Side channel power analysis resistance evaluation of masked adders on FPGA

International Journal of Reconfigurable and Embedded Systems (IJRES)
Vol. 12, No. 1, March 2023, pp. 97~112
ISSN: 2089-4864, DOI: 10.11591/ijres.v12.i1.pp97-112  97
Journal homepage: http://ijres.iaescore.com
Side channel power analysis resistance evaluation of masked
adders on FPGA
Yilin Zhao1
, Hiroki Nishikawa2
, Xiangbo Kong1
, Hiroyuki Tomiyama1
1
Graduate School of Science and Engineering, Ritsumeikan University, Shiga, Japan
2
Graduate School of Information Science and Technology, Osaka University, Osaka, Japan
Article Info ABSTRACT
Article history:
Received Oct 19, 2022
Revised Dec 12, 2022
Accepted Dec 26, 2022
Since many internet of things (IoT) devices are threatened by side-channel
attacks, security measures are essential for their safe use. However, there are
a variety of IoT devices, so the accuracy required depends on the system’s
application. In addition, security related to arithmetic operations has been
attracting attention in recent years. Therefore, this paper presents an
empirical experiment of masking for adders on field programmable gate
arrays (FPGAs) and explores the trade-off between cost and security by
varying the bit length of the mask. The experimental results show that
masking improves power analysis attack resistance, and increasing the bit
length of the random numbers used for masking increases security. In
particular, the series-connected masked adder is found to be effective in
improving power analysis attack resistance.
Keywords:
Adders
FPGA
Masking
Power analysis attack
Side channel attacks
T-test
Xilinx
This is an open access article under the CC BY-SA license.
Corresponding Author:
Yilin Zhao
Graduate School of Science and Engineering, Ritsumeikan University
1-1-1 Nojihigashi, Kusatsu, Shiga, 525-8577, Japan
Email: irin.cho@tomiyama-lab.org
1. INTRODUCTION
In recent years, our lives have become more convenient due to the spread of Internet of things (IoT)
devices. However, those devices are exposed to the physical environment, making them vulnerable to side-
channel attacks [1], [2]. Representative side-channel attacks include power analysis attacks that analyze
power consumption [3], timing attacks that use processing time [4], and electromagnetic wave analysis
attacks that use electromagnetic waves [5] and more [6]. Recently, software-based remote power side-
channel attacks have also been proposed, which allow attacks to be carried out without physically
approaching the target system [7]-[10]. Additionally, to improve the performance of side-channel analysis,
methods using deep learning [11] and conditional generative adversarial networks [12] are proposed.
Moreover, security is attracting increasing attention not only for specific devices and circuits but also for
arithmetic operations. Among them, power analysis attacks have attracted particular attention because the
equipment used to analyze power is not expensive. According to the work [3], the power analysis attacks are
a serious threat to security on field programmable gate arrays (FPGAs) as well as application-specific
integrated circuits. Örs et al. [13] introduces a setup for power analysis attacks on FPGAs. Therefore, target
devices and circuits must be designed securely so that attackers cannot extract security keys. Therefore, one
of the countermeasures against side channel attacks is a technique called masking. Masking is a technique
that uses a random mask to make the leakage of values handled by the implementation independent of
sensitive inputs and intermediate variables [14]. Since the random mask should be unbreakable, the side-
channel information from individual shares will not reveal sensitive variables. Even if an attacker acquires a
leak of the side-channel information, the sensitive intermediate variables are sufficiently mysterious to

