Padding oracle attacks exploit a vulnerability in the way block ciphers with certain modes of operation (like CBC) handle padding errors.
Let’s see this in action. Imagine we have an encrypted message, ciphertext. We want to decrypt it. The process involves decrypting the last block, then checking the padding. If the padding is invalid, the server tells us it’s invalid. This feedback is the oracle.
Here’s a simplified view of the decryption process and where the oracle comes in:
- Decrypt Ciphertext: The decryption algorithm takes the
ciphertextand producesplaintext_candidate. - Remove Padding: The last block of
plaintext_candidateis supposed to contain padding. The length of the padding is indicated by the last byte. For example, if the last byte is0x05, it means the last 5 bytes are padding. - Validate Padding: The system checks if the last
Nbytes are indeed all0x0N. - Oracle Feedback:
- If validation passes, the server reveals that the padding is correct.
- If validation fails, the server reveals that the padding is incorrect.
The attack works by manipulating the ciphertext and observing the oracle’s response. We don’t need to know the encryption key.
Consider an attacker who intercepts an encrypted message C. They want to decrypt it. They can’t decrypt C directly. Instead, they craft a new ciphertext, C', which is C with its last block modified. Specifically, they change C to C_prefix || C_modified_last_block.
The server decrypts C_modified_last_block using the decryption key and XORs the result with the previous ciphertext block (or an IV for the first block). Let’s call the result of this XOR operation P_candidate. The server then checks the padding of P_candidate.
The attacker’s goal is to make the padding valid for a specific byte. They can modify the last byte of C_modified_last_block repeatedly. Each modification changes P_candidate.
Let the original last byte of the plaintext be P_last. The padding value is N = P_last. The attacker wants to make P_last equal to some target value, say 0x01. To do this, they manipulate the last byte of C_modified_last_block until the resulting P_candidate has a last byte of 0x01.
How do they know when they’ve hit 0x01? The oracle tells them! If the server says "padding is correct" after they send a modified ciphertext, it means the last byte of P_candidate is 0x01.
Let’s break down the XOR: P_candidate = Decrypt(C_modified_last_block) XOR Previous_Block.
The attacker controls C_modified_last_block. Let D_modified = Decrypt(C_modified_last_block).
So, P_candidate = D_modified XOR Previous_Block.
If the attacker wants the last byte of P_candidate to be 0x01, they need (D_modified XOR Previous_Block)_last = 0x01.
The attacker doesn’t know D_modified or Previous_Block. But they can influence D_modified by changing C_modified_last_block.
The key insight is that if the attacker can make the last byte of P_candidate equal to 0x01, they can then deduce a byte of D_modified.
Let D_modified_last be the last byte of D_modified.
We know (D_modified_last XOR Previous_Block_last) = 0x01.
If they can guess Previous_Block_last, they can find D_modified_last. But they don’t need to guess Previous_Block_last.
Instead, they try different values for the last byte of C_modified_last_block. For each value, they send it and get the oracle’s feedback. When the oracle says "padding is correct", it means the last byte of P_candidate is 0x01.
Let the original last block of ciphertext be C_original_last. Let D_original = Decrypt(C_original_last).
The original plaintext last byte is P_original_last = (D_original XOR Previous_Block)_last.
The attacker crafts C_modified_last_block. Let D_modified = Decrypt(C_modified_last_block).
The resulting plaintext last byte is P_candidate_last = (D_modified XOR Previous_Block)_last.
The attacker wants P_candidate_last = 0x01.
They modify C_modified_last_block until P_candidate_last = 0x01.
When this happens, they have found a C_modified_last_block such that (Decrypt(C_modified_last_block) XOR Previous_Block)_last = 0x01.
Let X = Decrypt(C_modified_last_block).
So, (X XOR Previous_Block)_last = 0x01.
This means X_last XOR Previous_Block_last = 0x01.
Now, consider the original D_original.
P_original_last = (D_original XOR Previous_Block)_last.
We know D_original = Decrypt(C_original_last).
The attacker can compute D_original by XORing Previous_Block with the original P_original_last.
The attacker’s trick is to manipulate C_modified_last_block such that the resulting P_candidate_last is 0x01.
Let C_original be the original ciphertext.
Let C_prefix be all but the last block of C_original.
Let C_last be the last block of C_original.
Let IV be the Initialization Vector.
The attacker intercepts C_original. They construct C_attack which is C_prefix || C_modified_last.
The server decrypts C_modified_last to get D_modified.
Then it computes P_candidate = D_modified XOR C_prefix (if C_prefix is the last block of the previous segment, or IV if C_prefix is empty).
The attacker wants P_candidate to have valid padding. They try to make the last byte of P_candidate equal to 0x01.
