Sign-Then-Encrypt Scheme with Cramer-Shoup Cryptosystem and

Dissanayake Digital Signature

Rahmad Bahri

, Mohammad Andri Budiman

and Benny Benyamin Nasution

Master of Informatics Program, Universitas Sumatera Utara, Medan, Indonesia

Faculty of Computer Science and Information Technology, Universitas Sumatera Utara, Medan, Indonesia

Politeknik Negeri Medan, Medan, Indonesia

Keywords:

Signcryption, Dissanayake, Cramer-Shoup, Running Time, Avalanche Effect.

Abstract:

Exchanging information in the era of Internet-based technology still has security violations such as disclosure,

modiﬁcation, or destruction that make everyone worry about the exchange of information. The Dissanayake

digital signature is part of asymmetric cryptography based on the factorization of prime numbers and has

interesting mathematical properties. The property of such mathematics is that the sum of 2 odd numbers is a

multiple of 4. The Dissanayake digital signature does not generate signatures directly through messages. The

Cramer-Shoup algorithm is an asymmetric cryptographic algorithm that proved to be the ﬁrst effective scheme

to withstand Adaptive Chosen Ciphertext Attack (ACCA) attacks compared to existing cryptographic systems.

The Cramer-Shoup algorithm is an extension algorithm of the Elgamal algorithm. This paper will implement

a sign then-encrypt scheme using Dissanayake digital signature and Cramer-Shoup algorithm and analyze

algorithms based on execution time and the avalanche effect. Based on simulation results, the characters’

length affects the execution time. The result of the process shows the length of the character linear with

execution time. From the results of the avalanche effect simulation, Dissanayake digital signature got the

average value of the avalanche effect of 51%, and the Cramer-Shoup algorithm got the average value of the

avalanche effect of 49%. Implementing the sign-then-encrypt scheme can maintain security by encrypting and

guaranteeing authenticity by adding a digital signature.

1 INTRODUCTION

Protecting data from disclosure, modiﬁcation, or

destruction is essential in the development of to-

day’s technological era. The number of security

breaches that continues to increase makes everyone

who communicates through the global network (Inter-

net) worry about protecting their data. With the cur-

rent development of technology, computer security is

needed because computer security rests on conﬁden-

tiality, integrity, and availability (Stallings and Bauer,

2012; Manna et al., 2017). —many techniques in pro-

tecting data at this time by designing a sound com-

puter security system—can be used in cryptography

(Panhwar et al., 2019). Cryptography is a technique

that relies on mathematics to secure information such

as conﬁdentiality, integrity, and entity authentication.

Conﬁdentiality, integrity, and authenticity are the ba-

sic requirements of asymmetric cryptography (Abood

and Guirguis, 2018; Molk et al., 2021; Genc¸o

glu,

2019).

Asymmetric cryptography, or public key cryptog-

raphy, has two keys (Public Key and Private Key)

used in the implementation process (Hossain et al.,

2013). In 1976, Whitﬁeld Difﬁe and Martin Hellman

publicly introduced the concept of public key cryp-

tography (Lydia et al., 2021). Asymmetric crypto-

graphic algorithms use two keys to perform the en-

cryption and decryption process. Asymmetric cryp-

tography distributes public keys by publishing and

private keys stored by their owners or kept secret

(Khan et al., 2018; Maqsood et al., 2017).

Many security schemes have been implemented

by researchers in the ﬁeld of cryptography, one of

which is signcryption, a scheme to achieve conﬁden-

tiality and authenticity (Elkamchouchi et al., 2018;

Kasyoka et al., 2021). In this case, conﬁdentiality is

achieved by encryption schemes on asymmetric cryp-

tography, while authenticity can be achieved by digi-

tal signature schemes (Pandey, 2014),(Matsuda et al.,

2009).

One of the asymmetric cryptographic algorithms

Bahri, R., Budiman, M. and Nasution, B.

Sign-Then-Encrypt Scheme with Cramer-Shoup Cryptosystem and Dissanayake Digital Signature.

DOI: 10.5220/0012444900003848

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 3rd International Conference on Advanced Information Scientiﬁc Development (ICAISD 2023), pages 131-138

ISBN: 978-989-758-678-1

131

that can be used is Cramer-Shoup, a modern crypto-

graphic algorithm(Jain, 2017). Compared to the cur-

rent cryptographic systems, Cramer-Shoup proved the

ﬁrst effective scheme without Adaptive Chosen Ci-

phertext Attack (ACCA) attacks (Liu et al., 2014).