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remain secret. There are various methods of masking, such as multiplicative masking [15] and masked AND
operation [16]. Masoumi et al. [17] presents an example implementation of masking to advanced encryption
standard (AES). Gravellier et al. [18], masking is also effective as a countermeasure against remote attacks,
which have received attention in recent years. Wu and Picek [19] aims to investigate the effectiveness of a
deep learning technique called autoencoder for masking as a future work. However, detailed methods of
mystifying cryptographic variables by masking processes have rarely been studied [20]. Moreover, there are
some issues by implementing countermeasures, such as increased circuit area, power consumption and
implementation cost [21]. Therefore, a research is in progress to improve power analysis attack resistance at
low cost [22]. In addition, IoT devices have a variety of sizes and applications, and each device has different
acceptable cost, power and required safety accuracy. Therefore, by devising masking methods and mask
itself, we can expect a trade-off between implementation cost and safety.
This paper presents an empirical study on masking for adders on FPGA, focusing on one of the most
basic components of circuits, the adder. The contributions of this paper are three-fold. First, we examine
tolerance towards power analysis attacks for three types of adders with basic circuit configurations.
Specifically, we investigate a ripple carry adder (RCA), a carry lookahead adder (CLA), and a RCA with
built-in carry chains. Second, two types of masked adders will be compared: the series-connected masked
adder and the compression-based masked adder. We also evaluate the effect of the bit length of the mask on
the power analysis attack resistance. For each evaluation, we first synthesize the circuit and analyze the
power consumption. From the obtained power consumption, we statistically evaluate the degree of leakage of
power-based side-channel information by T-test. By applying masking to adders, this research aims to design
security circuits that are highly versatile, not for a specific device. Moreover, we will explore the trade-off
between cost and security by changing the bit length of the mask and performing the evaluation. To the best
of our knowledge, this is the first paper which studies the power side-channel leakage of different adders on
FPGA.
The rest of this paper is organized as follows. In section 2, we describe the three adders used in this
study. Section 3 presents the two circuits used in our study and introduces the masking methods in these
circuits. Section 4 describes the experimental scenario and the results of the side-channel attack resistance.
Section 5 summarizes this paper.
2. POWER SIDE CHANNEL LEAKAGE ANALYSIS OF NON-MASKED ADDERS
An adder is the simplest of the arithmetic circuits and is an essential component in the processing of
the system. In recent years, as devices have become smaller and faster, performance aspects such as power
consumption, Circuit area and delay time have become more important factors. Knowles [23] proposes a
circuit with a reduced area compared to existing adders. In addition, the structure in the work Tyagi [24] is
implemented considering the trade-off between circuit area and delay. However, there are few studies that
provide a detailed survey of adder security. Therefore, this study evaluates the power analysis attack
resistance of simple adders. This section describes the structure of three adders on the FPGA. Then we
evaluate the power analysis attack tolerance for the three adders presented in subsection 2.1.
2.1. Adders on FPGA
This subsection describes features and structures of the three adders on a FPGA. Moreover, we
explain the flow of operations in each adders with equations. A FPGA is integrated devices that allow
designers to configure the logic circuit and we can change the behavior of the circuitry as often as we like. In
this study, we examine a RCA, a CLA, and an RCA with fast carry chains. These three types of adders have
different characteristics in terms of circuit area and arithmetic delay. In this study, Xilinx 7-series FPGA is
assumed [25].
2.1.1. Ripple carry adder
RCA has the most basic structure of all adders. A N-bit RCA is designed by sequentially chaining N
full-adders (FAs). Figure 1 shows an organization of a 4-bit RCA. RCA has A, B and carry-in as inputs and
outputs carry-out and sum. As shown in Figure 1, in RCA the carry of the previous digit is connected to the
input of the next digit. Therefore, the worst-case carry propagation goes through all digits, resulting in large
computation times.
Each FA calculates a sum of the digit and a carry signal to the next FA as shown in:
𝑆𝑖 = 𝐴𝑖⨁𝐵𝑖⨁𝐶𝑖 (1)
𝐶𝑖+1 = 𝐴𝑖 ∙ 𝐵𝑖 + 𝐵𝑖 ∙ 𝐶𝑖 + 𝐶𝑖 ∙ 𝐴𝑖 (2)

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Side channel power analysis resistance evaluation of masked adders on FPGA (Yilin Zhao)
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the Xilinx FPGA consists of 6-input LUTs, and each 6-input LUT can be configured as two 5-input LUTs.
Therefore, an FA is mapped to a 6-input LUT, and a N-bit RCA utilizes N LUTs.
Figure 1. Circuit diagram of a 4-bit RCA
2.1.2. Carry lookahead adder
CLA is another common circuit. CLA reduces delay time by calculating carries first, before all
calculations are completed. Figure 2 shows an organization of a 4-bit CLA. CLA calculates carry generation
and carry propagation as shown in (3), (4).
𝐺𝑖 = 𝐴𝑖 ∙ 𝐵𝑖 (3)
𝑃𝑖 = 𝐴𝑖 + 𝐵𝑖 (4)
Then, carry to the next digit is computed by (5).
𝐶𝑖+1 = 𝐺𝑖 + 𝑃𝑖𝐶𝑖 (5)
By recursively calculating (5), we obtain (6)-(9).
𝐶1 = 𝐺0 + 𝑃0𝐶0 (6)
𝐶2 = 𝐺1 + 𝑃1𝐶1 = 𝐺1 + 𝑃1𝐺0 + 𝑃1𝑃0𝐶0 (7)
𝐶3 = 𝐺2 + 𝑃2𝐶2 = 𝐺2 + 𝑃2𝐺1 + 𝑃2𝑃1𝐺0 + 𝑃2𝑃1𝑃0𝐶0 (8)
𝐶4 = 𝐺3 + 𝑃3𝐶3 = 𝐺3 + 𝑃3𝐺2 + 𝑃3𝑃2𝐺1 + 𝑃3𝑃2𝑃1𝐺0 + 𝑃3𝑃2𝑃1𝑃0𝐶0 (9)
In this circuit, the carry signals can be computed in parallel and all digit carries are determined from
the inputs Ai and Bi only, so the arithmetic time is not proportional to the number of digits as in the RCA.
Therefore, CLAs compute faster than RCAs at the cost of more LUTs. According to the work Uma et al.
[26], CLA has a shorter delay time than many adders including RCA.
Figure 2. Circuit diagram of a 4-bit CLA
FA0
A
B
S
Cout
Cin
FA3
A
B
S
Cout
Cin
FA2
A
B
S
Cout
Cin
FA1
A
B
S
Cout
Cin
B0 A0
B1 A1
B2 A2
B3 A3
C4 S3 S2 S1 S0
C2
C3 C1
C0

