Workshop Challenges Startup code in PyCharm Projects
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1 INTRODUCTION TO CRYPTOGRAPHIC ATTACKS
2 EXERCISE LOGISTICS Workshop Challenges Startup code in PyCharm Projects
3 BLOCK CIPHERS Fixed sized input Random looking output for each message and key Block Cipher Modes
4 ECB MODE ENCRYPTION
5 ECB MODE DECRYPTION
6 PENGUINS AND ELECTRONIC CODE BOOK
7 CIPHER BLOCK CHAINING
8 CBC MODE ENCRYPTION
9 CBC MODE DECRYPTION
10 WARM-UP: KEY = IV IN CBC MODE Ciphertext blocks: Submit 00 to a decryption oracle Recover IV=key
11 EXAMPLE Key = IV = "YELLOW SUBMARINE" Message = "This is a sample message" Ciphertext = Decrypt: e9c0fce699eef e4f29db caca7f6be14b131d677c0159c8e8 e9c0fce699eef e4f29db e9c0fce699eef e4f29db71
12 RESPONSE FROM ORACLE Decryption: d706c b42189a8aebdb905f5fae271f33 0d2d253f6f3e e203f Compute XOR of: d706c65 0d2d253f6f3e e203f392220
13 NOTES ON BLOCK CIPHER CHALLENGES Using AES which has 16 byte block size In hex that equals 32 characters
14 PADDING ORACLE ATTACK
15 PKCS#7 PADDING Count how many bytes needed to finish block Append that many bytes to the last block Set the value of each of those bytes to the number added dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd 0c 0c 0c 0c 0c 0c 0c 0c 0c 0c 0c 0c
16 AFFECTING DECRYPTION
17 DESCRIPTION OF ATTACK Changing the second to last block produces predictable change to pad Guess byte at a time starting with the last byte If you guess is correct you have a valid pad
18 EXAMPLE GUESS FOR THE LAST BYTE guess_and_pad = xor_string(b'\x00'*15+guess,b'\x00'*15+b'\x01') modified_ciphertext = xor_string(ciphertext, guess_and_pad)
19 EXAMPLE Take the same plaintext and key IV: ciphertext: New pad: Guess: c0103a601101dec2acfb3d869bb96985 ef7b84991fa8fda6b8d429ffdf1091b9 22E2B24B E79E75B6966B
20 MODIFICATION OF PENULTIMATE BLOCK
21 DECRYPTION ORACLE Decryption: 787C41849A F6C1C4D96F3023C 206D D Return bad pad
22 CORRECT GUESS
23 DECRYPTION ORACLE Decryption: B7F19E2E7035EE6E2BBB0CDDEDCBE D Return good pad
24 FINDING PADDING ORACLES Find ciphertext that's multiple blocks long Change the first byte of the first block and observe response Compare to response from changing the last byte of the second to last block Possible signs of invalid/valid pads Timing differences Differences in error messages/status codes
25 REAL WORLD EXAMPLES POODLE CVE Apache mod_session_crypto CVE
26 (EC)DSA HOW DOES IT WORK?
27 FOR ALL PUBLIC KEY SLIDES Numbers will be written in base 16 Modulus of an equation may not always be explicit
28 KEY GENERATION Choose cryptographic hash function and bit lengths and Choose -bit prime where is less than the length of the hash function Choose -bit prime where divides Choose number whose order mod is Choose random with 0< < Compute Public key is Private key is
29 SIGNING Generate per message value where 0< < Calculate choose new. Calculate, start over. Signature is. If. If
30 VERIFICATION Reject if or are not satisfied Calculate Calculate Calculate Calculate Signature is invalid unless
31 KNOWN NONCE ATTACK
32 EXAMPLE KEY PARAMETERS
33 SIGNATURE
34 COMPUTING PRIVATE KEY
35 REPEATED NONCE ATTACK Suppose and with are valid signatures
36 EXAMPLE: NEW PUBLIC KEY Same as before
37 EXAMPLE: FIRST SIGNATURE
38 EXAMPLE: SECOND SIGNATURE
39 COMPUTING THE PRIVATE KEY
40 EXAMPLES FROM THE REAL WORLD Some Bitcoin Implementations SSH servers typically on embedded systems Sony's Playstation 3 ECDSA implementation
41 RSA
42 RSA KEY GENERATION Choose two distinct primes and at random and similar in magnitude, but differ in length by a few digits Compute Compute Choose an integer such that 1< < Find Public Key is, private key is
43 RSA ENCRYPTION AND DECRYPTION To encrypt message 0< <, compute To decrypt, compute
44 RSA SIGNATURES To sign message, Verify signature by verifying
45 HOMOMORPHIC PROPERTIES OF RSA
46 ADAPTIVE CHOSEN CIPHERTEXT ATTACK Consider an oracle that decrypts ciphertext it hasn't seen before Consider an unknown ciphertext and corresponding plaintext message Generate random and compute Get decryption
47 EXAMPLE RSA KEY
48 EXAMPLE CIPHERTEXT (ASCII encoding of "This is a test")
49 EXAMPLE RANDOM CIPHERTEXT
50 SUBMITTING TO THE ORACLE
51 RESPONSE FROM THE ORACLE
52 BLEICHENBACHER '06
53 RSA SIGNATURES IN PRACTICE Don't sign the message, but hash of message Hashes are small so pad hash before signing
