=Paper=
{{Paper
|id=Vol-3101/Paper32
|storemode=property
|title=Using hash functions to protect critical messages from changes in risky computing systems
|pdfUrl=https://ceur-ws.org/Vol-3101/Paper32.pdf
|volume=Vol-3101
|authors=Andrzej Smolarz,Nadiia Pasieka,Andrzej Kotyra,Vasyl Sheketa,Mykola Pasieka,Svitlana Chupakhina,Petro Krul,Mykola Suprun
|dblpUrl=https://dblp.org/rec/conf/citrisk/SmolarzPKSPCKS21
}}
==Using hash functions to protect critical messages from changes in risky computing systems==
https://ceur-ws.org/Vol-3101/Paper32.pdf
Using Hash Functions to Protect Critical Messages from
Changes in Risky Computing Systems
Andrzej Smolarz1, Nadiia Pasieka2, Andrzej Kotyra1, Vasyl Sheketa3, Mykola Pasieka3,
Svitlana Chupakhina2, Petro Krul2 and Mykola Suprun4
1
Lublin University of Technology, Nadbystrzycka 38D, Lublin, 20 – 618, Poland
2
Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, 76000, Ukraine
3
National Tech. University of Oil & Gas, Ivano-Frankivsk, 76068, Ukraine
4
National Pedagogical Dragomanov University, Kyiv, 01601, Ukraine
Abstract
Nowadays, information security has become an integral part of risky digital operations in cyberspace.
To solve such problems associated with risky operations, the use of hash functions occupies one of the
key places among information security technologies in modern cryptography. After all, these crypto-
resistant functions process critical data of limited length while creating a small, fixed-size digital code
called a hash or digest. The classic use of risk-dependent crypto functions is to check the integrity of the
processed data, as well as authentication schemes for user messages. However, as the volume of risk-
dependent processed critical data grows, the criterion of hash function throughput comes to the fore.
Thus, SHA (Secure Hash Algorithm 3) is the latest member of the Secure Hash Algorithm family of
standards, released by NIST on August 5, 2015. Although SHA-3 belongs to the same series of standards,
it is internally different from the MD5-like structure of SHA-1 and SHA-2. The Secure Hash Algorithm is
considered one of the first generally accepted hashing standards and, according to the currently
published literature, is considered the fastest implementation of the SHA-512 (SHA-3 variant)
cryptographic algorithm, providing acceptable bandwidth for protecting risk-dependent critical data.
Keywords 1
Hash functions, security risk, cryptography, critical data, secure hash algorithm.
1. Introduction
The use of cryptographic hash functions to protect risk dependent critical data, are related to the
usual hash functions, which have additional properties, at the same time usual hash functions do
not necessarily have them. These functions convert the final input of an information data stream
to protect risk-dependent critical information into a small output of a fixed size, sometimes called
CITRisk’2021: 2nd International Workshop on Computational & Information Technologies for Risk-Informed Systems, September
16–17, 2021, Kherson, Ukraine
EMAIL: a.smolarz@pollub.pl (A.Smolarz); pasyekanm@gmail.com (N.Pasieka); a.kotyra@pollub.pl (A.Kotyra);
vasylsheketa@gmail.com (V.Sheketa); pms.mykola@gmail.com (M.Pasieka); cvitlana2706@gmail.com (S.Chupakhina);
krulp59@gmail.com (P.Krul); suprun62@ukr.net (M.Suprun)
ORCID: 0000-0002-6473-9627 (A.Smolarz); 000-0002-4824-2370 (N.Pasieka); 0000-0002-9442-6090 (A.Kotyra);
0000−0002−1318−4895 (V.Sheketa); 0000−0002−3058−6650 (M.Pasieka); 0000-0003-1274-0826 (S.Chupakhina);
0000−0002−5274−3215 (P.Krul); 0000-0002-4198-9527 (M.Suprun)
© 2021 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)
a summation. A good hash function has foreground image resistance, second foreground image
resistance, and strong collision resistance. Resistance to the forward image means that it is
computationally impossible to find any input that yields a digest equal to the predefined output.
Second-image robustness means that it should be computationally infeasible to find any second
input that has the same output as any given input. Anti-collision means that it is computationally
infeasible to find two different input hashes with the same output.
Hash functions can be divided into two categories: keyed and hunkered. Hash functions with a
key are used in message authentication schemes. Such functions accept not only the hashed data,
but also a second parameter, called a key. The hashing algorithm uses the actual data and the
provided key to create the hash.