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2.1.3. Ripple carry adder with fast carry chains
Xilinx FPGAs have special hardware blocks, named Carry4 [27], to rapidly propagate carry signals.
At the output of each LUT, an XOR gate and a 2-input multiplexer are placed, and the multiplexers are
chained, as shown in Figure 3. In this circuit, one LUT is used to perform 1-bit addition. The carry output
Cout of the last stage can be extended to 128 bits by connecting it to the carry input Cin of the next digit.
Using the carry chains, adders can be calculated in (10)-(12).
𝑃𝑖 = 𝐴𝑖⨁𝐵𝑖 (10)
𝑆𝑖 = 𝑃𝑖⨁𝐶𝑖𝑛 (11)
𝐶𝑖+1 = 𝐺𝑖 + 𝑃𝑖 ∙ 𝐶𝑖 = 𝑃𝑖
̅ ∙ 𝐴𝑖 + 𝑃𝑖 ∙ 𝐶𝑖 (12)
As shown in (10), (11) and (12) are calculated by an LUT, an XOR gate, and a multiplexer, respectively. The
carry propagation P is computed as the exclusive OR of A and B. The sum S is calculated by the exclusive
OR of A, B, and the carry input Cin. The carry output of the next digit is represented by (12). Similar to the
32-bit RCA, a 32-bit RCA with fast carry chains uses 32 LUTs. Unlike the RCA, however, the carry-out
signal of a digit does not go into the LUT of the next digit. Carry signals are propagated through the built-in
fast carry chains, leading to a shorter critical-path delay than the RCA shown in sub-subsection 2.1.1.
Figure 3. Circuit diagram of a 4-bit RCA with fast carry chains
2.2. Synthesis result
First, we synthesize the three 32-bit adders. We synthesize with AMD Xilinx Vivado 2019.2. The
target device is assumed to be Artix-7 FPGA. Our synthesis has been performed with enabling a couple of
optimization options to the performance. The results on hardware resources and delay are shown in Table 1.
In terms of both hardware cost and performance, RCA with fast carry chains is the best among the three.
Table 2 shows the number of resources and delay times for 128-bit CLA and RCA with fast carry chains.
128-bit adder is an extended circuit of the 32-bit adder described in subsection 2.1. The RCA is not evaluated
for performance and tolerance at 128 bits because its delay time is larger than that of the other two adders as
shown in Table 1. The results in Table 2 show that the RCA with fast carry chains outperforms the CLA in
both number of resources and performance. Comparing Tables 2 and 3, the number of LUTs and the delay
time are larger for the 128-bit circuit than for the 32-bit circuit for both CLA and RCA with fast carry chains.
Table 1. Resource and delay of the 32-bit adders
Adders LUTs Delay (ns)
RCA 64 18.991
CLA 195 7.012
RCA with fast carry chains 32 6.118
Cout MUX
MUX
MUX MUX
P3
P2 P1 P0
C3 C2 C1 C0
Cin
S0
S1
S2
S3
LUT2
LUT3 LUT1 LUT0
B0 A0
B1 A1
B2 A2
B3 A3
C4

