=Paper= {{Paper |id=Vol-3187/short6 |storemode=property |title=Improving the RC5RA Algorithm’s Crypto Resistance for Embedded Computers (short paper) |pdfUrl=https://ceur-ws.org/Vol-3187/short6.pdf |volume=Vol-3187 |authors=Andrii Sahun,Vladyslav Khaidurov,Pavlo Gikalo |dblpUrl=https://dblp.org/rec/conf/cpits/SahunKG21 }} ==Improving the RC5RA Algorithm’s Crypto Resistance for Embedded Computers (short paper)== https://ceur-ws.org/Vol-3187/short6.pdf

Improving the RC5RA Algorithm’s Crypto Resistance
for Embedded Computers
Andrii Sahun1, Vladyslav Khaidurov2, and Pavlo Gikalo3
1
National University of Life and Environmental Sciences of Ukraine, 15 Heroyiv Oborony str., 03041, Kyiv,
Ukraine
2
Institute of Engineering Thermophysics of NAS of Ukraine, 2а Mariyi Kapnist str., 03057, Kyiv, Ukraine
3
National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” 37 Peremohy str., 03056,
Kyiv, Ukraine

Abstract
An approach to increase the cryptographic stability of the RC5RA classical cryptographic
algorithm. The proposed approach does not increase the computational complexity of the
RC5RA algorithm due to the fact that it does not involve increasing the encryption rounds, key
or block length. The approach to crypto resistance improvement of this algorithm is based on
the use of nonlinear round shift functions. These functions are continuous throughout the entire
range of their existence. The obtained model of the RC5RA crypto system demonstrates
resistance to encryption of encrypted data up to 210 times (using differential analysis) at 14
rounds of encryption, at 12 rounds—the difference in crypto resistance of the modified RC5RA
(unmodified version) is 24. The modified model of the RC5RA crypto system does not show
an increase in computational time (compared to the base RC5RA). In the obtained RC5RA
crypto system there are no collisions and statistical correlations between the blocks of incoming
messages and outgoing blocks.

Keywords 1
Block cipher, symmetric encryption, nonlinear shift function, RC5RA, symmetric block cipher
cryptanalysis.

1. Introduction
Data encryption in computer network channels can be implemented at any of the seven levels of the
OSI model [1]. Encryption is more often implemented either at the upper (application) or lower
(channel, network) levels of the OSI model. In addition to "useful" information traffic, information
about the routing of the message, information about the routing protocol are also encrypted. In this case,
the network switch must decrypt the data stream in order to process it correctly. Then the switch
encrypts the traffic again for transmission to another network switch. For this reason, «Internet of
Things» networks, especially those based on low-power controllers (Arduino, NodeMCU, ESP32), use
special methods of information security to protect network traffic. Firewalls are most often used for this
purpose. It should be noted that channel encryption in such cases is an effective means of information
protection [2].
Despite the high efficiency, channel encryption has disadvantages:
– the cost of implementing encryption at the channel level increases sharply with increasing network
size;
– the data must be encrypted each time it is transmitted over a network channel.
Trends in the development of cryptographic protection (for example, the hardware implementation
in the computing cores of the microprocessor of the AES encryption algorithm [3]) indicate the
prospects for the implementation of block XOR-ciphers. Thus, a large number of means of
cryptographic computer protection is implemented in the form of hardware units or devices.

CPITS-II-2021: Cybersecurity Providing in Information and Telecommunication Systems, October 26, 2021, Kyiv, Ukraine
EMAIL: avd29@ukr.net (A. Sahun); allif0111@gmail.com (V. Khaidurov); p.gikalo@gmail.com (P. Gikalo)
ORCID: 0000-0002-5151-9203 (A. Sahun); 0000-0002-4805-8880 (V. Khaidurov); 0000-0002-8058-8267 (P. Gikalo)
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)

