversing tables. An Oblivious Password Cracking Server / 26
22 Rainbow Tables Just one table with M 2 entries. Collisions are avoided by using a different reduction function for each step. This is the most popular kind of hash reversing tables. An Oblivious Password Cracking Server / 26
23 Rainbow Tables Just one table with M 2 entries. Collisions are avoided by using a different reduction function for each step. This is the most popular kind of hash reversing tables. An Oblivious Password Cracking Server / 26
24 Table sizes Number of chains = M 2 M chains for each of the M tables for Hellman Tables and Hellman Tables With Distinguished Endpoints. Chain length = M Average chain length for Hellman Tables With Distinguished Endpoints. M = 3 ln(1 α) N where: N is the size of the preimage α is the probability that a preimage can be found using the table. An Oblivious Password Cracking Server / 26
25 Table sizes Number of chains = M 2 M chains for each of the M tables for Hellman Tables and Hellman Tables With Distinguished Endpoints. Chain length = M Average chain length for Hellman Tables With Distinguished Endpoints. M = 3 ln(1 α) N where: N is the size of the preimage α is the probability that a preimage can be found using the table. An Oblivious Password Cracking Server / 26
26 Table sizes Number of chains = M 2 M chains for each of the M tables for Hellman Tables and Hellman Tables With Distinguished Endpoints. Chain length = M Average chain length for Hellman Tables With Distinguished Endpoints. M = 3 ln(1 α) N where: N is the size of the preimage α is the probability that a preimage can be found using the table. An Oblivious Password Cracking Server / 26
27 Table sizes Number of chains = M 2 M chains for each of the M tables for Hellman Tables and Hellman Tables With Distinguished Endpoints. Chain length = M Average chain length for Hellman Tables With Distinguished Endpoints. M = 3 ln(1 α) N where: N is the size of the preimage α is the probability that a preimage can be found using the table. An Oblivious Password Cracking Server / 26
28 Table sizes Number of chains = M 2 M chains for each of the M tables for Hellman Tables and Hellman Tables With Distinguished Endpoints. Chain length = M Average chain length for Hellman Tables With Distinguished Endpoints. M = 3 ln(1 α) N where: N is the size of the preimage α is the probability that a preimage can be found using the table. An Oblivious Password Cracking Server / 26
29 Table sizes Number of chains = M 2 M chains for each of the M tables for Hellman Tables and Hellman Tables With Distinguished Endpoints. Chain length = M Average chain length for Hellman Tables With Distinguished Endpoints. M = 3 ln(1 α) N where: N is the size of the preimage α is the probability that a preimage can be found using the table. An Oblivious Password Cracking Server / 26
30 Table sizes Number of chains = M 2 M chains for each of the M tables for Hellman Tables and Hellman Tables With Distinguished Endpoints. Chain length = M Average chain length for Hellman Tables With Distinguished Endpoints. M = 3 ln(1 α) N where: N is the size of the preimage α is the probability that a preimage can be found using the table. An Oblivious Password Cracking Server / 26
31 Agenda 1 Intro And Motivation 2 Standing On The Shoulders of Giants Hash-Reversing Tables Private Information Retrieval 3 Our Work 4 Future Work An Oblivious Password Cracking Server / 26
32 Problem to be solved Ask for a bit in a database stored by a server without revealing the requested bit to the server. Without sending the entire database (!). An Oblivious Password Cracking Server / 26
33 Problem to be solved Ask for a bit in a database stored by a server without revealing the requested bit to the server. Without sending the entire database (!). An Oblivious Password Cracking Server / 26
34 Problem to be solved "Something being imposible does not imply that it has never been done" (Fernando Russ) An Oblivious Password Cracking Server / 26
35 Classic PIR Eyal Kushilevitz and Rafail Ostrovsky Replication is not needed: Single database, computationally-private information retrieval. Proceedings of the 38th Annu. IEEE Symp. on Foudations of Computer Science, pages: , An Oblivious Password Cracking Server / 26
36 Classic PIR - Complexities Server processing complexity: O(n). Client processing complexity: O( n). Transfer complexity: O( n). Where n is the number of bits in the database. An Oblivious Password Cracking Server / 26
37 Classic PIR - Complexities Server processing complexity: O(n). Client processing complexity: O( n). Transfer complexity: O( n). Where n is the number of bits in the database. An Oblivious Password Cracking Server / 26
38 Classic PIR - Complexities Server processing complexity: O(n). Client processing complexity: O( n). Transfer complexity: O( n). Where n is the number of bits in the database. An Oblivious Password Cracking Server / 26
39 Classic PIR - Complexities Server processing complexity: O(n). Client processing complexity: O( n). Transfer complexity: O( n). Where n is the number of bits in the database. An Oblivious Password Cracking Server / 26
40 Agenda 1 Intro And Motivation 2 Standing On The Shoulders of Giants Hash-Reversing Tables Private Information Retrieval 3 Our Work 4 Future Work An Oblivious Password Cracking Server / 26
41 Our Work Hellman Tables With Distinguished Endpoints as Hash-Reversing Tables queried using Classic PIR. An Oblivious Password Cracking Server / 26
42 Calculating the tables (begin, end) pairs are stored in a closed hash table. The size of each table is βm, where β > 1. Each entry has an index, representing the initial plain-text, and the end-of-chain hash. The key of the entry is the end-of-chain hash. Hash-Table Collisions are discarded when the tables are generated. An Oblivious Password Cracking Server / 26