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Table 2. Resource and delay of the 128-bit adders
Adders LUTs Delay (ns)
CLA 681 11.718
Table 3. The number of T-values violating a security criterion (>|±4.5|) of the 32-bit adders
Adders No. of T-values over |±4.5| Maximum T-value
RCA 50 29.72
CLA 43 23.86
2.3. Power analysis
Next, we analyze the power consumption of the three adders based on post-synthesis simulation. We
use the power analysis tool presented in the work [28] and Vivado toolkit for power analysis. This tool can
observe dynamic temporal changes in power. The results are shown in Figure 4. The X-axis represents
hundreds of testbenches of which each contains 2000 test vectors, and the Y-axis represents the power
consumption. RCA, CLA, and RCA with fast carry chains results are shown in gray, orange and blue
respectively. Only the logic and signal power are evaluated since the adders designed for this study are too
small compared with the FPGA capacity. The results show the RCA with fast carry chains consumes the least
power. Figure 5 shows the power consumption of the two 128-bit adders. This result shows that RCA with
fast carry chains operates at lower power consumption than CLA. Comparing Figures 4 and 5, the power
consumptions of both CLA and RCA with fast carry chains are higher for the 128-bit circuit than for the 32-
bit circuit.
Figure 4. Power consumption of 32-bit adder
Figure 5. Power consumption of 128-bit adder
0
500
1000
1500
2000
2500
3000
3500
4000
1 11 21 31 41 51 61 71 81 91
Power
consumption
(μW)
Testbench
RCA CLA RCA with fast carry chains
0
2000
4000
6000
8000
10000
12000
14000
16000
1 11 21 31 41 51 61 71 81 91
Power
consumption
(μW)
Testbench
CLA RCA with fast carry chains

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2.4. Power side channel leakage analysis
In order to evaluate tolerance to side-channel leakage, we conduct T-test [29]-[31] for the adder
circuits. Side-channel attacks such as power analysis attacks, use information about intermediate values in the
side-channel traces observed from a device. Therefore, a statistical hypothesis test can be used to detect
whether sensitive intermediate values have a significantly effect on the measured data. The Welch's T-test is
one of the measures of side-channel attack resistance and is a test of the difference between the means of two
sets of data. This test can determine whether the power traces obtained by an attacker leak data about the
secret information. The equation of the T-test is shown (13).
𝑡 =
𝑋1
̅̅̅̅−𝑋2
̅̅̅̅
√𝑆1
2 𝑁1
⁄ +𝑆2
2 𝑁2
⁄
(13)
Here, 𝑋1
̅̅̅ and 𝑋2
̅̅̅ represent the average power consumption for random and fixed inputs, 𝑆1 and 𝑆2 are the
standard deviation, and 𝑁1 and 𝑁2 represent the number of samples. The T-value t is desire to be less than
±4.5 to meet security criteria. Details on safety criteria and specific method of the T-test are described in the
work [29].
We conduct a T-test for the power traces obtained in subsection 2.3. The obtained T-values of the
32-bit adders are shown in Figure 6. The X-axis represents hundreds of testbenches of which each contains
2000 test vectors, and the Y-axis represents the T-value. The red lines in the graph indicate the standard
values of 4.5 and -4.5 for the attack tolerance evaluation. The results show that all circuits have many points
with T-values above ±4.5, indicating that they are vulnerable to power analysis attacks. Table 3 shows the
number of T-values over ±4.5 and the maximum T-value for each circuit. Table 3 shows that RCA is the
least tolerant since T-values exceeds ±4.5 in 50 test benches. The maximum T-value of RCA is also the
largest among the three circuits. Based on this result, RCA evaluation is omitted for the 128-bit adder. The
RCA with fast carry chains is superior in terms of both the number of times the T-value exceeds ±4.5 and the
maximum value. However, the RCA with fast carry chains also still exceeds the security criteria for T-values
in 21 test benches. Figure 7 and Table 4 show the results of side channel leakage analysis for 128-bit CLA
and RCA with fast carry chains. Figure 7 indicates that T-values are frequently exceeded over 4.5 both CLA
and RCA with fast carry chain. Also, the T-values of CLA are seemingly larger than that of RCA with fast
carry chains. Table 4 shows that the RCA with fast carry chains has a smaller number of times the T-value
exceeds ±4.5 than the CLA, and that the maximum value is also smaller. Comparing the 32-bit and 128-bit
results for CLA and RCA with fast carry chains, it can be seen that the 128-bit adder has a higher T-value
exceeding ±4.5 more times. The maximum T-value is larger for the 128-bit circuit than for the 32-bit circuit
for the CLA, and slightly larger for the 32-bit circuit for the RCA with fast carry chains. This result indicates
that vulnerability tends to increase as the number of bits increases. In addition, for the adders verified in this
section, there are some patterns which failed to meet the safety criterion. Therefore, a simple adder without
countermeasures against power analysis attacks is not completely secure in terms of security.
Figure 6. T-values of 32-bit adder
-35
-30
-25
-20
-15
-10
-5
0
5
10
15
20
1 11 21 31 41 51 61 71 81 91
T
value
Testbench
RCA CLA RCA with fast carry chains