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Hardware encryption has a higher speed. For example, the RC5 cryptographic algorithm consists of
a large number of modulus arithmetic operations that are performed on plaintext bits. However, modern
microcontrollers are practically not adapted to perform efficient bit crypto transformations. The creators
of the RC5 cryptographic algorithm provided that it could be easily implemented by both hardware and
software methods, which allows to protect network traffic for Internet of Things (IoT) technology.
Although at the moment firewalls and some other means and technologies of data protection are more
often used for this [4–7]. The algorithms of the RC5 family provide for the division of the message into
a certain number of parts of a fixed size. Each of these parts undergoes a separate encryption procedure.
This simplifies the encryption task. The given practical capabilities of the RC5 algorithm can confirm
that the block symmetric RC5 encryption algorithm has prospects in IoT. It provides prospects for
enhancing the quality of encryption and reducing the computational load on the computing mechanisms
of microcontrollers [3, 8].
In their work [3], the authors of the RC5 crypto algorithm note that the proposed algorithm can be
easily implemented in hardware. At the same time, the ways of enhancing its cryptographic power
without increasing the computational complexity are also proposed [8]. This feature of RC5 is important
in its application and is a convenient basis for modification [3]. Although, the classical algorithm is
built on one shift function, it can be modified by using several sequentially nonlinear shift functions
[3, 9].

2. Analysis of the Principle of Operation and Parameters of the RC5 Algorithm
Some of the main parameters of the RC5 algorithm are variable parameters [3, 8]. As a basic
algorithm for modification, we choose its RC5RA variation [10]. In it, the cyclic shift occurs by a
variable number of bits, which depends on the algorithm round number, determined by a function f ().
This function processes all bits of another sub block as an input value. The scheme of cryptographic
transformation in rounds of the RC5RA algorithm is shown in Figure 1. In the algorithms of the RC5RA
family, in addition to the secret key, there are some others, namely:
– the size of the word w (in bits). The algorithm encrypts blocks of two words (hereinafter referred
to as A and B respectively). Valid values of w are natural numbers 16, 32 or 64. The recommended
word size is 32 bits;
– the number of rounds of the R-algorithm (any integer in the range from 0 to 255 inclusive);
– secret key size b (in bytes) – variable value (any integer in the range from 0 to 255 inclusive).
When encrypting for two blocks A and B in the binary representation, the RC5 algorithm is executed
in such a way that before the first encryption round the operations of superimposing the extended key
S on the encrypted data according to expression (1) are performed.
The maximum RC5 key size for RC5 family algorithms is 2040 bits. An example of the formation
of the extended key S is given in [1]. The RC5RA algorithm performs a cryptographic conversion of
the kind:

𝐴𝑖+1 = ((𝐴𝑖 ⊕ 𝐵𝑖 ) << 𝑓(⋅)) + 𝑆2𝑖 , 𝐵𝑖+1 = ((𝐵𝑖 ⊕ 𝐴𝑖 ) << 𝑓(⋅)) + 𝑆2𝑖+1 . (1)

The proposed approach to improvement involves not so much a modification of the algorithm, but an
increase in its crypto resistance by choosing the nonlinear shift functions used in (1). This function, in
turn, is the basis for modifying the algorithm. Obviously, the main point for improving the RC5RA is
the choice of nonlinear functions of the form 𝑓(𝐾, 𝑟), where the 𝐾 – round key and 𝑟 – number of the
round. The using of the following functions is proposed as nonlinear functions:
1) the first shift function:
𝑤
(2)
𝑓(𝐾, 𝑟) = |𝑟 + [𝑤 𝑠𝑖𝑛 (𝑤𝑟 ∑ 𝐿𝑏𝑖𝑡𝑠 )]| 𝑚𝑜𝑑 𝑤,
𝑠=1
where 𝑚 = 𝑟 2 𝑚𝑜𝑑 𝑤;
𝑟 – round number;
𝑤 – the length of half of the coded block;

269
[𝑥] – an integer part of the x number;
𝐿𝑚 – is the length of the initial message block (plaintext) in the encryption round;
𝐿𝑏𝑖𝑡 – a binary representation of the symbol Lm encoded by the symbol of the word 𝐾, the length of
which is 𝑤 in a bit representation.