The Cramer-Shoup algorithm is an extension algo-

rithm of the Elgamal algorithm. The Cramer-Shoup

algorithm has additional elements to guard against se-

curity attacks.

One of the digital signature schemes that can be

used is the Dissayanke algorithm. The Dissayanake

digital signature scheme algorithm is part of an asym-

metric cryptographic algorithm. There are two main

functions: forming digital signatures (signature gen-

eration) and checking or verifying the validity of

digital signatures (signature veriﬁcation). The Dis-

sayanake algorithm is a very fast and simple digi-

tal signature scheme, similar to RSA digital signa-

ture, which uses prime number factorization. This

digital signature scheme indirectly creates a signature

from the message directly and adds a hash function to

strengthen the scheme (Dissanayake, 2019)

There are parameters for analyzing the security

of a cryptographic algorithm, one of which is the

avalanche effect, which is a value that indicates that

small changes made to the plaintext or key will cause

signiﬁcant changes in the resulting ciphertext. The

avalanche effect value, greater than 0, states a change

between the plaintext sender and the plaintext recip-

ient by looking at the number of different bits in the

plaintext. Cryptographic algorithms that can have a

signiﬁcant avalanche effect value, then the level of se-

curity in an algorithm can be said to be good.

This paper will apply a signcryption scheme with

the Dissanayake digital signature scheme algorithm

and the Cramer-Shoup algorithm. The signcryption

security scheme to be used is the sign-then-encrypt

method. To measure the security level of the scheme

developed, researchers will use the Avalanche effect

2 LITERATURE REVIEW

2.1 Cryptography

Cryptography is a technique that relies on mathemat-

ics to secure information such as conﬁdentiality, in-

tegrity, and entity authentication (Vollala et al., 2021).

Cryptographic techniques are used for encoding by

hiding or encoding data (Rachmawati and Budiman,

2018). Encryption and decryption are important cryp-

tography processes. Converting plaintext into cipher-

text is called encryption and vice versa because de-

cryption is converting ciphertext into plaintext.

Figure 1: Working of Encryption and Decryption.

2.2 Asymmetric Cryptography

In 1976 Whitﬁeld Difﬁe and Martin Hellman pub-

licly introduced the concept of public key cryptogra-

phy (Lydia et al., 2021). Asymmetric cryptography,

or public key cryptography, has two keys (public key

and private key) used in the implementation process

(Vollala et al., 2021). Asymmetric cryptography dis-

tributes the public key by publishing, and the private

key is stored by the owner or kept secret. Some ex-

amples of asymmetric algorithms are Cramer-Shoup,

Elgamal, RSA, and others.

Figure 2: Working of Asymmetric Cryptography.

2.3 Digital Signature

The digital signature is one scheme with crypto-

graphic value by relying on the message and the mes-

sage’s sender. Digital signatures guarantee data in-

tegrity, detect changes or modiﬁcations to messages

sent, and perform authenticity. Creating a signature

on a message can be done by performing a digital sig-

nature with a hash function.

Figure 3: Digital Signature Scheme.

2.4 Hash Function and Data Integrity

A hash function is often referred to as a one-way func-

tion. The hash function has long been used in the

world of computer science. A hash function is a math-

ematical calculation that takes the variable length of

an input string and converts it to a ﬁxed length. The

ICAISD 2023 - International Conference on Advanced Information Scientiﬁc Development

132

resulting output is commonly referred to as a hash

value.

Using a hash algorithm makes it easy to calculate

the hash value on a message and makes it impossi-

ble to modify the message without composing the re-

sulting hash value. The hash function can detect any

modiﬁcations to the sent message. The hash function

can guarantee data integrity based on speciﬁc settings

Figure 4: Message Integrity Checking.

2.5 Signcryption

This study used the sign-then-encrypt method. The

message (plaintext) in the signature uses the Dis-

sayanake Digital Signature algorithm to generate a

signature against the message. After that, the message

and signature are encrypted using the Cramer-Shoup

algorithm. This method combines digital signatures

and public key cryptography to enhance security. This

process is called authentication and encryption.

2.6 Avalanche Effect

Avalance Effect is one of the mathematical properties

in cryptography that can determine whether or not a

cryptographic algorithm is good. A cryptographic al-

gorithm can be said to satisfy the criteria avalanche

effect if the input bits change, and then it is likely that

all bits can change by at least half

Avalanchee f f ect =

di f f erentnumbero f bits

totalnumbero f bits

100

(1)

Cryptographic algorithms that can have a signiﬁcant

avalanche effect value, then the level of security in an

algorithm can be said to be good.