54 PKCS1.5 PADDING FF FF... FF 00 ASN.1 HASH
55 IMPROPER VERICATION FF FF... FF 00 ASN.1 HASH GARBAGE
56 DESCRIPTION OF VULERNABILITY Improper parsing during verification Choosing small public exponent such as 3 Can exploit this in one of two ways Through clever choice of values and the fact that Take cube root of FF 00 ASN.1 HASH GARBAGE and round
57 EXAMPLE MODULUS 9016dafb596855c95c0d01e95d2ada94 e5f702b7d081fd708ea205e0811cf4a2 9e8ffa1e64ca1bc3cdf7d21512b654b9 f4bac42c52fb f11ec901b8b3 eb86ed0d96d4c8d1adbcf2fdc5a2bb6f 2254a406c62a627bf348d572dc284f02 ab3e0b5f9f00c217a1d97b15e3bf0399 b403b54f857f54d0dc57831cc717c427 dde4aeccaa9af05b4bffce39b4c63a8b 922dfd82320c2873facdf7c6e4ca092f a540c9db77c1d176f27b2d89a40f ba95bf18aac584c92b9ade6 2a80bfae78e6d79078d5f2bfefb89e c95770fcdb3c a1acb f9fecfbfe95e625a6ef9c87a97edb5ea 57b713736f57596ef3c79ecbe7f89a0b
58 FORGING A SIGNATURE Forge a signature for the message "This is a test message" Public exponent
59 EXAMPLE TAG 32c bf125c3cf15343cee 1389f8cf00f9ae3781a29e611d939748cf 6f7578fc47f53fa6a24e f37741f 78a7a418741a849eb eefe609eb bb9ccafa891e5d5aa38e68945d
60 VERIFICATION BY CUBING 0001ff d f a90c5b bf38bf26e39e57c6e bedbef9060b8d47e6b8eee48d37 d69793a7948e72d9b25c94c16231fab4 9d4158c01053ccb3651f4a98256b1bfb 79529a94398ac27e d5561a9cc e5dd7abf14661bb2b31c1c40109d53da 940b8faf96e0579a8a2ce3249b995f8e bebd25e6441ab3b1bb4a3605cf42ff6a c7db183fb6ada31188ad10319fcf584c 9077bbafe259524adc249ad278bf633c e566c80b23b2d805354a4beba308374d d5b59575a3d0cd076aaac19f339b488c cf6a afbf dfbdba dabe491e3a3e61d6c3b4bfc5218ce205
61 EXAMPLES FROM THE REAL WORLD CVE Bouncy Castle Java API CVE python-rsa (Bleichenbacher '06 variant)
62 BAD SIGNATURE WHEN USING SUNZI'S THEOREM
63 SUNZI'S THEOREM AND RSA Knowing private exponent as well as public expone and modulus equivalent to knowing and so and likewise Much more efficient than working mod
64 FAULT IN ONE COMPONENT Suppose is incorrect is correct, but is divisible by, but not
65 EXAMPLE: RSA PUBLIC KEY cdd806846f7a82de d44e45e ae6a99da3f25eb28cc1a44d5269bb2cc dc5cd89afe7df8c55b0ca d8d e462b8b3d e5efcd2 12a4e82ba75c9a8b49623ac675e10e12 68c0f54bd0ee154bf1843f7b23e56f7b 5ff33579a25e1f0c36a4b d795 47f99d411089f638e8cc7fa00c596d5b
66 BAD SIGNATURE Message: "This is a test message" Using SHA-256 Signature: 330a05472cd5c6188c78f85444efed2b 45d1b7930afc815a69c09948ea4d7991 9b6b610a680e19dce936ab56b937f b624cbd8c8a2e78f47b84fdb9cc1 15b6205d b7e3ce59b17fa9fd 8436b2946a089a01f96a372c0734b647 c874381f7a04e7a243c10633bdf51c7a 559e5d918b17dbe8d34e806715e1201f
67 VERIFICATION PRODUCES 56a526f2975e45d80a35b3f2e e5dfb5499bcfb403b662a4d87cc fc9c210158bf32a8ff228570bae7069e 6f6cbea49c8a716ef0d7d4ea0a68ae d58bdf8a62463a1c02a72caaa12 9f04758d8d60c5e1a9bf721eee492d8f d754e7e3d75b19cb0839a515db297e db00f47f49da3b712aab4ebe
68 SHOULD BE 0001ffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffff ffffffffffffffffffffffff d f a90c5b bf38bf2 6e39e57c6e bedbef906
69 DIFFERENCE 56a326f2975e45d80a35b3f2e e5dfb5499bcfb403b662a4d87cc fc9c210158bf32a8ff228570bae7069e 6f6cbea49c8a716ef0d7d4ea0a68ae d58bdf8a62463a1c02b729a78e2 91fe6c2d0718c47ca6bb701de949296f 6820afe3c63170bead236d834f35f273 d3cb2e086c6be37ef35836e53cec55b8
70 COMPUTE GCD gcd= = d988c222a820f802390e94e7580e7c9c 7a1b04239b6b73c6f321fdc7b0fc19bb 1c5bbfc05f2b74a5886d90db9b9a87d3 bf a9f94f42a61cf3208e3 = f23e12af65391aee2efabbb76d8d5ec8 d477772c1594be55d894debe1039b8a fc48d50fcc8e4aefd3c8c17c fb7af77c906972c7e5c12af322aecb29
71 WIENER'S ATTACK
72 PRELIMINARIES If we let then Let and with
73 OUTLINE OF THE ATTACK is made up of public values and approximates Use Continued Fractions algorithm to find When checking our guesses we will find when is sufficiently small See handout for algorithm details
74 DETECTING THE VULNERABILITY Very large public exponent indicates a likely small private exponent
75 BATCH GCD
76 ENTROPY REUSE During key generation one prime may be chosen that was chosen for another key Computing the GCD of such modulii will find the common prime and thus factor each Batch GCD efficiently computes GCD of each modulus and the product of the rest in a large list
77 THE ALGORITHM Compute product product tree Compute Compute of modulii using using remainder tree
78 REFERENCES private-keys.html doi= &rep=rep1&type=pdf
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