AES in CBC Mode

• Repeat of theory from tutorial

The IV

• Suggest some ideas

The Signature

• Timing attack
• Show firmware

Bootloader Source Code

Inside the bootloader's main loop, it does three tasks that we're interested in:

• it decrypts the incoming ciphertext;
• it applies the IV to the decryption's result; and
• it checks for the signature in the resulting plaintext.

This snippet from bootloader.c shows all three of these tasks:

// Continue with decryption
trigger_high();                
aes256_decrypt_ecb(&ctx, tmp32);
trigger_low();
             
// Apply IV (first 16 bytes)
for (i = 0; i < 16; i++){
    tmp32[i] ^= iv[i];
}

//Save IV for next time from original ciphertext                
for (i = 0; i < 16; i++){
    iv[i] = tmp32[i+16];
}

// Tell the user that the CRC check was okay
putch(COMM_OK);
putch(COMM_OK);

//Check the signature
if ((tmp32[0] == SIGNATURE1) &&
   (tmp32[1] == SIGNATURE2) &&
   (tmp32[2] == SIGNATURE3) &&
   (tmp32[3] == SIGNATURE4)){
   
   // Delay to emulate a write to flash memory
   _delay_ms(1);
}   

This gives us a pretty good idea of how the microcontroller is going to do its job. However, we can go one step further and find the exact assembly code that the target will execute. If you have Atmel Studio and its toolchain on your computer, you can get the assembly file from the command line with

avr-objdump -m avr -D bootloader.hex > disassembly.txt

This will convert the hex file into assembly code, making it more human-readable. The important part of this assembly code is:

 344:	d3 01       	movw	r26, r6
 346:	93 01       	movw	r18, r6
 348:	f6 01       	movw	r30, r12
 34a:	80 81       	ld	r24, Z
 34c:	f9 01       	movw	r30, r18
 34e:	91 91       	ld	r25, Z+
 350:	9f 01       	movw	r18, r30
 352:	89 27       	eor	r24, r25
 354:	f6 01       	movw	r30, r12
 356:	81 93       	st	Z+, r24
 358:	6f 01       	movw	r12, r30
 35a:	ee 15       	cp	r30, r14
 35c:	ff 05       	cpc	r31, r15
 35e:	a1 f7       	brne	.-24     	;  0x348
 
 360:	fe 01       	movw	r30, r28
 362:	b1 96       	adiw	r30, 0x21	; 33
 364:	81 91       	ld	r24, Z+
 366:	8d 93       	st	X+, r24
 368:	e4 15       	cp	r30, r4
 36a:	f5 05       	cpc	r31, r5
 36c:	d9 f7       	brne	.-10     	;  0x364

 36e:	84 ea       	ldi	r24, 0xA4	; 164
 370:	0e 94 16 02 	call	0x42c	;  0x42c
 374:	84 ea       	ldi	r24, 0xA4	; 164
 376:	0e 94 16 02 	call	0x42c	;  0x42c

 37a:	89 89       	ldd	r24, Y+17	; 0x11
 37c:	88 23       	and	r24, r24
 37e:	09 f0       	breq	.+2      	;  0x382
 380:	98 cf       	rjmp	.-208    	;  0x2b2

 382:	8a 89       	ldd	r24, Y+18	; 0x12
 384:	8b 3e       	cpi	r24, 0xEB	; 235
 386:	09 f0       	breq	.+2      	;  0x38a
 388:	94 cf       	rjmp	.-216    	;  0x2b2

 38a:	8b 89       	ldd	r24, Y+19	; 0x13
 38c:	82 30       	cpi	r24, 0x02	; 2
 38e:	09 f0       	breq	.+2      	;  0x392
 390:	90 cf       	rjmp	.-224    	;  0x2b2

 392:	8c 89       	ldd	r24, Y+20	; 0x14
 394:	8d 31       	cpi	r24, 0x1D	; 29
 396:	09 f0       	breq	.+2      	;  0x39a
 398:	8c cf       	rjmp	.-232    	;  0x2b2

 39a:	83 e3       	ldi	r24, 0x33	; 51
 39c:	97 e0       	ldi	r25, 0x07	; 7
 39e:	01 97       	sbiw	r24, 0x01	; 1
 3a0:	f1 f7       	brne	.-4      	;  0x39e
 3a2:	87 cf       	rjmp	.-242    	;  0x2b2

We'll use both of the source files throughout the tutorial.