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Figure 7. T-values of 128-bit adder
Table 4. The number of T-values violating a security criterion (>|±4.5|) of the 128-bit adders
Adders No. of T-values over |±4.5| Maximum T-value
CLA 65 31.65
3. POWER SIDE CHANNEL LEAKAGE ANALYSIS OF MASKED ADDERS
The results in section 2 show that adders without attack countermeasures are vulnerable to power
analysis attacks. Therefore, we focus on a side-channel attack countermeasure called masking and apply
masking to adders. In this section, we introduce two types of masked adders and evaluate their attack
resistance. First, the structures of two types of 128-bit masked adders are presented. Then, the power analysis
attack resistance of each masked adder is evaluated and compared to the resistance of a simple non-masked
adder.
3.1. Fully masked arithmetic adders
In this subsection, we describe the structure of the two masked adders used in this study.
Specifically, we examine a masked adder using fast carry chain of Xilinx and a masked adder using carry
save adder. In this paper, we make the following assumptions. An attacker inputs augend A to the adder and
tries to identify the addend B through observing a side-channel leakage of the power consumption. Note that
we assume the attacker cannot observe B and the sum C. In addition, the adders presented in this section
assume Xilinx 7-series FPGA the same as section 2.
3.1.1. Series-connected masked adder
Figure 8 shows the structure of a simple masked adder. It consists of two carry-propagate adders and
one carry-propagate subtractor connected in series. First, the random number R generated by the pseudo-
random number generator (PRNG) is added to A. Then, B is added to the output of A+R. Finally, R is
subtracted to derive the final output of C (=A+B). In this example, we assume that A is masked with adding
R, and its intermediate variable mystifies the side-channel leakage of the power consumption by the
subsequent calculation. The RCA with fast carry chains introduced in Section 3 is used for the additive part
of this masked adder. Based on the results in section 3, the RCA with fast carry chains is the best adder in
terms of number of resources, delay time, and power analysis attack resistance. In this experiment, the
pseudo-random number generator is excluded from the attack resistance evaluation, and only the arithmetic
unit part is evaluated. Therefore, a detailed description of the PRNG scheme is omitted.
3.1.2. Compression-based masked adder
Figure 9 shows the compression-based masked adder. The series-connected masked adder
previously presented has a long delay in adding the augend A, addend B, and random number R, since it is
connected to two carry-propagate adders in series. Therefore, to reduce the delay, the three inputs are first
compressed into two terms by carry save adder (CSA). The architecture of CSA is given in Figure 10. CSA is
used to compute the sum of three or more numbers. Unlike other adders, it outputs two numbers of the same
size as the input. The delay due to the carry is reduced in this structure since the carry is not propagated
-30
-20
-10
0
10
20
30
40
1 11 21 31 41 51 61 71 81 91
T
value
Testbench
CLA RCA with fast carry chains

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through the stages [32]. According to the work [33], the CSA achieves the shortest latency among seven
types of adders.
The three numbers A, B, and R are computed by CSA as partial sum and shift carry as shown in
(14), (15).
𝑆𝑖 = 𝐴𝑖⨁𝐵𝑖⨁𝑅𝑖 (14)
𝐶𝑖 = (𝐴𝑖 ∙ 𝐵𝑖) + (𝐴𝑖 ∙ 𝑅𝑖) + (𝐵𝑖 ∙ 𝑅𝑖) (15)
Figure 8. Series-connected masked adder Figure 9. Compression-based masked adder
Figure 10. Circuit diagram of a 4-bit CSA
In this subsection, we synthesize the two types of masked adders described in subsection 3.1 and
compare their performance. Masked adders have 128 bits and use AMD Xilinx Vivado 2019.2 for synthesis.
The target device is assumed to be an Artix-7 FPGA. We have enabled several optimization options for
performance when synthesizing the circuit. Table 5 shows the number of LUTs and delay times for the non-
masked circuit and the two masked circuits. However, this result does not include the area and delay of the
pseudo-random number generator. Table 5 shows that the non-masked adder uses 128 LUTs and has the
smallest circuit area and shortest delay time because there are no additional calculations for masking.
Comparison of the two masked adders shows that the series-connected masked adder has fewer LUTs than
the compression-based masked adder, and the compression-based masked adder operates with a shorter delay
than the series-connected masked adder.
Table 5. The number of LUTs, delay and power consumption for the synthesized adder circuits
Masks Adders LUTs Delay (ns) Power consumption (µW)
0-bit (Non-masked) Carry propagate adder 128 8.470 699
128-bit (Fully masked) Series-connected masked adder 384 11.048 9675
Compression-based masked adder 511 10.268 9708

