Lightweight authentication scheme based on Elliptic Curve El Gamal

Figures & data

Figure 1. Taxonomy of elliptic curves (Lara-Nino et al., 2018).

Figure 2. Operations in elliptic curve cryptography divided by four levels.

Figure 3. Proposed model for generating encoding parameters.

Figure 4. ECEG based on authentication scheme using encoding parameters.

Table 1. ASCII-map table.

ASCII code	Symbol	$\mathrm{Ek}=(\alpha \ast k+\beta )\ast G$	Mapped Point with selected curve
0	NUL	.	.
1	SOH	.	.
.	.	.	.
.	.	.	.
255	Y	.	.

Figure 5. Implementation phases of enhanced ECEG.

Figure 6. The results of analysing the proposed protocol using the SCYTHER tool.

Table 2. Key size of RSA and ECC (Mahto & Yadav, 2017).

Security level (bits)	Key size
	RSA	ECC
80	1024	160−233
112	2048	224−255
128	3072	256−383
192	7980	384−541
256	15360	512+

Figure 7. The time complexity comparison of RSA and enhanced ECEG algorithms with 8-bit input.

Figure 8. The time complexity comparison of RSA and enhanced ECEG algorithms with 64-bit input.

Figure 9. The time complexity comparison of RSA and enhanced ECEG algorithms with 64-bit input.

Table 3. Time complexity analysis of RSA and enhanced ECEG algorithms with 8-bit input (in seconds).

	Input 8bits
	Encryption		Decryption
Security level	Enhanced ECEG Enc. time	RSA Enc. time	Enhanced ECEG Dec. time	RSA Dec. time
80	0.697	0.258	0.026	0.774
112	1.769	0.997	0.958	3.456
128	3.458	1.922	1.587	8.978
144	4.185	2.764	2.021	12.987

Table 4. Time complexity analysis of RSA and enhanced ECEG algorithms with 64-bit input (in seconds).

	Input 64 bits
	Encryption		Decryption
Security level	Enhanced ECEG Enc. time	RSA Enc. time	Enhanced ECEG Dec. time	RSA Dec. time
80	4.881	0.923	1.971	7987
112	8.446	3.895	4.524	16,902
128	12.603	5.250	6.876	27,612
144	19.026	11.087	8.810	62,055

Table 5. Time complexity analysis of RSA and enhanced ECEG algorithms with 256-bit input (in seconds).

	Input 256 bits
	Encryption		Decryption
Security level	Enhanced ECEG Enc. time	RSA Enc. time	Enhanced ECEG Dec. time	RSA Dec. time
80	18.932	2.856	4.980	19,890
112	29.909	6.850	8.023	71,002
128	54.300	13.565	11.363	180,612
144	88.321	31.890	18.196	268,055

Figure 10. ECC (Mahto & Yadav, 2017) versus enhanced ECEG with 8 bit computation time.

Figure 11. ECC (Mahto & Yadav, 2017) versus enhanced ECEG with 64-bit computation time.

Figure 12. ECC (Mahto & Yadav, 2017) versus enhanced ECEG with 256-bit computation time.

Table 6. Enhanced ECEG and ECC (Mahto & Yadav, 2017) with 8-, 64-, and 256-bit time complexity (in seconds).

	Input 8 bits		Input 64 bits		Input 256 bits
Security level	Enhanced ECEG	ECC	Enhanced ECEG	ECC	Enhanced ECEG	ECC
80	0.723	1.8152	6.852	8.0784	23.912	30.8091
112	2.727	3.7893	12.97	16.9188	37.932	66.0339
128	5.045	5.6453	19.479	22.4466	65.663	85.8446
144	6.206	6.7288	27.836	28.7093	106.517	109.6556

Table 7. Time and space complexity of authentication.

ECEG key size	Authentication time (seconds)	Authentication space (bits)
Secp160r2	199.581	832
Secp224r1	353.112	960
Secp256r1	509.201	1024
Secp384r1	844.367	1280

Table 8. Comparison of space and time complexity.

Scheme	Space complexity (bits)	Time complexity (hash operation)
Our proposed scheme	1024	4th
(Zheng et al., 2022)	2357	16th

Lara-Nino, C. A., Diaz-Perez, A., & Morales-Sandoval, M. (2018). Elliptic curve lightweight cryptography: A survey. IEEE Access, 6, 72514–72550. http://doi.org/10.1109/ACCESS.2018.2881444

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Mahto, D., & Yadav, D. K. (2017). RSA and ECC: A comparative analysis. International Journal of Applied Engineering Research, 12(19), 9053–9061.

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Zheng, J., Wang, X., Yang, Q., Xiao, W., Sun, Y., & Liang, W. (2022). A blockchain-based lightweight authentication and key agreement scheme for internet of vehicles. Connection Science, 34(1), 1430–1453. http://doi.org/10.1080/09540091.2022.2032602

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