43 Calculating the tables (begin, end) pairs are stored in a closed hash table. The size of each table is βm, where β > 1. Each entry has an index, representing the initial plain-text, and the end-of-chain hash. The key of the entry is the end-of-chain hash. Hash-Table Collisions are discarded when the tables are generated. An Oblivious Password Cracking Server / 26
44 Calculating the tables (begin, end) pairs are stored in a closed hash table. The size of each table is βm, where β > 1. Each entry has an index, representing the initial plain-text, and the end-of-chain hash. The key of the entry is the end-of-chain hash. Hash-Table Collisions are discarded when the tables are generated. An Oblivious Password Cracking Server / 26
45 Calculating the tables (begin, end) pairs are stored in a closed hash table. The size of each table is βm, where β > 1. Each entry has an index, representing the initial plain-text, and the end-of-chain hash. The key of the entry is the end-of-chain hash. Hash-Table Collisions are discarded when the tables are generated. An Oblivious Password Cracking Server / 26
46 Calculating the tables (begin, end) pairs are stored in a closed hash table. The size of each table is βm, where β > 1. Each entry has an index, representing the initial plain-text, and the end-of-chain hash. The key of the entry is the end-of-chain hash. Hash-Table Collisions are discarded when the tables are generated. An Oblivious Password Cracking Server / 26
47 Reversing a Hash The client calculates the M ends-of-chain for the hash being reversed. One for each table. It requests the corresponding server buckets, via M PIR requests. For each response, it checks if the end-of-chain is the one needed. If so, it navigates the chain looking for the preimage of the hash being reversed. An Oblivious Password Cracking Server / 26
48 Reversing a Hash The client calculates the M ends-of-chain for the hash being reversed. One for each table. It requests the corresponding server buckets, via M PIR requests. For each response, it checks if the end-of-chain is the one needed. If so, it navigates the chain looking for the preimage of the hash being reversed. An Oblivious Password Cracking Server / 26
49 Reversing a Hash The client calculates the M ends-of-chain for the hash being reversed. One for each table. It requests the corresponding server buckets, via M PIR requests. For each response, it checks if the end-of-chain is the one needed. If so, it navigates the chain looking for the preimage of the hash being reversed. An Oblivious Password Cracking Server / 26
50 Complexity Single hash-reversing client processing complexity: O(M 2 ). Single hash-reversing server processing complexity: O(M 2 ). Transfer complexity: O(M 3/2 ). Server storage complexity: O(M 2 ). Table calculation complexity: O(M 3 ). An Oblivious Password Cracking Server / 26
51 Complexity Single hash-reversing client processing complexity: O(M 2 ). Single hash-reversing server processing complexity: O(M 2 ). Transfer complexity: O(M 3/2 ). Server storage complexity: O(M 2 ). Table calculation complexity: O(M 3 ). An Oblivious Password Cracking Server / 26
52 Complexity Single hash-reversing client processing complexity: O(M 2 ). Single hash-reversing server processing complexity: O(M 2 ). Transfer complexity: O(M 3/2 ). Server storage complexity: O(M 2 ). Table calculation complexity: O(M 3 ). An Oblivious Password Cracking Server / 26
53 Complexity Single hash-reversing client processing complexity: O(M 2 ). Single hash-reversing server processing complexity: O(M 2 ). Transfer complexity: O(M 3/2 ). Server storage complexity: O(M 2 ). Table calculation complexity: O(M 3 ). An Oblivious Password Cracking Server / 26
54 Complexity Single hash-reversing client processing complexity: O(M 2 ). Single hash-reversing server processing complexity: O(M 2 ). Transfer complexity: O(M 3/2 ). Server storage complexity: O(M 2 ). Table calculation complexity: O(M 3 ). An Oblivious Password Cracking Server / 26
55 Experimental Results An Oblivious Password Cracking Server / 26
56 Agenda 1 Intro And Motivation 2 Standing On The Shoulders of Giants Hash-Reversing Tables Private Information Retrieval 3 Our Work 4 Future Work An Oblivious Password Cracking Server / 26
57 Future Work Optimize using other PIR schemes Paralelize cracking Devise a way to use the current rainbow tables with a PIR scheme Use PIR to reverse hashes in the client while the server brute forces it (no tables stored). An Oblivious Password Cracking Server / 26
58 Future Work Optimize using other PIR schemes Paralelize cracking Devise a way to use the current rainbow tables with a PIR scheme Use PIR to reverse hashes in the client while the server brute forces it (no tables stored). An Oblivious Password Cracking Server / 26
59 Future Work Optimize using other PIR schemes Paralelize cracking Devise a way to use the current rainbow tables with a PIR scheme Use PIR to reverse hashes in the client while the server brute forces it (no tables stored). An Oblivious Password Cracking Server / 26
60 Future Work Optimize using other PIR schemes Paralelize cracking Devise a way to use the current rainbow tables with a PIR scheme Use PIR to reverse hashes in the client while the server brute forces it (no tables stored). An Oblivious Password Cracking Server / 26
61 Any Question? An Oblivious Password Cracking Server / 26
62 Thank you! An Oblivious Password Cracking Server / 26
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