<< f ()
<
K2 +
*r

<< f ()
<
K2* +
r+11

Figure 1: Scheme of cryptographic transformation in RC5RA algorithm rounds

2) the second offset function:
𝑤
𝑤 (3)
𝑓(𝐾, 𝑟) = [𝑤 𝑒𝑥𝑝 (− | 𝑠𝑖𝑛 (𝑤𝑟 ∑ 𝐿𝑏𝑖𝑡𝑠𝑚𝑠 )|)] 𝑚𝑜𝑑 𝑤.
10
𝑠=1

3) the third offset function:
𝑤
𝑤 (4)
𝑓(𝐾, 𝑟) = [3𝑟 |𝑡ℎ ( 𝑠𝑖𝑛 (𝑤𝑟 ∑ 𝐿𝑏𝑖𝑡𝑠𝑚𝑠 ))|] 𝑚𝑜𝑑 𝑤.
10
𝑠=1

4) the fourth offset function:
𝑤 𝑤
(5)
𝑓(𝐾, 𝑟) = (|𝑟𝑤 ∑ 𝐿𝑏𝑖𝑡𝑠𝑚𝑠 + [𝑟𝑤 𝑐𝑜𝑠 (3 ∑ 𝐿𝑏𝑖𝑡𝑠𝑚𝑠 + 2𝑟)]|) 𝑚𝑜𝑑 𝑤.
𝑠=1 𝑠=1

5) the fifth offset function:

270
𝑤 𝑤
(6)
𝑓(𝐾, 𝑟) = (|∑ 𝐿𝑏𝑖𝑡𝑠𝑚𝑠 + [𝑙𝑜𝑔2 (1 + 𝑟𝑤 |∑ 𝐿𝑏𝑖𝑡𝑠𝑚𝑠 |)] 𝑚𝑜𝑑 𝑟|) 𝑚𝑜𝑑 𝑤.
𝑠=1 𝑠=1

The given nonlinear shift functions (2)–(6) have a range of admissible values for the whole period
of their existence. This is necessary to form the coefficients in the encryption rounds.

3. Formation of Test Samples for the RC5RA Algorithm
The implementation of a modified algorithm requires test data for encryption. When forming test
samples, we will assume that for the RC5 cipher or RC5RA modification there are no confirmed direct
relationships between the sizes/multiplicities of the sample text files with open text and the obtained
encryption result. And all the more there is no influence of these parameters on crypto resistance of the
received encrypted text or emergence of collisions. Files containing only integer data were used for test
samples. When encoding graphics and texts using known and current coding systems, we obtain a file
in the form of a sequence of integers. Thus, text test datasets are 81 to 1968 kilobytes long, and graphical
data sets are 351 to 3412 kilobytes long. Text data are files with English characters. Graphic data is a
set of simple images of standard formats, such as the jpg format. Encryption keys are generated using
a pseudo-random number generator with modular arithmetic. In this case, the keys are formed
immediately in the bit representation. 10 keys are generated for each input data set.

4. Application of a RC5RA Algorithm’s Modification
A software application in the Matlab modeling environment was created to determine the parameters
of the obtained RC5RA modification. The program interface provides the ability to change the
encryption parameters of the modification of the RC5 algorithm. To test the obtained modification of
the RC5RA algorithm and obtain the results of its work, identical data of key parameters, encryption
rounds and function numbers of each series of test samples were used. A sequence of different bits (16,
32, 64 bits) was used as the encryption key. The key sequence was generated by a standard built-in of
the Matlab programming language congruent pseudo-random number generator.
The results obtained for modifying the RC5RA using the proposed shift functions (2)–(6) for
different parameters of the algorithm are shown in Figures 2–5.
Text data encryption
2
Run-time, sec

0
80 580 1080 1580
16 32 64 File size, Kb

Figure 2: Text data encryption time at r = 16 and k = 16, 32, 64 bits
Text data dencryption
2
Run-time, sec

0
80 580 1080 1580
16 32 64 File size, Kb
Figure 3: Text data decryption time at r = 16 and k = 16, 32, 64 bits

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4 Graphical data encryption

Run-time, sec
2

0
350 850 1350 1850 2350 2850 3350

16 32 64 File size, Kb
Figure 4: Graphic data encryption time at r = 16 and k = 16, 32, 64 bits

Graphical data decryption
4
Run-time,sec

0
350 1350 2350 3350
16 32 64 File size, Kb

Figure 5: Graphic data decryption time at r = 16 and k = 16, 32, 64 bits

The data in Figures 2–5 are obtained with the classical round shift and the use of the five nonlinear
functions proposed above. The results of the work obtained as a result of processing the test samples
by the modified RC5RA algorithm are given in Tables 1, 2. Coincidences appear on all used test
samples.