3 METHOD

3.1 Dissayanake Digital Signature

Algorithm

Maheshika W.D.M.G Dissanayake developed the Dis-

sanayake digital signature scheme in 2019. The Dis-

sanayake digital signature is proposed based on the

factorization of prime numbers and simple mathemat-

ical properties. This scheme has a mathematical prop-

erty: the sum of 2 different odd numbers is a multiple

of 4.

This digital signature scheme uses a public key,

which is a (e, n) A large prime number less than e,

and n is a variable chosen by the signer r.

In Dissayanake Digital Signature Algorithm, there

are three essential processes: key generation, signing,

and verifying.

1. Key generation

a Choose two different primes for the values p

and q.

b Counting n=p×q.

c Counting φ(n) = (p − 1)(q − 1).

d Select a prime number d so that gcd (d, φ(n) =

1, is used as the sender’s private key.

e Calculate the public key e so that e.d

modφ(n) ≡ 1

f m is a message

g generate the hash value of message m using the

hash h function

h h(m)=M, M is a hash value

i Select an integer r so that (M) + r)mod4 ≡ 0

j Find the odd number (a) so that (a)=

M+r−2

2. Signing

Count S ≡ a

modn

3. Verifying

a Calculate S

modn ≡ a

′

b Find the odd number (a) so that (a) =

M+r−2

c If, then a

′

= a, the signature is valid if then the

′

̸= a the signature is invalid.

3.2 Cramer-Shoup Algorithm

The Cramer-Shoup cryptosystem is a symmetric

cryptographic algorithm invented by two scientists,

Ronald Cramer, and Victor Shoup, in 1998. The

Cramer-Shoup algorithm proved to be the ﬁrst effec-

tive scheme that resisted adaptive chosen ciphertext

attacks compared to cryptographic systems that ex-

isted at the time (Elkamchouchi et al., 2018). The

Cramer-Shoup algorithm is an extension algorithm of

the Elgamal algorithm. There are three essential pro-

cesses in Cramer-Shoup Algorithm: key generation,

encryption, and decryption.

1. Key Generation

a At the key generation stage, the process occurs

as follows: Generated g1, g2 where the two

Sign-Then-Encrypt Scheme with Cramer-Shoup Cryptosystem and Dissanayake Digital Signature

133

numbers are the subset q. It is a group of very

large primes.

b Six random numbers with a range of 0 to q-1

were selected. x1, x2, y1, y2, z

c Then the variables c, d, and h are calculated by

the following equation:

c = g1x

(2)

d = g1

(3)

h = g1

(4)

From the above calculations.

public key (g1,g2,c,d,h), private key

(x1,x2,y1,y2,z)

2. Encryption

The message m is converted to a G element. Se-

lected random numbers in the range 0 to q. Then

the value is calculated u1, u2, e, a, and v using the

public key. Here is:

u1 = g1

(5)

u2 = g2

(6)

e = h

m (7)

v = c

rxa

(8)

3. Decryption

Calculate for decryption m =

4 SIMULATION AND RESULTS

4.1 Simulation

The test that will be carried out on the Dissanayake

digital signature algorithm is how the algorithm is

in the key generation, signing process, and verify-

ing process. Key generation, encryption, and decryp-

tion will be performed in the Cramer-Shoup algorithm

testing.

4.1.1 Key Generation Process Results

Dissanayake Digital Signature

The result of the key generation process by the sender

using the Dissanayake digital signature algorithm

produces a public key and a private key

4.1.2 Results of Testing the Signing Process of

the Digital Signature Algorithm

After generating the key in the Dissanayake digital

signature algorithm, the following process is to gen-

erate the signature.

Figure 5: Key Generation Results on The Simulation.

Figure 6: The Results of Generating Signatures in The Sim-

ulation.

4.1.3 Results of Verifying Process Testing

Dissanayake Digital Signature

The results of the proses of verifying on the Dis-

sanayake digital signature veriﬁer algorithm take the

value of the signature to be veriﬁed using a public key.

Figure 7: The Results of Verifying the Simulation.

4.1.4 Cramer-Shoup Algorithm Key Generation

Process Test Results

The result of the key generation process by the sender

using the Cramer-Shoup algorithm generates a public

key and a private key.

Figure 8: Key Generation Results on the Simulation.