105
3.3. Power analysis
Next, we evaluate the power consumption. We use Vivado and the tools presented in the work [28]
to perform power analysis. This tool is capable of observing the dynamic time variation of power
consumption and can analyze power changes in detail. Figure 11 shows the non-masked circuit and the two
masked circuits power consumption. The X-axis represents hundreds of testbenches of which each contains
2000 test vectors, and the Y-axis represents the power consumption. In the results, we focus on only the logic
and signal power consumption. Table 5 also shows the average power consumption for each circuit. The
results show the non-masked circuit consumes the least power since due to none of additional computation
for masking. The power consumption on series-connected masked adder looks almost the same as that on
compression-based masked adder.
Figure 11. Analysis results of power consumption
Finally, we perform a T-test on the results of the power consumption analysis to evaluate the
resistance against side-channel attacks. The results of the T-test for the two types of mask adders are shown
in Figure 12 and Table 6. Figure 12 shows the T-values for each test bench, with the security criterion of ±4.5
indicated by the red line. Table 6 shows the number of times T-values exceeded ±4.5 and the maximum T-
value among the 100 test cases. Figure 4 shows that without masking, the T-value exceeds the security
criterion in many cases, 23 times from Table 6. On the other hand, in the masked circuit, the T-value of the
series-connected masked adder stays between -4.5 and 4.5 in any case. The T-value of the compression-based
masked adder is clearly larger than that of the series-connected mask adder, and Table 6 shows that the T-
value exceeds the security criterion eight times. This result shows that the series-connected masked adder is
highly resistant to power analysis attacks.
Figure 12. The results of T-test

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Table 6. The number of T-values violating a security criterion (>|±4.5|)
Masks Adders No. of T-value over |±4.5| Maximum T-value
0-bit (Non-masked) Carry propagate adder 23 12.10
128-bit (Fully masked) Series-connected masked adder 0 3.07
Compression-based masked adder 8 6.35
4. POWER SIDE CHANNEL LEAKAGE ANALYSIS OF PARTIALLY MASKED ADDERS
In the previous section, we have compared the circuits with non-masked and full-masked in 128-bit
adders. In this section, unlike the previous section, we utilize the masks whose bit-widths of random numbers
are different (Random number is 32, 64 or 96 bits). We present how to design masks that use 32, 64 or 96
bits random numbers in subsection 4.1. Then, we conduct the same experiments as in section 3 for the
masked adders introduced in subsection 4.1 to evaluate power analysis attack resistance. The experiments
aim to explore the trade-off between the resource cost, power consumption, and side-channel attack
resistance.
4.1. Partially masked arithmetic adders
This subsection describes two methods of creating masks when random numbers are 32, 64, or 96
bits. In this study, masks are designed in two different ways for each bit of random numbers used. The first
method is called lower bit mask, in which random numbers are placed in the lower bits. The second method
is called distributed bit mask, which alternates random numbers and zeros. A total of six masks are prepared
by these two methods.
4.1.1. Lower n-bit mask
Figure 13 shows the structure of three masks. The adder uses the same circuit as in section 4, which
performs 128-bit addition. This method uses random numbers for the lower N-bits (N=32, 64, 96) and assigns
0 to the upper (128-N) bits. We prepare the following three masks:
- Lower 32-bit mask: Upper 96 bits in 128-bit are set to 0. The rest of lower 32 bits are assigned to a 0-1
random value R as shown in Figure 13(a).
random value R as shown in Figure 13(b).
random value R as shown in Figure 13(c).
(a)
(b)
(c)
Figure 13. Lower random masks (a) lower 32-bit mask, (b) lower 64-bit mask, and (c) lower 96-bit mask
4.1.2. Distributed n-bit mask
Second method is to alternately input 0 and a random number. Figure 14 shows the mask structures
when random numbers are 32-bit, 64-bit and 96-bit. For each bit, a mask is created by distributing a random
number and 0, starting with the least significant bit. We created the three masks:

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- Distributed 32-bit mask: A 0-1 random value R is set every four bits and there is the mask for 32-bit in
total as shown in Figure 14(a).
- Distributed 64-bit mask: A 0-1 random value R is set every two bits and there is the mask for 64-bit in
total as shown in Figure 14(b).
- Distributed 96-bit mask: 0 is set every four bits and the others are set to 0-1 random values 𝑅. The total
number of bits for the mask is 96-bit as shown in Figure 14(c).
(a)
(b)
(c)
Figure 14. Distributed random masks (a) distributed 32-bit mask, (b) distributed 64-bit mask, and
(c) distributed 96-bit mask
We synthesize masked adders the same as in the previous section. The results of the number of look-
up-tables (LUTs) and delay for each circuit are shown in Table 3. Distributed n-bit masks are denoted as
Dist. n-bit in the table. The best value for each bit number is shown in red. If the number of LUTs for the
masked circuits are larger than that for the non-masked circuit shown Table 5 since the masked circuits
require to mystify the intermediate variable by masking. In addition, in the series-connected masked adder
with the lower bits masked, the number of LUTs is increased as increasing the number of bits to mask. We
highlight the circuits with the smallest number of LUTs and the shortest delay. In the case of 32-bit masks,
the series-connected masked adder by the lower 32-bit mask uses 288 LUTs. In terms of the delay, the
compression-based masked adder by the lower 32-bit mask takes 10.268 ns. As shown in the table, it is found
that the trend has been observed in any case. Overall, the series-connected masked adder uses the smallest
number of LUTs, and the compression-based masked adder takes the shortest delay. We focus on the type of
masks, the lower-bit masked adders require fewer resources and have shorter delay than distributed-bit
masked adder.
4.3. Power analysis
The average power consumption of hundred test patterns for each adder is shown in Table 7. From
Table 7, the power consumption of the compression-based masked adder is larger than that of the series-
connected masked adder for any number of bits. This is due to the larger circuit area of the compression-
based masked adder. Compared to the masks, the lower-bit masking shows the smaller power consumption
than the distributed-bit masking. Thus, masks with upper bits tend to have higher dynamic power
consumption. Figure 15 shows the power consumption of the Lower n-bit masked adder and Figure 16 shows
the power consumption of the distributed n-bit masked adder. The X-axis represents hundreds of testbenches,
and the Y-axis represents the power consumption. Looking at lower-bit series-connected masked adders
which have the lowest power consumption, the average power consumption for 32-bit is 4283 µW, for 64-bit
is 6128 µW and for 96-bit is 7934 µW. As the Figure 15 and 16 illustrates, this trend is also seen in other
masked adders. To sum up, the power consumption increases if the number of bits for masking is large.

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Table 7. Synthesis results with regard to the number of LUTs, delay and power consumption
Masks Adders LUTs Delay (ns) Power consumption (µW)
0 bit
(Non-masked)
Carry propagate adder 128 8.470 699
Lower 32 bits Series-connected masked adder 288 11.048 4283
Dist. 32 bits Series-connected masked adder 512 11.494 4772
128 bits
(Fully masked)
Series-connected masked adder 384 11.048 9675
Figure 15. Power consumption of lower-bit masked adders
Figure 16. Power consumption of distributed-bit masked adders
The T-test was performed using the results of the power analysis obtained in subsection 4.3, and the
results obtained are shown in Table 8. Table 8 shows the number of times the T-value for each circuit
exceeded ±4.5 out of 100 test patterns and the maximum T-value. If the T-value is greater than ±4.5, the
circuit is considered less tolerant to power analysis attacks.
Table 8 shows that in the series-connected mask adder, the T-value exceeds ±4.5 32 times for the
lower 32-bit mask and 28 times for the distributed 32-bit mask, more than in the unmasked circuit, which

