Table 16.

Comparison of the statistical results of diffusion effect for the two proposed structures with $\left|h\right|$ = 256 bits with the standards SHA-3, SHA-2 and with some chaos-based hash functions.

Hash Function	${\mathit{B}}_{\mathit{min}}$	${\mathit{B}}_{\mathit{max}}$	$\overline{\mathit{B}}$	P(%)	$\Delta \mathit{B}$	$\Delta \mathit{P}\%$
Structure 1	101	155	128.10	50.04	7.96	3.11
Structure 2 with $n_r$ = 8	99	156	127.70	49.88	8.22	3.21
Structure 2 with $n_r$ = 24	99	154	127.88	49.95	8.02	3.13
Abdoun et al. ${\mathit{Structure}}_{\mathit{MD}}$ 1 [47]	100	154	127.95	49.98	8.03	3.13
Abdoun et al. ${\mathit{Structure}}_{\mathit{MD}}$ 2-${\mathit{n}}_{\mathit{r}}$ = 8 [47]	103	157	127.97	49.99	8.01	3.13
Abdoun et al. ${\mathit{Structure}}_{\mathit{MD}}$ 2-${\mathit{n}}_{\mathit{r}}$ = 24 [47]	100	157	127.88	49.95	7.94	3.10
SHA3-256 [13]	101	153	128.05	50.02	8.01	3.13
SHA2-256 [27]	104	154	128.01	50.00	7.94	3.10
Xiao et al. [51]	-	-	63.85	49.88	5.78	4.52
Lian et al. [52]	-	-	63.85	49.88	5.79	4.52
Zhang et al. [53]	46	80	63.91	49.92	5.58	4.36
Wang et al. [84]	-	-	63.98	49.98	5.53	4.33
Xiao et al. [67]	-	-	64.01	50.01	5.72	4.47
Deng et al. [85]	-	-	63.91	49.92	5.58	4.36
Deng et al. [68]	-	-	63.84	49.88	5.88	4.59
Yang et al. [69]	-	-	64.14	50.11	5.55	4.33
Xiao et al. [70]	-	-	64.09	50.07	5.48	4.28
Amin et al. [86]	-	-	63.84	49.88	5.58	4.37
Li et al. [71]	45	81	63.88	49.90	5.37	4.20
Wang et al. [72]	-	-	63.90	49.93	5.64	4.41
Akhavan et al. [87]	42	83	63.91	49.92	5.69	4.45
Huang [73]	-	-	63.88	49.91	5.75	4.50
Li et al. [74]	-	-	63.80	49.84	5.75	4.49
Wang et al. [88]	44	82	64.15	50.11	5.76	4.50
Li et al. [3]	-	-	63.56	49.66	7.42	5.80
Li et al. [75]	-	-	63.97	49.98	5.84	4.56
He et al. [4]	45	83	64.03	50.02	5.60	4.40
Jiteurtragool et al. [89]	43	81	62.84	49.09	5.63	4.40
Teh et al. [10]	-	-	64.01	50.01	5.61	4.38
Chenaghlu et al. [90]	-	-	64.12	50.09	5.63	4.41
Akhavan et al. [91]	43	82	63.89	49.91	5.77	4.50
Nouri et al. [92]	-	-	64.08	50.06	5.72	4.72
Xiao et al. [76]	47	83	63.92	49.94	5.62	4.39
Yu-Ling et al. [77]	-	-	64.17	50.14	5.74	4.49
Xiao et al. [78]	-	-	64.18	50.14	5.59	4.36
Li et al. [79]	-	-	64.07	50.06	5.74	4.48
Li et al. [80]	-	-	63.89	49.91	5.64	4.41
Ren et al. [93]	-	-	63.92	49.94	5.78	4.52
Guo et al. [94]	-	-	63.40	49.53	7.13	6.35
Yu et al. [95]	45.6	81.8	63.98	49.98	5.73	4.47
Zhang et al. [96]	-	-	64.43	49.46	5.57	4.51
Jiteurtragool et al. [89]	101	153	126.75	49.51	7.98	3.12
Chenaghlu et al. [90]	101	168	128.08	50.03	8.12	3.21
Teh et al. [97]	-	-	64.00	50.00	5.44	4.25
Li et al. [82]	45	84	64.27	50.21	5.59	4.36
Ahmad et al. [81]	45	82	63.87	49.90	5.58	4.36
Lin et al. [83]	-	-	64.10	50.08	5.58	4.36