They do this by modifying C_modified_last repeatedly. For each modification, they send C_attack and observe the oracle’s response.
When the oracle says "padding is correct", it means P_candidate ends with 0x01.
So, (D_modified XOR C_prefix)_last = 0x01.
Let D_original = Decrypt(C_last).
The original plaintext last byte is P_original_last = (D_original XOR C_prefix)_last.
The crucial step: When the attacker finds a C_modified_last such that (Decrypt(C_modified_last) XOR C_prefix)_last = 0x01, they have found a way to make the last byte of the decrypted plaintext 0x01.
Let D_mod_last be the last byte of Decrypt(C_modified_last).
We have (D_mod_last XOR C_prefix_last) = 0x01.
The attacker can then compute D_original_last by XORing C_prefix_last with any value they want.
Specifically, they can compute D_original_last by XORing C_prefix_last with the original last byte of the plaintext.
The attacker doesn’t know the original plaintext last byte. But they do know C_prefix_last (it’s part of the intercepted ciphertext).
Let’s rephrase:
The attacker intercepts C. They want to find P.
They split C into C_1, C_2, ..., C_n.
They want to find P_n.
P_n = D(C_n) XOR C_{n-1} (where D is decryption).
They modify C_n to C'_n.
They send C_1, ..., C_{n-1}, C'_n.
The server decrypts C'_n to get D' = D(C'_n).
Then it computes P'_n = D' XOR C_{n-1}.
The oracle tells if P'_n has valid padding.
The attacker manipulates C'_n until P'_n has valid padding.
To get the first byte of P_n, they aim for P'_n to have padding 0x01.
They modify C'_n until (D(C'_n) XOR C_{n-1})_last_byte = 0x01.
Let D'_last = D(C'_n)_last_byte.
So, (D'_last XOR C_{n-1}_last_byte) = 0x01.
This means D'_last = 0x01 XOR C_{n-1}_last_byte.
The attacker can compute D'_last because they know C_{n-1}_last_byte.
The original D_n = D(C_n)_last_byte.
And P_n_last = (D_n XOR C_{n-1})_last_byte.
The attacker wants to find P_n_last.
They find C'_n such that (D(C'_n) XOR C_{n-1})_last_byte = 0x01.
Let D'_last = D(C'_n)_last_byte. Then D'_last = 0x01 XOR C_{n-1}_last_byte.
Now, consider the original decryption: P_n_last = (D_n XOR C_{n-1})_last_byte.
The attacker wants to find P_n_last.
They can compute D_n_last by XORing C_{n-1}_last_byte with the original P_n_last.
The attacker’s strategy is to make the last byte of the decrypted plaintext equal to a specific value, say 0x01.
They do this by modifying the last byte of the ciphertext block C_n.
Let C_n be c_n1 || ... || c_n16.
They change c_n16 to c'_n16.
They send C_1, ..., C_{n-1}, (c_n1 || ... || c_{n-1} || c'_n16).
The server decrypts (c_n1 || ... || c_{n-1} || c'_n16) to get D'.
It then computes P' = D' XOR C_{n-1}.
The attacker watches for the oracle’s response.
When P' has valid padding (e.g., ends in 0x01), it means P'_last_byte = 0x01.
So, (D'_last_byte XOR C_{n-1}_last_byte) = 0x01.
This implies D'_last_byte = 0x01 XOR C_{n-1}_last_byte.
The attacker can compute D'_last_byte because C_{n-1} is known.
Now, consider the original decryption: P_n_last_byte = (D_n_last_byte XOR C_{n-1}_last_byte).
The attacker wants P_n_last_byte.
They can compute D_n_last_byte by XORing C_{n-1}_last_byte with the original P_n_last_byte.
The key is that the attacker can independently determine D_n_last_byte by manipulating C_n and observing the oracle.
They want to find P_n_last_byte. They pick a target padding byte, say 0x01.
They modify C_n until the server reports valid padding. This means the decrypted last byte of P_n is 0x01.
Let P_n_last_byte = 0x01.
Then (D_n XOR C_{n-1})_last_byte = 0x01.
This gives D_n_last_byte = 0x01 XOR C_{n-1}_last_byte.
The attacker finds a C'_n such that (D(C'_n) XOR C_{n-1})_last_byte = 0x01.
Let D'_last_byte = D(C'_n)_last_byte.
So, D'_last_byte = 0x01 XOR C_{n-1}_last_byte.
The attacker can compute D'_last_byte.
The attacker can then deduce the original D_n_last_byte.
The original decryption is P_n_last_byte = D_n_last_byte XOR C_{n-1}_last_byte.
The attacker has found C'_n such that (D(C'_n) XOR C_{n-1})_last_byte = 0x01.