Table 1
The time of encryption and decryption of text files with the number of rounds r = 16
File size, Kbytes Program run-time, File size, Kbytes Program run-time,
seconds: Encryption/decryption seconds:
Encryption/decryption w=16/w=16 Encryption/decryption
w=16/w=16 w=16/w=16
81 0,17 / 0,20 0,24 / 0,20 0,34 / 0,31
439 0,39 / 0,35 0,55 / 0,56 0,78 / 0,78
445 0,40 / 0,35 0,56 / 0,52 0,79 / 0,83
525 0,43 / 0,42 0,61 / 0,64 0,86 / 0,81
601 0,46 / 0,48 0,65 / 0,68 0,92 / 0,93
631 0,47 / 0,49 0,67 / 0,70 0,94 / 0,92
662 0,48 / 0,49 0,68 / 0,73 0,96 / 1,00
916 0,57 / 0,57 0,80 / 0,81 1,13 / 1,13
959 0,58 / 0,53 0,82 / 0,86 1,16 / 1,14
1029 0,60 / 0,62 0,85 / 0,88 1,20 / 1,20
1244 0,66 / 0,64 0,93 / 0,90 1,32 / 1,37
1406 0,70 / 0,72 0,99 / 0,95 1,40 / 1,42
1684 0,77 / 0,77 1,09 / 1,07 1,54 / 1,51
1968 0,83 / 0,87 1,17 / 1,17 1,66 / 1,61

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Table 2
Encryption and decryption time of graphic file modules at the number of rounds r = 16
File size, Kbytes Program run-time, File size, Kbytes Program run-time,
seconds: Encryption/decryption seconds:
Encryption/decryption w=16/w=16 Encryption/decryption
w=16/w=16 w=16/w=16
351 0,35 / 0,32 0,50 / 0,53 0,70 / 0,72
446 0,40 / 0,39 0,56 / 0,60 0,79 / 0,78
465 0,40 / 0,41 0,57 / 0,54 0,81 / 0,84
565 0,45 / 0,44 0,63 / 0,62 0,89 / 0,93
789 0,53 / 0,54 0,74 / 0,73 1,05 / 1,03
817 0,54 / 0,49 0,76 / 0,71 1,07 / 1,08
1298 0,67 / 0,70 0,95 / 0,91 1,35 / 1,37
1600 0,75 / 0,79 1,06 / 1,08 1,50 / 1,47
1825 0,80 / 0,83 1,13 / 1,10 1,60 / 1,59
2169 0,87 / 0,84 1,23 / 1,27 1,74 / 1,77
2288 0,90 / 0,94 1,27 / 1,28 1,79 / 1,79
2379 0,91 / 0,95 1,29 / 1,34 1,83 / 1,86
3273 1,07 / 1,08 1,52 / 1,54 2,14 / 2,18
3412 1,09 / 1,06 1,55 / 1,52 2,19 / 2,22

The Tables 1, 2 show the obtained time parameters of the modified version of the RC5RA algorithm
in the mode of encryption and decryption of graphic information with the number of rounds r = 16 and
different values of the w-parameter.

5. Cryptanalysis of the Resulting RC5RA Modification
In order to determine the value of crypto resistance of the obtained modification of the RC5RA
crypto algorithm using the above-mentioned shift functions, a classical differential analysis was used
[11–13].
The test data set (texts) consisted of the first 5 characters of the Latin alphabet. These specially
prepared texts contained 2 and 4 consecutive symbols. A "differential" was calculated for different pairs
of texts from this sample. On the basis of the received "differential" the estimation of "differential" of
other pairs of encrypted texts was carried out. The model on the basis of which the cryptanalysis of the
received texts was carried has the form of (7):

1 1 1 1 (7)
𝑆(𝑅𝐶5𝑅𝐴) = + + ≈ .
296 1 296 296 2 92 1 5
(1 + )⋅ (1 + ⋅ 2) (1 + ⋅ 23 ) (1 + 88 ) ⋅ 3
272 211 272 292 2 2

The layout of the software interface, which performs cryptanalysis of the obtained modification of
RC5RA is shown in Figure 6.

273
Figure 6: Layout of the software interface, which performs cryptanalysis of the obtained RC5RA
modification

Cryptanalysis was performed with the number of rounds of RC5RA modifications from 10 to 14, as
shown in Table 3. The number of plain texts required to hack the modified RC5RA algorithm is
estimated.