A function without a key is usually used to check the integrity of the data. The raw data is
passed through the function and a summary of the results is stored. Later, a copy of the data is
hashed and the two hashes are compared. If they are the same, the original data and the copy are
the same for all intents and purposes. However, if they are different, the integrity of the copy
cannot be trusted because the data could have been altered due to transmission errors or, even
worse, by an external source for malicious purposes. A more detailed description and analysis of
the hash function can be found in [1].
Thus hash functions require more and more computational resources. And because of the
iterative nature of such functions, implementations of these algorithms cannot use computational
techniques such as parallel processing to significantly improve performance. General-purpose
processors are poorly suited to efficiently perform the basic operations required for a given hashing
algorithm. Hence, hardware implementations of such algorithms are being developed to improve
performance.
As new hash functions emerge, there must also be a way to compare them for authenticity. In
such comparisons it is crucial to distinguish between software and hardware implementations of
hash functions. Software implementations running on general-purpose processors are used for
many authentication protocols as well as for independent computing applications. Hardware
implementations created using dedicated circuits are typically used for devices that are impractical
or impossible to implement with software, such as embedded systems or high-speed network
devices. Runtime and memory usage are two critical metrics to consider when comparing software
implementations of hash functions. Thus, the lower the runtime and memory usage, the more
advantageous the hash function is. In hardware, runtime and total area are two important metrics
to consider. For this type of implementation, runtime can usually be reduced by increasing the
total area. This area can be calculated based on the physical size occupied by the final
implementation and the number of logic gates used to build it. A hardware implementation can be
used to achieve faster execution times than software can provide. Hardware devices such as
FPGAs can provide the highly optimized operations needed for hashing algorithms. Therefore,
such implementations are usually orders of magnitude better than software implementations.
2. Model analysis of cryptographic algorithms for hash functions
compression of critical messages
There is no paper discussing the hardware implementation of the Phash algorithm, but many papers
discussing the hardware implementation of SHA-512 have been published and Whirlpool
algorithm. The proposed cryptographic models are generally used for the process of obtaining the
maximum throughput of critical message compression by hashing functions. These
implementations are usually aimed at high throughput or efficient resource utilization [1, 3, 4, 7].
Often, it is impossible to know a priori which design choice for a given component will be the best
choice to achieve a particular design goal. Whenever possible, several descriptions and
implementations of specific components are provided. After implementing and executing an
algorithm using different components, it is possible to comment on the quality of a given
implementation, as it is related to achieving high throughput or low total area.
This publication contains information about currently available and existing hardware
implementations of SHA-512. Including descriptions and analysis of each implementation [2, 5,
6]. These publications describe the message expansion and compression steps in some detail. Most
of the implementations reviewed acknowledge the existence of a key fill phase, but do not include
details. Similarly, the hash update phase is partially mentioned, but its implementation is not
always correctly described. One of the reasons, in our opinion, for omitting the details of the fill
phase and the hash update phase is the hypothesis that the practical implementation of these phases
will not have a significant negative impact on the overall performance characteristic of the hash
function algorithm.
Simple Hash Function Implementation
Some of the first released hardware implementations of SHA-512 are described in scientific
publications [8, 9, 11, 13, 17]. In [19], the implementation of SHR(x) and ROTR(x) operations, used
in the extension and compression phase of the algorithm message processing, is discussed in detail.
Thus, a block of ROM (Read Only Memory) is used to store the constant variable Kt required for
the message compression phase. Several 64-bit adders and simple combinatorial circuits are used
to calculate these values, which are necessary for the algorithm. Using the 64-bit adder with five
inputs which is involved to calculate the time value T1, and the 64-bit adder with two inputs which
is involved to calculate the total time value T2. On this basis the functions Ch(x, y, z) and Maj(x, y, z)
are realized by simple combinational circuits.
A more detailed description of the SHA-512 implementation is given in [10, 14]. The
construction of the disclosure phase of the message hash function is shown in Figure 1.