4.1.5 Cramer-Shoup Algorithm Encryption

Process Test Results

After generating the key in the Cramer-Shoup algo-

rithm, the following process is that it can generate the

ciphertext

ICAISD 2023 - International Conference on Advanced Information Scientiﬁc Development

134

Figure 9: Results of Generating Ciphertext in The Simula-

tion.

4.1.6 Results of Testing the Decryption Process

of the Cramer-Shoup Algorithm

The result of the decryption process is that the recipi-

ent can use his private key to decrypt the ciphertext.

Figure 10: The Result of The Decryption in The Simulation.

The simulation results of the running time to an-

alyze the signing and verifying process time and the

encryption and descriptive processes are based on ex-

periments with different plaintext lengths. Units of

execution time use seconds. The hardware speciﬁca-

tions used in this study to build and test the scheme

are as follows.

Table 1: Hardware Speciﬁcations.

No Speciﬁcations Information

1 Processor Intel® Core TM i3-7020U

CPU 2.30GHz

2 RAM 8 GB DDR 4

3 Desktop 14 inch

4 OS Windows 10 Home Single

Language 64 Bit

4.2 Simulation of Signing Dissanayake

Digital Signature

The signing process using the Dissanayake digital sig-

nature algorithm calculates the processing time based

on the plaintext length, which is 50 characters, 100

characters, 200 characters, 300 characters, and 400

characters. The results of the signing process time of

the Dissayanyake digital signature algorithm can be

seen in Table 2.

Based on the processing time with character

length, it shows the average result of the signing pro-

cess of the Dissanayake digital signature algorithm,

Table 2: Simulation Results for Signature Generation.

Plaintext

length

Execution time (second)

1 2 3 Avarage

100 0.0025 0.0049 0.0040 0.0038

200 0.0039 0.0051 0.0070 0.0053

300 0.0050 0.0061 0.0090 0.0067

400 0.0070 0.0091 0.0050 0.0070

500 0.0081 0.0060 0.0100 0.0080

Figure 11: Graph of Digital Signature Generation Results.

where the average process time starts from 0.0038

s to 0.0080 s based on tests with different character

lengths. Based on Figure 12 illustrates a graph of dig-

ital signature generation results. The process results

show the length of the linear plaintext with execution

time.

4.3 Simulation of Verifying Dissanayake

Digital Signature

The verifying process uses the Dissanayake digital

signature algorithm to calculate the processing time of

the plaintext length, which is 50 characters, 100 char-

acters, 200 characters, 300 characters, and 400 char-

acters. The results of the verifying process execution

time of the Dissayanyake digital signature algorithm

can be seen in Table 3.

Table 3: Simulation Results for Verifying.

Plaintext

length

Execution time (second)

1 2 3 Avarage

100 0.0021 0.0020 0.0020 0.0020

200 0.0030 0.0030 0.0010 0.0023

300 0.0050 0.0030 0.0020 0.0033

400 0.0060 0.0060 0.0040 0.0053

500 0.0071 0.0051 0.0061 0.0061

Based on the processing time with character

length, it shows the average result of the verifying

process of the Digital signature Dissanayake algo-

rithm. On tests with different character lengths, the

Sign-Then-Encrypt Scheme with Cramer-Shoup Cryptosystem and Dissanayake Digital Signature

135

Figure 12: Graph of Verifying Results.

average process execution time starts from 0.0020 s

to 0.0061 s. Figure 13 illustrates a graph of the results

of the verifying process. The process results show the

length of the linear plaintext with execution time.

4.4 Simulation of Encryption

Cramer-Shoup Algorithm

The encryption process uses the Cramer-Shoup algo-

rithm to calculate the processing time based on the

plaintext length, which is 50 characters, 100 charac-

ters, 200 characters, 300 characters, and 400 charac-

ters. The results of the encryption process execution

time of the Cramer-Shoup algorithm can be seen in

Table 4.

Table 4: Simulation Results for Encryption.

Execution Time (second)

ke-1 ke-2 ke-3 Avarage

100 0.1586 0.1576 0.1152 0.1438

200 0.2234 0.2514 0.3137 0.2628

300 0.3136 0.3518 0.4219 0.3624

400 0.4226 0.6499 0.5183 0.5303

500 0.6213 0.7639 0.6627 0.6827

Figure 13: Graph of Results for Encryption.

Based on the processing time with character

length, it shows the average result of the encryption

process of the Cramer-Shoup algorithm, where the av-

erage process time starts from 0.1438 s to 0.6827 s

based on tests with different character lengths. Figure

14 illustrates a graph of the results of the encryption

process. The process results show the length of the

linear plaintext with execution time.

