Statistical Tools FlavorSide-Channel Collision Attacks17. April 2012
Amir MoradiEmbedded Security Group, Ruhr University Bochum, Germany
2
Embedded Security Group
Outline Challenges
– Side-Channel Attacks (SCA)– Collision SCA– Problems and our solution
What is new in this paper Some experimental results
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
3
Embedded Security Group
What is the story? SCA (implementation attacks)
– recovering the key of crypto devices– hypothetical model for power consumption– compare the model with side-channel leakage (power)
How?
Sbox
kp
p 12 3d 78 … f9 ab 3d power 0.12 0.01 0.14 … 0.20 0.06 0.02
[k=00] S c9 27 bc … 99 62 274 4 5 … 4 3 4
[k=01] S 7d eb b6 … 41 ac eb6 6 5 … 2 4 6
[k=ff] S 55 25 17 … 6f 20 254 3 4 … 6 1 3
0.0110.060
…
0.231…
0.095
Correlation
…
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
4
Embedded Security Group
Sbox
k1
p1
p2
k2
Side-Channel Collision
p112 3d 78 … f9 ab 3d
power …
when the circuit uses a module (Sbox) more than once (in e.g., a round)
once a collision found?
false positive collision detections– a couple of heuristic and systematic ways to handle
p245 9a cf … 04 17 e2
power …? ? ? ?
known as linear collision attack
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
5
Embedded Security Group
Sbox
k1
p1
p2
k2
Our Solution at CHES 2010 (Correlation-Enhanced) p1
12 3d 78 … f9 ab 3d power 0.01 0.15 0.12 … 0.24 0.05 0.11( )
p100 01 02 … fd fe ff0.23 0.12 0.21 … 0.06 0.09 0.14 average
p245 9a cf … 04 17 e2
power 0.32 0.20 0.05 … 0.19 0.27 0.26( )
average
average
…
average
0.2300.408
…
0.839…
0.312
00 01 02 … fd fe ff
00 01 02 … fd fe ff
00 01 02 … fd fe ff
0.32 0.20 0.05 … 0.19 0.27 0.26
0.20 0.32 0.17 … 0.09 0.26 0.27
0.26 0.27 0.19 … 0.05 0.20 0.32
Correlation
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
6
Embedded Security Group
Problems having a countermeasure (secret sharing)
– computations on all shares at the same time (Threshold Imp.)– a univariate leakage– a MIA might be applicable– a CE collision might NOT
• averaging...
how about higher-order statistical moments
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
Varianceskewnesskurtosis
7
Embedded Security Group
Sbox
k1
p1
p2
k2
Solution (applying higher-order moments) p1
12 3d 78 … f9 ab 3d power 0.01 0.15 0.12 … 0.24 0.05 0.11( )
p100 01 02 … fd fe ff1.70 2.05 0.70 … 3.12 1.96 1.79 variance
p245 9a cf … 04 17 e2
power 0.32 0.20 0.05 … 0.19 0.27 0.26( )
variance
variance
…
variance
0.3050.412
…
0.780…
0.309
00 01 02 … fd fe ff
00 01 02 … fd fe ff
00 01 02 … fd fe ff
2.67 3.96 0.84 … 3.04 1.64 4.78
3.96 2.67 2.09 … 1.83 4.78 1.64
4.78 1.64 3.04 … 0.84 3.96 2.67
Correlation
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
8
Embedded Security Group
Sbox
k1
p1
p2
k2
Solution (applying higher-order moments) p1
12 3d 78 … f9 ab 3d power 0.01 0.15 0.12 … 0.24 0.05 0.11( )
p100 01 02 … fd fe ff1.70 2.05 0.70 … 3.12 1.96 1.79 skewness
p245 9a cf … 04 17 e2
power 0.32 0.20 0.05 … 0.19 0.27 0.26( )
skewness
skewness
…
skewness
0.3050.412
…
0.780…
0.309
00 01 02 … fd fe ff
00 01 02 … fd fe ff
00 01 02 … fd fe ff
2.67 3.96 0.84 … 3.04 1.64 4.78
3.96 2.67 2.09 … 1.83 4.78 1.64
4.78 1.64 3.04 … 0.84 3.96 2.67
Correlation
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
9
Embedded Security Group
Sbox
k1
p1
p2
k2
General Form (no specific moment) p1
12 3d 78 … f9 ab 3d power 0.01 0.15 0.12 … 0.24 0.05 0.11( )
p100 01 02 … fd fe ff
p245 9a cf … 04 17 e2
power 0.32 0.20 0.05 … 0.19 0.27 0.26( )
…
0.1040.094
…
0.006…
0.143
00 01 02 … fd fe ff
00 01 02 … fd fe ff
00 01 02 … fd fe ff
…
…
…
JeffreysDivergence
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
∑ (𝑝 ( )−𝑞 ()) log 𝑝 ()𝑞()
10
Embedded Security Group
Practical Issues higher statistical moments, lower estimation accuracy
– more traces (measurements) required estimating pdf by e.g., histogram
– reducing accuracy as well Jeffreys divergence
– based on Kullback-Leibler divergence– symmetric
Experimental Platforms– Virtex II-pro FPGA (SASEBO)– Atmel uC (smartcard)
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
11
Embedded Security Group
Experimental Results (PRESENT TI) J. Cryptology 24(2)
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
12
Embedded Security Group
Experimental Results (PRESENT TI)
Average
Variance
Skewness
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
13
Embedded Security Group
Experimental Results (AES TI) EC 2011
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
14
Embedded Security Group
Experimental Results (AES TI)
Average
Variance
Skewness
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
15
Embedded Security Group
Experimental Results (masked software)
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
time to move toward multivariate case– joint pdfs can be estimated– joint statistical moments also can be estimated
• the same as doing a preprocess (by multiplication) step prior to a univariate attack
17
Embedded Security Group
Measurement Speed? (Threshold)
UART
PC sends a small number of bytes (~20)Control FPGA communicates with the Target FPGA
sending/receiving ~10K plaintext/ciphertextwhile the oscilloscope measures
Speed of the measurement depends on the length of each trace
In this case, 2000 points, 100M traces in 11 hours!
18
Embedded Security Group
Experimental Results (masked software)
EUROCRYPT 2012 | Cambridge | 17. April 2012 Amir Moradi
Recommended
![Speeding up detection of SHA-1 collision attacks using ... · a 76-step freestart collision [12] (cost 250 SHA-1) and more recently a freestart collision for full SHA-1 [26].](https://img.pdfslide.net/doc/110x75/5ad47f377f8b9aff228beaba/speeding-up-detection-of-sha-1-collision-attacks-using-76-step-freestart-collision.jpg)
![LNCS 7237 - Statistical Tools Flavor Side-Channel ... Tools Flavor Side-Channel Collision Attacks 429 (DPA) [13] and its successor form, thecorrelation power analysis (CPA) [7], use](https://img.pdfslide.net/doc/110x75/5aad97a17f8b9a9c2e8e8121/lncs-7237-statistical-tools-flavor-side-channel-tools-flavor-side-channel.jpg)