Power Traces

After the bootloader is finished the decryption process, it executes a couple of distinct pieces of code:

• To apply the IV, it uses an XOR operation;
• To store the new IV, it copies the previous ciphertext into the IV array;
• It sends two bytes on the serial port;
• It checks the bytes of the signature one by one.

We should be able to recognize these four parts of the code in the power traces. Let's modify our capture routine to find them.

Re-run the capture script and change a few settings:

1. We'd like to skip over all of the decryption process. The source code around this point is:

   trigger_high(); 
   aes256_decrypt_ecb(&ctx, tmp32); /* encrypting the data block */
   trigger_low();
   

   so we can skip straight over the AES-256 function by triggering on a falling edge instead of a rising edge. Change this in the scope settings.

2. We don't need as many samples now. Change the number of samples to 3000.
3. If we decrypt multiple ciphertexts in a row, only the first one will use the secret IV - all of the others will use the previous ciphertext instead. To avoid this, we'll have to automatically reset the board.
   1. In the General Settings tab, change the Auxiliary Module to Reset AVR/XMEGA via CW-Lite.
   2. In the Aux Settings tab, change both delays to around 100 ms.
4. Capture one trace and make sure that everything works.

If everything worked out, you should be able to see all of the code's features:

With all of these things clearly visible, we have a pretty good idea of how to attack the IV and the signature. We should be able to look at each of the XOR spikes to find each of the IV bytes - each byte is processed on its own. Then, the signature check uses a short-circuiting comparison: as soon as it finds a byte in error, it stops checking the remaining bytes. This type of check is susceptible to a timing attack.

Let's grab a lot of traces so that we don't have to come back later. Save the project somewhere memorable, set up the capture routine to record 1000 traces, hit Capture Many, and grab a coffee.

Attack Theory

The bootloader applies the IV to the AES decryption result by calculating

where DR is the decrypted ciphertext, IV is the secret vector, and PT is the plaintext that the bootloader will use later. We only have access to one of these: since we know the AES-256 key, we can calculate DR.

Specifically, the assembly code to calculate the plaintext is the loop

 344:	d3 01       	movw	r26, r6
 346:	93 01       	movw	r18, r6
 348:	f6 01       	movw	r30, r12
 34a:	80 81       	ld	r24, Z
 34c:	f9 01       	movw	r30, r18
 34e:	91 91       	ld	r25, Z+
 350:	9f 01       	movw	r18, r30
 352:	89 27       	eor	r24, r25
 354:	f6 01       	movw	r30, r12
 356:	81 93       	st	Z+, r24
 358:	6f 01       	movw	r12, r30
 35a:	ee 15       	cp	r30, r14
 35c:	ff 05       	cpc	r31, r15
 35e:	a1 f7       	brne	.-24     	;  0x348

This code includes two ld instructions, one eor, and one st: the DR and IV are loaded and XORed to get PT, which is then stored back where DR was. All of these instructions should be visible in the power traces.

This is enough information for us to attack a single bit of the IV. Suppose we only wanted to get the first bit (number 0) of the IV. We could do the following:

• Split all of the traces into two groups: those with DR[0] = 0, and those with DR[0] = 1.
• Calculate the average trace for both groups.
• Find the difference between the two averages. It should include a noticeable spike during the first iteration of the loop.
• Look at the direction of the spike to decide if the IV bit is 0 (PT[0] = DR[0]) or if the IV bit is 1 (PT[0] = ~DR[0]).

This is effectively a DPA attack on a single bit of the IV. We can repeat this attack 128 times to recover the entire IV.