Figure 1: Model design of message expansion stage iteration
So the advantage of the considered implementation is the reuse of memory registers. A simple
implementation requires would require eighty 64-bit registers to store all the necessary critical
data generated during the message expansion phase, but because of resource sharing only 16 such
registers and a multiplexer are needed. From the considered scheme we see that each of the sixteen
registers has a width of 64 bits, and the multiplexer is used to determine the time of loading the
first block of critical data in the register of the computing system. Thus the data output Wi from
the leftmost register of the circuit algorithm is used as input to the compression stage of the
generated message. As soon as the first block of critical data is loaded into all registers, the
multiplexer immediately returns the result of the specified calculation of the hash function in the
leftmost register. The considered design of the hash function algorithm at the message
compression stage in [1] is shown in Figure 2. Based on this scheme, the eight 64-bit registers
represent the intermediate values of the message hash, which will be used in the update phase after
the 80 iterative cycle of the compression phase [12, 15, 18]. For a more simplified understanding
of the proposed algorithm, the details of the implementation of the computational operations
SHR(x) and ROTR(x) are omitted. On this basis, we used two two-port Block RAMs to store the Kt
constants used in this iterative stage. Block RAMs are on-chip memory components which can be
instantiated and addressed like regular memory modules. The details of the adders used in this
implementation are also omitted in this publication.
Figure 2: Model design of message compression stage iteration
A more detailed implementation of the message expansion step diagram is shown in Figure 3. To
reduce the total number of additions to be performed on the critical path, it is crucial to use the
algorithm to compute the total Kt + Wt in the previous loop [16, 17, 21]. The Rkw register ensures
that the quantity is available during the correct iteration. The output of this register is used in the
intermediate step of message compression. The combination of CSA and CPA is used to minimize
the mathematical calculations and thus the delay that occurs when adding multiple 64-bit numbers
to the processing. If you only use cascade CPA, in this case the delay will be even longer. Since
the LUT Shift A and LUT Shift B blocks in this algorithm scheme are shift registers. They are
designed using the "shift register mode" CLB slices available in the Virtex FPGA. Thus they are
designed to significantly reduce the overall footprint while not affecting performance.
The design model of the message compression stage structure is shown in Figure 3. In this case,
the multiplexer automatically determines whether the current Kt+0 – Kt+7 values should be used
additionally. For these calculations, the multiplexer selects a value of zero for addition at all stages,
except for the last stage of compression of the desired message [20, 22, 24, 26]. The last iteration
of the model will additionally use the calculated current Kt+0 – Kt+7 value. Thus, the basic operation
of these multiplexers serves as a key step to update the hash of the message.
Figure 3: Model design of message expansion stage iteration
Based on this, the critical path in the compression phase of the proposed message must be further
transformed into seven complements. P Cs, CSA and CPA, which we use to optimize the
mathematical delay of this calculation. In this way, the parallel operations counter significantly
reduces the number of operations added by the model from five to three. Similarly, we use CSA
and CPA to replace the cascading CPA in order to significantly minimize the computational delay.
To do this, we need to significantly reduce the total area of the adder. Based on this, in addition to
using the traditional 64-bit adders for calculations, 16 and 32-bit adders for the necessary additions
are also involved
A more advanced implementation model
Figure 3 shows only a part of the SHA-512 algorithm implementation model. In this case, the
phase of calculating the required message is doubled. The peculiarity for the realization of this
algorithm step is that six inputs are involved, from b to d and from f to h, which are fed directly to
the output, and only two inputs, a and e figure 4, require additional mathematical calculations,
which directly delay the work of the proposed algorithm. Thus deployment allows us to parallelize
the process of mathematical calculations by performing two iterations simultaneously. For the
same reason, the algorithm of the necessary message expansion stage is also subject to the process
of modification to obtain the next two values of Wt almost simultaneously.
The design model of the necessary message compression process in two iterations is presented
in figure 4, and the thickened line shows the critical path of mathematical calculations, which
create delays in message compression [23]. On this basis we can notice that when message
compression step is extended then working frequency of the algorithm is reduced approximately
by half, thus negating the purpose of expansion. On this basis, it should be noted that in order to
significantly increase the operating frequency of compression of the necessary message, it is
necessary to perform part of the operations in parallel. The study proposes a quasi-conveyor
implementation of the SHA-512 mathematical encryption algorithm. For this purpose, a pipeline
approach is used in the phase of compression of the necessary message, and since it forms the key
delay on the execution of the algorithm [25]. Then the disclosure phase of the main necessary
message has been optimized, so as to significantly reduce the delay of a single mathematical
calculation step. Thus, in order to significantly reduce the delay in the pre-math phase, it is
necessary to use delay balancing technology [27]. Based on this, CSA and CLA must be used to
make the necessary critical additions [28]. Analyzing the presented model design scheme figure 3
we can notice that the section τ is influenced by variables Kt and Wt the section τt-1 is indirectly
influenced by variables Kt-1 and Wt-1 through τ.