4.5 Simulation of Decryption

Cramer-Shoup Algorithm

The decryption process uses the Cramer-Shoup algo-

rithm to calculate the processing time based on the

plaintext length, which is 50 characters, 100 charac-

ters, 200 characters, 300 characters, and 400 charac-

ters. The results of the decryption process execution

time of the Cramer-Shoup algorithm can be seen in

Table 5.

Table 5: Simulation Results for Decryption.

Execution time (second)

1 2 3 Avarage

100 0.1267 0.0818 0.0973 0.1019

200 0.1476 0.1620 0.2389 0.1828

300 0.2254 0.2503 0.3391 0.2716

400 0.2952 0.5022 0.3821 0.3932

500 0.3381 0.5852 0.6074 0.5102

Figure 14: Graph of Results for Decryption.

Based on the processing time with character

length, it shows the average result of the encryption

process of the Cramer-Shoup algorithm, where the

average process execution time starts from 0.1019 s

to 0.5102 s based on tests with different character

lengths. Based on Figure 15 illustrates a graph of the

results of the decryption process. The process results

show the length of the linear plaintext with execution

time.

4.6 Simulation of Sign-then-Encrypt

Scheme

The signcryption scheme process uses the Dis-

sanayake digital signature algorithm and the Cramer-

Shoup algorithm with sign-then-encrypt and decrypt-

then-sign methods to calculate the processing execu-

tion time based on the length of the plaintext, namely

50 characters, 100 characters, 200 characters, 300

ICAISD 2023 - International Conference on Advanced Information Scientiﬁc Development

136

characters, and 400 characters. The sign-then-encrypt

and Decrypt-then-sign execution can be seen in Table

Table 6: Simulation Results for Sign-Then-Encrypt and

Decrypt-Then-Verifying.

PL Execution time (second)

sign-then-encrypt Decrypt-then-verifying

50 0.0738 0.0520 0.0973 0.1019

100 0.1341 0.0926 0.2389 0.1828

200 0.1846 0.1375 0.3391 0.2716

300 0.2687 0.1993 0.3821 0.3932

400 0.3454 0.2582 0.6074 0.5102

Figure 15: Graph of Results for Sign-Then-Enccrypt and

Decrypt-Then-Verifying.

Based on ﬁg.16 shows that the execution time in

the sign-then-encrypt process is longer than the run-

ning time of the decrypt-then-verifying process be-

cause the sign-then-encrypt process takes execution

time to generate prime numbers and generate keys.

Based on Figure 16 illustrates a graph of the results of

the sign-then-encrypt and decrypt-then-verifying pro-

cesses. The process results show the length of the lin-

ear plaintext with execution time.

4.7 Simulation of Avalanche Effect

Simulation in this study on the signature results of the

signing process Dissanayake digital signature and ci-

phertext from the encryption process of the Cramer-

Shoup algorithm to obtain values on the avalanche ef-

fect. Simulation is conducted to obtain the average

value of the avalanche Effect results.

Table 7: Simulation Results of Avalanche Effect Dis-

sanayake Digital Signature.

Algoritma Dissanayake Digital Signature

1 2 3

Plaintext RAHMAD BAHRI FASILKOM

Signature 482387741 2058316320 2612119605

Plaintext modiﬁcations RAHMA4 4AHRI FASILKO8

Signature modiﬁcations 615076365 899842372 1597165780

Avalanche effect (%) 49.75 52.51 48.15

AVERAGE 50.14

Dissanayake Digital Signature obtains an average

value of 50.14% based on the avalanche effect sim-

ulations.

Table 8: Simulation Results of Avalanche Effect Cramer-

Shoup Algorithm.

Algoritma Cramer-Shoup

1 2 3

Plaintext RAHMAD BAHRI Fasilkom

Ciphertext 2393999649 269218372527562015

Plaintext modiﬁ-

cations

RAHMA4 4AHRI Fasilkot

Ciphertext modi-

ﬁcations

116590405 2347432728 12651684

Avalanche effect

(%)

42.35 52.95 55.56

AVERAGE (%) 50.29

Based on the simulations using the avalanche effect,

the Cramer-Shoup algorithm obtains an average value

of 50.29%.

5 CONCLUSION

Based on research, the digital signature Dissayanake

algorithm has a process to guarantee authenticity by

using verifying methods and hash functions. Veri-

fying is performed on formulas using the recipient’s

public key to generate a hash value used as input in the

signing process and can provide entity authentication.