109
may compromise security. We now focus on the series-connected masked adder that use distributed masks.
When the mask is 32 bits, the T-value exceeds ±4.5 28 times, but as the number of bits in the mask increases
to 64, 96, and 128 bits, the number of times the T-value exceeds ±4.5 decreases to 16, 1, and 0 times. Also, as
the number of bits in the mask increases, the maximum T-value also decreases. This tendency is also seen in
adders using other masks. This result indicates that using a random number of 64 bits or more for masks
improves the attack resistance compared to an adder without masking. Also, the vulnerability decreases as
the number of random bits used for masking increases. Figures 16 and 17 show the results of comparing the
T-values of the adders for each type of mask. The X-axis shows the T-value and the Y-axis represents the
number of testbenches. The red line indicates the security standard. Figures 17 and 18 show that circuits with
non-mask or a mask of 32 bits greatly exceed the security standard. However, in fully masked circuits, T-
value stays within ±4.5 in many test cases. Comparing the results for each type of adder shows that the
series-connected masked adder on the left in both Figures 17 and 18 tends to have a smaller T-value overall
than the compression-based masked adder, indicating that it is more secure against power analysis attacks.
These results show that series-connected masked adders using 64 bits or more random numbers as
masks are more attack resistant than non-masked adders. However, in the case of 64-bit and 96-bit masks, the
T-value still exceeds ±4.5 in some cases and is not completely safe. Therefore, when the highest priority is
placed on safety, it is preferable to use the series-connected masked adder that uses 128 bits of random
numbers and is completely masked. On the other hand, if costs in terms of power consumption and number of
resources are more important than security, we use the series-connected masked adder with a smaller random
number such as 96 bits or 64 bits used for masking. By doing this, we can use circuits that are smaller area
and lower power than fully masked adders, and more secure than non-masked adders.
Table 8. The number of T-values violating a security criterion (>|±4.5|)
Masks Adders No. of T-values over |±4.5| Maximum T-value
0-bit
(Non-masked)
Carry propagate adder 23 12.10
Lower 32-bit Series-connected masked adder 32 12.26
Dist. 32-bit Series-connected masked adder 28 10.98
128-bit
(Fully masked)
Series-connected masked adder 0 3.07
Figure 17. T-value of lower-bit masked adders

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Figure 18. T-value of distributed-bit masked adders
5. CONCLUSION
This paper evaluates the resistance of masked adders against power analysis attacks and investigates
the effectiveness of masking. The results show that circuits without masking are vulnerable to attacks even
when the number of bits in the adder is small. And it was found that for masked adders, the greater the
number of bits in the mask, the better the attack. Comparison of performance showed that the series-
connected masked adder has a smaller circuit area and the compression-based masked adder is superior in
terms of delay time. In terms of safety, the series-connected masked adder was found to be safer than the
compression-based masked adder. Overall, the higher the attack resistance, the higher the power
consumption. In particular, the circuit area also increases as the number of bits increases for the series-
connected masked adder. Therefore, it is necessary to consider the type of adder and masking method
depending on whether safety or implementation cost is a priority. Future work will include a more detailed
analysis of the relationship between the internal structure of the masked circuit and its resistance to power
analysis attacks. We also plan to evaluate not only the adders introduced in this paper, but also other types of
circuits in the same way.
ACKNOWLEDGEMENTS
This work is supported partly by KAKENHI 20H00590, 20K23333, 21K19776 and 22K21276.
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BIOGRAPHIES OF AUTHORS
Yilin Zhao received her BE degree in electronic and computer engineering from
Ritsumeikan University in 2021. She is in the Master's degree program at Ritsumeikan
University. Her research interests include design methodologies for embedded systems. She
can be contacted at email: irin.cho@tomiyama-lab.org.

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Hiroki Nishikawa received his BE, ME and Ph.D. degrees from Ritsumeikan
University in 2018, 2020, and 2022, respectively. In 2022, he joined the Graduate School of
Information Science and Technology, Osaka University as an assistant professor. His research
interests include system-level design methodologies, design methodologies for cyber-physical
systems, and so on. He is a member of IEEE, IEICE, and IPSJ. He can be contacted at email:
nishikawa.hiroki@ist.osaka-u.ac.jp.
Xiangbo Kong received B.E. degree from Nankai University in 2012 and he
received M.E. and Ph.D degrees from Ritsumeikan University in 2018 and 2020, respectively.
In 2020, he joined the College of Science and Engineering, Ritsumeikan University as an
assistant professor. His research interests include artificial intelligence, image processing,
embedded system, etc. He is a member of IEEE and IPSJ. He can be contacted at email:
kong@fc.ritsumei.ac.jp.
Hiroyuki Tomiyama received his BE, ME, and DE degrees in computer science
from Kyushu University in 1994, 1996, and 1999, respectively. He worked as a visiting re-
searcher at UC Irvine, as a researcher at ISIT/Kyushu, and as an associate professor at Nagoya
University. Since 2010, he has been a full professor with the College of Science and
Engineering, Ritsumeikan University. He has served on program and organizing committees
for several premier conferences including DAC, ICCAD, DATE, ASP-DAC, CODES+ISSS,
CASES, ISLPED, RTCSA, FPL, and MPSoC. He has also served as an editor-in-chief for IPSJ
TSLDM; an associate editor for ACM TODAES, IEEE ESL, and Springer DAEM; and a chair
for the IEEE CS Kansai Chapter and IEEE CEDA Japan Chapter. His research interests
include, but are not limited to, design methodologies for embedded and cyber-physical
systems. He can be contacted at email: ht@fc.ritsumei.ac.jp.

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