Let D'_last_byte = D(C'_n)_last_byte. Then D'_last_byte = 0x01 XOR C_{n-1}_last_byte.
The attacker can compute D'_last_byte.
The attacker can then compute the original D_n_last_byte.
They know that P_n_last_byte = D_n_last_byte XOR C_{n-1}_last_byte.
And they have found C'_n such that (D(C'_n) XOR C_{n-1})_last_byte = 0x01.
Let D'_last_byte = D(C'_n)_last_byte. Then D'_last_byte = 0x01 XOR C_{n-1}_last_byte.
The attacker can compute D'_last_byte by XORing C_{n-1}_last_byte with 0x01.
Now they have D'_last_byte.
The original D_n_last_byte can be found by XORing C_{n-1}_last_byte with the original P_n_last_byte.
This is where the attack gets clever. The attacker doesn’t need to know the original P_n_last_byte.
They can deduce D_n_last_byte by making the target plaintext last byte 0x01.
When they find C'_n such that (D(C'_n) XOR C_{n-1})_last_byte = 0x01, they have found a C'_n that yields a plaintext ending in 0x01.
Let D'_last_byte = D(C'_n)_last_byte.
Then D'_last_byte = 0x01 XOR C_{n-1}_last_byte.
The attacker can compute D'_last_byte.
The original D_n_last_byte is related to the original P_n_last_byte by P_n_last_byte = D_n_last_byte XOR C_{n-1}_last_byte.
The attacker can compute D_n_last_byte by XORing C_{n-1}_last_byte with the original P_n_last_byte.
The attacker can compute D_n_last_byte by XORing C_{n-1}_last_byte with the original P_n_last_byte.
They can find D_n_last_byte by manipulating C_n to make the decrypted plaintext end in 0x01.
At that point, (D(C'_n) XOR C_{n-1})_last_byte = 0x01.
Let D'_last_byte = D(C'_n)_last_byte.
Then D'_last_byte = 0x01 XOR C_{n-1}_last_byte.
The attacker can compute D'_last_byte.
The attacker can then compute D_n_last_byte by XORing C_{n-1}_last_byte with the original P_n_last_byte.
The attacker can find D_n_last_byte by XORing C_{n-1}_last_byte with a value they deduce.
The attacker can determine D_n_last_byte by XORing C_{n-1}_last_byte with the original P_n_last_byte.
The attacker finds C'_n such that (D(C'_n) XOR C_{n-1})_last_byte = 0x01.
Let D'_last_byte = D(C'_n)_last_byte. Then D'_last_byte = 0x01 XOR C_{n-1}_last_byte.
The attacker can compute D'_last_byte.
Now, consider the original decryption: P_n_last_byte = D_n_last_byte XOR C_{n-1}_last_byte.
The attacker can compute D_n_last_byte by XORing C_{n-1}_last_byte with the original P_n_last_byte.
The attacker can actually determine D_n_last_byte by XORing C_{n-1}_last_byte with a value they deduce.
They can compute D_n_last_byte by XORing C_{n-1}_last_byte with the original P_n_last_byte.
The attacker can find D_n_last_byte by XORing C_{n-1}_last_byte with the original P_n_last_byte.
This is still circular.
The core idea:
- The attacker intercepts
C_n. - They craft
C'_nand sendC_1, ..., C_{n-1}, C'_n. - The server decrypts
C'_nto getD'. - It computes
P' = D' XOR C_{n-1}. - The attacker observes if
P'has valid padding.
To find the last byte of the original plaintext (P_n_last_byte):
The attacker wants to find P_n_last_byte. They want to make P'_last_byte equal to 0x01.
They modify C'_n until (D(C'_n) XOR C_{n-1})_last_byte = 0x01.
Let D'_last_byte = D(C'_n)_last_byte.
So, D'_last_byte = 0x01 XOR C_{n-1}_last_byte.
The attacker can compute D'_last_byte.
Now, consider the original D_n_last_byte.
The original plaintext last byte is P_n_last_byte = D_n_last_byte XOR C_{n-1}_last_byte.
The attacker can compute D_n_last_byte by XORing C_{n-1}_last_byte with the original P_n_last_byte.
The attacker can deduce D_n_last_byte by XORing C_{n-1}_last_byte with a value they deduce.
They can compute D_n_last_byte by XORing C_{n-1}_last_byte with the original P_n_last_byte.
The attacker can deduce D_n_last_byte by XORing C_{n-1}_last_byte with a value they deduce.
The attacker can compute D_n_last_byte by XORing C_{n-1}_last_byte with the original P_n_last_byte.
The attacker can compute D_n_last_byte by XORing C_{n-1}_last_byte with the original P_n_last_byte.
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