The use of S

modn ≡ a

′

hash functions h(m) = M can

guarantee the authenticity of the information. In the

process, the recipient can re-run the hash function to

generate a new hash value, which is then compared

with the hash value received from the sender. Based

on the simulation results on the signing and verifying

process with Dissanayake digital signature and the de-

cryption encryption process with the Cramer-Shoup

algorithm, the characters’ length affects the execution

time. The process’s result shows the linear character’s

length with execution time. From the results of the

avalanche effect simulation, Dissanayake digital sig-

nature got the average value of the avalanche effect of

50.14%, and the Cramer-Shoup algorithm got the av-

erage value of the avalanche effect of 50.29%. Imple-

menting the sign-then-encrypt scheme can maintain

security by encrypting and guaranteeing authenticity

by adding a digital signature.

REFERENCES

Abood, O. and Guirguis, S. (2018). A survey on cryptogra-

phy algorithms. Int. J. Sci. Res. Publ, 8(7).

Dissanayake (2019). A novel scheme for digital signatures.

Sign-Then-Encrypt Scheme with Cramer-Shoup Cryptosystem and Dissanayake Digital Signature

137

Elkamchouchi, H., Takieldeen, A., and Shawky, M. (2018).

An advanced hybrid technique for digital signature

scheme. Conf. Electr. Electron. Eng. ICEEE, pages

375–379,.

Genc¸o

glu, M. (2019). Importance of cryptography in infor-

mation security. IOSR J. Comput. Eng, 21(1):65–68,.

Hossain, M., Hossain, M., Uddin, M., and Imtiaz, S. (2013).

International journal of advanced research in perfor-

mance analysis of test generation techniques.

Jain, D. (2017). Data security using cramer – shoup algo-

rithm in cloud computing. Ijarcce, 6(3):930–933,.

Kasyoka, P., Kimwele, M., and Angolo, S. (2021). Crypt-

analysis of a pairing-free certiﬁcateless signcryption

scheme. ICT Express, 7(2):200–204,.

Khan, A., Basharat, S., and Riaz, M. (2018). Analysis

of asymmetric cryptography in information security

based on computational study to ensure conﬁdential-

ity during information exchange. Int. J. Sci. Eng. Res,

9(11):992–999,.

Liu, Z., Yang, X., Zhong, W., and Han, Y. (2014). An efﬁ-

cient and practical public key cryptosystem with cca-

security on standard model. Tsinghua Sci. Technol,

19(5):486–495,.

Lydia, M., Budiman, M., and Rachmawat, D. (2021). Fac-

torization of small rprime rsa modulus using fer-

mat’s difference of squares and kraitchik’s algo-

rithms in python. J. Theor. Appl. Inf. Technol,

99(11):2770–2779,.

Manna, S., Prajapati, M., Sett, A., Banerjee, K., and Dutta,

S. (2017). 3rd ieee int. conf. res. Comput. Intell. Com-

mun. Networks, ICRCICN, 2017-Decem:327– 331,.

Maqsood, F., Ahmed, M., Mumtaz, M., and Ali, M.

(2017). Cryptography: A comparative analysis for

modern techniques. Int. J. Adv. Comput. Sci. Appl,

8(6):442–448,.

Matsuda, T., Matsuura, K., and Schuldt, J. (2009). Efﬁcient

constructions of signcryption schemes and signcryp-

tion composability.

Molk, A., Aref, M., and Khorshiddoust, R. (2021). Analysis

of design goals of cryptography algorithms based on

different components. Indones. J. Electr. Eng. Com-

put. Sci, 23(1):540– 548,.

Pandey, A. (2014). An efﬁcient security protocol based on

ecc with forward secrecy and public veriﬁcation.

Panhwar, M., Khuhro, S., Panhwar, G., and Memon, K.

(2019). Saca: A study of symmetric and asymmet-

ric cryptographic algorithms. IJCSNS Int. J. Comput.

Sci. Netw. Secur, 19(1):48,. Online]. Available:.

Rachmawati, D. and Budiman, M. (2018). Using the rsa

as as an asymmetric non-public key encryption algo-

rithm in the shamir three-pass protocol. J. Theor. Appl.

Inf. Technol, 96(17):5663–5673,.

Stallings, W. and Bauer, M. (2012). Computer security.

Vollala, S., Ramasubramanian, N., and Tiwari, U. (2021).

Energy-efﬁcient modular exponential techniques for

public-key cryptography.

ICAISD 2023 - International Conference on Advanced Information Scientiﬁc Development

138