A 1-Bit Attack

Unfortunately, we can't use the ChipWhisperer Analyzer to attack this XOR function. Instead, we'll write our own Python code. One thing that we don't need to do is write our own AES-256 implementation: there's some perfectly fine code in the PyCrypto library. Install PyCrypto and make sure you can use its functions:

python
Python 2.7.10 (default, May 23 2015, 09:40:32) [MSC v.1500 32 bit (Intel)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> from Crypto.Cipher import AES
>>> AES
<module 'Crypto.Cipher.AES' from 'C:\WinPython-32bit-2.7.10.3\python-2.7.10\lib\site-packages\Crypto\Cipher\AES.pyc'>

Next, open a new Python script wherever you like and load your data that you recorded earlier. You might want to rename the files to make them easier to work with. It'll also be helpful to know how many traces we have and how long they are:

# Load data
import numpy as np

traces = np.load(r'traces\traces.npy')
textin = np.load(r'traces\textin.npy')
numTraces = len(traces)
traceLen = len(traces[0])

print numTraces
print traceLen

It's also a good idea to plot some traces and make sure they look okay:

# Plot some traces 
import matplotlib.pyplot as plt
for i in range(10):
    plt.plot(traces[i])
plt.show()

Since we know the AES-256 key, we can decrypt all of this data and store it in a list of decryption results:

# Decrypt ciphertext with the key that we now know
from Crypto.Cipher import AES
knownkey = [0x94, 0x28, 0x5D, 0x4D, 0x6D, 0xCF, 0xEC, 0x08, 0xD8, 0xAC, 0xDD, 0xF6, 0xBE, 0x25, 0xA4, 0x99,
            0xC4, 0xD9, 0xD0, 0x1E, 0xC3, 0x40, 0x7E, 0xD7, 0xD5, 0x28, 0xD4, 0x09, 0xE9, 0xF0, 0x88, 0xA1]
knownkey = str(bytearray(knownkey))
dr = []
aes = AES.new(knownkey, AES.MODE_ECB)
for i in range(numTraces):
    ct = str(bytearray(textin[i]))
    d = aes.decrypt(ct)
    d = [bytearray(pt)[i] for i in range(16)]
    dr.append(d)
print dr

That's a lot of data to print! Now, let's split the traces into two groups by comparing bit 0 of the DR:

# Split traces into 2 groups
groupedTraces = [[] for _ in range(2)]
for i in range(numTraces):
    bit0 = dr[i][0] & 0x01
    groupedTraces[bit0].append(traces[i])
print len(groupedTraces[0])

If you have 1000 traces, you should expect this to print a number around 500 - roughly half of the traces should fit into each group. Now, NumPy's average function lets us easily calculate the average at each point:

# Find averages and differences
means = []
for i in range(2):
    means.append(np.average(groupedTraces[i], axis=0))
diff = means[1] - means[0]

Finally, we can plot this difference to see if we can spot the IV:

plt.plot(diff)
plt.grid()
plt.show()

This makes a plot with some pretty obvious spikes:

However, one of these spikes is meaningless to us. The spike around sample 1600 is caused by the signature check, which we aren't attacking yet. Let's ignore this peak and zoom in on the smaller spikes at the start of the trace:

This is it! We've got a pretty clear signal telling us where the decryption result is used. You can make sure this isn't a coincidence by using the second byte instead:

These peaks are about 60 samples later (or 15 cycles, since we're using an ADC clock that's 4 times faster than the microcontroller). Also, most of these peaks are upside down! This is a pretty clear indicator that we can find the IV bits from these differential traces. The only thing that we can't tell is the polarity of these signals; there's no way to tell if right-side-up peaks indicate a bit that's set or cleared. However, that means we can narrow down the IV to two possibilities, which is a lot better than .

The Other 127

The best way to attack the IV would be to repeat the 1-bit conceptual attack for each of the bits. Try to do this yourself! (Really!) If you're stuck, here are a few hints to get you going:

• One easy way of looping through the bits is by using two nested loops, like this:

for byte in range(16):
    for bit in range(8):
        # Attack bit number (byte*8 + bit)

• The sample that you'll want to look at will depend on which byte you're attacking. We had success when we used location = 51 + byte*60, but your mileage will vary.
• The bitshift operator and the bitwise-AND operator are useful for getting at a single bit:

# This will either result in a 0 or a 1
checkIfBitSet = (byteToCheck >> bit) & 0x01

If you're really, really stuck, there's a working attack in Appendix ?. You should find that the secret IV is C1 25 68 DF E7 D3 19 DA 10 E2 41 71 33 B0 EB 3C.