Table 3
Number of input (simple) texts for cryptanalysis
Number of rounds / r=10 r=11 r=12 r=13 r=14
Number of nonlinear
function
The first function 246 250 256 262 280
The second function 246 252 258 266 288
46
The third function 2 254 260 266 290
46
The fourth function 2 254 262 266 292
The fifth function 246 256 264 268 296

The result of cryptanalysis of the encrypted text (Table 3) is considered successful when the
evaluation of the "differential" receives a limit value of 25%. This means that with a probability of 0.25
with such structure of data, you can open half of the key or the whole key. Based on the results shown
in Table 3 (by number of texts), when implementing this algorithm on low-power microcontrollers in
IoT technology, the recommended number of rounds should not be less than 11. Otherwise, the crypto
resistance index will not be satisfactory [13].

6. Conclusion
As a result of the analysis and generalization, the answer to the question of the influence of the
nature of the round shift in RC5 on increase of the crypto resistance of this crypto algorithm was
partially obtained [11].
As can be seen in Table 3, the best values of crypto resistance are demonstrated by the modified
algorithm for those functions whose variance of output values is most homogeneous. Selection of a
"strong" nonlinear shift function for the RC5RA improvement reduces the number of rounds to 10,
while the encrypted message will be well protected from differential cryptanalysis. At the same time,
the computational complexity of the algorithm implementation remains comparable to the classic
version of RC5RA.

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7. References
[1] ITU-T Recommendations. ITU-T X.200, Committed to Connecting the World, 1994. URL:
https://www.itu.int/rec/T-REC-X.200-199407-I.
[2] R. L. Rivest, The RC5 Encryption Algorithm, in: Proceedings of the Second International
Workshop on Fast Software Encryption (FSE) 1994, pp. 86–96. URL: http://people.csail.mit.edu/
rivest/Rivest-rc5rev.pdf.
[3] S. Gueron, White Paper: Intel Advanced Encryption Standard (AES), New Instructions Set,
Revision 3.01, 2012. URL: https://software.intel.com/content/dam/develop/external/us/en/
documents/aes-wp-2012-09-22-v01-165683.pdf.
[4] A. Blozva, et al., IoT Devices Integration and Protection in available Infrastructure of a University
computer Network, Journal of Theoretical and Applied Information Technology 99(08) (2021)
1820–1830.
[5] V. Lakhno, et al., The information technologies in the tasks of planning of smart city development,
Journal of Theoretical and Applied Information Technology 99(14) (2021) 3645–3662.
[6] V. Lakhno, et al., Methodology for assessing the effectiveness of measures aimed at ensuring
information security of the object of informatization, Journal of Theoretical and Applied
Information Technology 99(14) (2021) 3417–3427.
[7] V. Lakhno, et al., Development of a Model for Choosing Strategies for Investing in Information
Security, Eastern-European Journal of Enterprise Technologies 2(3) (2021) 43–51.
doi:10.15587/1729–4061.2021.228313.
[8] O. Elkeelan, A. Olabisi, Performance Comparisons, Design, and Implementation of RC5
Symmetric Encryption Core using Reconfigurable Hardware, Journal of Computers 3(3) (2008)
48–55.
[9] T. Zhovnovach, et al., Modification of RC5 cryptoalgorythm for electronic data encryption
systems, Ukrainian Scientific Journal of Information Security 25(3) (2019) 138–143.
doi:25.10.18372/2225-5036.25.14458.
[10] S. Panasenko, Algorithms are encrypted, Special reference, BHV, Sankt-Peterburh, 2009. (In
Russian).
[11] A. Biryukov, E. Kushilevitz, Improved cryptanalysis of RC5, in: K. Nyberg (Eds.), volume 1403
of Lecture Notes in Computer Science. Advances in Cryptology – Eurocrypt, Springer, Berlin,
Heidelberg, 1998. doi:10.1007/BFb0054119.
[12] B. S. Kaliski, Y. L. Yin, On Differential and Linear Cryptanalysis of the RC5 Encryption
Algorithm, in: D. Coppersmith (Eds.), vol. 963 of Lecture Notes in Computer Science. Advances
in Cryptology, CRYPTO, Springer Verlag, Berlin, Heidelberg, 1995. doi:10.1007/3-540-44750-
4_14.
[13] L. R. Knudsen, W. Meier, Differential Cryptanalysis of RC5, European Transactions on
Telecommunications 8(5) (1997) 445–454.

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