Figure 4: Design two iterations of message compression stage iteration
Based on the operation of the cryptographic algorithm at the stage of reading the last pair of values
Kt and Wt it is necessary to carry out three consecutive clock cycles for the final completion of the
critical message compression stage. Thus, at the first stage of the cryptographic algorithm for
critical message compression registers are used to transmit new values. Which is used in the
second step of generating the final values from E to H. And the third step of the execution of the
cryptographic algorithm performs the generation of values from A to D. Also note that in the third
step of the algorithm the variables from E to H must not be synchronized in any way.
Thus, for effective delay balancing is used to significantly reduce the critical path of
mathematical calculations still in the critical message expansion phase, but this method is not quite
suitable for its use in combination with the unpacking process, so a modified algorithm was
developed to implement the message expansion phase. Based on this effective deployment of this
cryptographic model architecture, the values of the variables Wt and Wt+1 are required to execute
the algorithm in one clock cycle. This usually uses sixteen sixty-four bit registers, and in a
modifying algorithm, up to eight registers, but this doubles the width to one hundred and twenty-
eight bits. And the first sixty-four-bit word of the new register is used to calculate the variable
value Wt, and the second sixty-four-bit word is used to calculate the value Wt+1. The
combinatorial logic of the message expander was copied to calculate the variable values Wt and
Wt+1 in one loop of the algorithm. To do this, the multiplexer selection of one hundred and twenty-
eight bits instead of sixty-four bits was changed. In this case the outputs of the variable values Wt
and Wt+1 are fixed, to ensure that they do not affect the critical delay path of the mathematical
calculations.
Thus, after the completion of the cryptographic algorithm at the 80th iteration of the critical
message compression stage, the created hash code must be updated. In the classical version, this
requires eight 64-bit adders, but we consider a hash modification scheme which uses only two
adders. Assuming that, most hash variables are only moved to create a new output sequence, and
hence, there was definitely an interdependency between the hash variables. Thus, using this
interdependence, only two adders are needed to complete the critical message compression
cryptographic algorithm to generate six partial results of hash modification iterations, and the other
two value variables are calculated differently.
Using these interdependencies, the partial results of the hash modification iterations can also
be determined. Based on the above, only two adders can also be used to perform the necessary
number of calculations.
3. Practical implementation of the proposed hash function
compression algorithm for critical message compression in risk
dependent computer systems
In order to analyze how a cryptographic algorithm of hash function compression of critical
messages in risk dependent computer systems will behave, a program model was developed, on
which the testing of Figure 5-8 was carried out.
Figure 5: File with initial data
Figure 6: Data file after SHA-512 hash function
Figure 7: File with decoded data
Figure 8: Model program hash function compression of critical messages
In this paper, the informational and technological impact of risk protection requirements in relation
to critical data for regulation on the software development process has been evaluated. In doing
so, the main changes in the hashing of information flows to which this process is defined and how
to be prepared for them are described. It is prepared for the division of the critical risk-dependent
personal data of the users into ordinary and special categories.
The way and the reasons for their collection, processing and disclosure are explained. In
addition, it is necessary to ensure the security of these data, to prevent their leakage outside the
organization where they are stored. This can cause damage to the data subject and lead to fines of
considerable magnitude.
4. Conclusion
Conducting a critical analysis of the use of cryptographic hash functions to protect risk-dependent
critical data, as well as to quickly compress critical messages in risk-dependent computer systems,
we can argue that the use of mathematical algorithms has significant promise for information
security technologies in modern cryptography. After all, these crypto-resilient functions for
protecting risk-dependent data process critical information of limited length while creating a small
digital code of fixed size. Along with classic applications of these crypto-resilient hash functions,
such as verifying the integrity of the data being processed, and authentication schemes for critical
user messages. Research has shown that with a significant increase in the amount of critical
information being processed to protect risk-dependent critical data, the hash function's throughput
criterion comes to the fore. Therefore, information security research today to protect risk
dependent critical data has become an integral part of risky digital operations in cyberspace, and
solving such problems with hash functions occupies one of the key places in modern cryptography.
Thus, the modification of hash algorithms for protection of risk-dependent critical data, in order
to increase the throughput is extremely relevant.
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