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arxiv: 1907.05406 · v1 · pith:7B4INWYUnew · submitted 2019-07-11 · 💻 cs.IT · math.CO· math.IT

Using Chinese Characters To Generate Text-Based Passwords For Information Security

Bing Yao , Yarong Mu , Yirong Sun , Hui Sun , Xiaohui Zhang , Hongyu Wang , Jing Su , Mingjun Zhang
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Sihua Yang Meimei Zhao Xiaomin Wang Fei Ma Ming Yao Chao Yang Jianming Xie
This is my paper

Pith reviewed 2026-05-24 22:47 UTC · model grok-4.3

classification 💻 cs.IT math.COmath.IT
keywords graphical passwordsChinese charactersHanzi-graphstext-based passwordsflawed graph labellingstopological passwordsinformation security
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The pith

Chinese characters transformed into disconnected graphs with flawed labellings generate text-based passwords.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes using Chinese characters to create Hanzi-graphs and Hanzi-gpws as a new form of topological graphic password. These structures combine a graph topology with a set of discrete labelled elements to form passwords described as telling an interesting story. The authors plan to apply this to produce text-based passwords through flawed graph labellings on disconnected Hanzi-graphs obtained via speaking, writing or keyboard input. A reader would care if the method yields passwords that are both more memorable for users familiar with Chinese characters and resistant to standard attacks.

Core claim

A Topsnut-gpw consists of a topological structure and a graph labelling that connects discrete elements into an interesting story. Chinese characters can be transformed into computer equipment with touch screens by speaking, writing and keyboard input to form Hanzi-graphs and Hanzi-gpws, which are then used to produce text-based passwords via flawed graph labellings on disconnected Hanzi-graphs.

What carries the argument

Hanzi-graphs formed from Chinese characters, equipped with flawed graph labellings on disconnected structures, that generate text-based passwords from topological graphic passwords.

If this is right

  • Text-based passwords can be systematically derived from Hanzi-gpws.
  • Flawed labellings on disconnected graphs provide a distinct mechanism from existing graphical password schemes.
  • Input via speaking, writing or keyboard on touch screens enables direct mapping from characters to password elements.
  • The topological structure plus labelling creates passwords that incorporate narrative connections between elements.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Users familiar with Chinese characters might find these passwords easier to remember than random strings, though this remains untested.
  • The approach could extend to other character-based writing systems if the graph-labelling method generalizes beyond Hanzi.
  • Security claims would require separate analysis of how the flawed labellings resist common password attacks.
  • Device integration with touch screens suggests potential for direct drawing or selection interfaces during password creation.

Load-bearing premise

Representing Chinese characters as disconnected graphs with flawed labellings will produce passwords that are both secure and practical for users.

What would settle it

A test showing that passwords generated from these Hanzi-graphs are either easily guessed by attackers or too difficult for typical users to recall and enter on touch screens.

Figures

Figures reproduced from arXiv: 1907.05406 by Bing Yao, Chao Yang, Fei Ma, Hongyu Wang, Hui Sun, Jianming Xie, Jing Su, Meimei Zhao, Mingjun Zhang, Ming Yao, Sihua Yang, Xiaohui Zhang, Xiaomin Wang, Yarong Mu, Yirong Sun.

Figure 2
Figure 2. Figure 2: (a) A popular matrix A(T4706) of T4706; (b) the Hanzi-matrix A ∗ (H gpw 4706) of H gpw 4706. pointed that the number τ (Kn) of spanning trees (tree-like Topsnut-gpws) of a complete graph (network) Kn is non￾polynomial, so Topsnut-gpws are computationally security; Topsnut-gpws are suitable for people who need not learn new rules and are allowed to use their private knowledge in making Topsnut-gpws for the … view at source ↗
Figure 1
Figure 1. Figure 1: (a) A simplified Chinese character H4706 defined in [42]; (b) a mathematical model T4706 of H4706; (c) another mathematical model H gpw 4706 of H4706. There are many advantages of Topsnut-gpws, such as, the space of Topsnut-gpws is large enough such that the decrypting Topsnut-gpws will be terrible and horrible if using current computer. In graph theory, Cayley’s formula (Ref. [10]) τ (Kn) = n n−2 (1)   … view at source ↗
Figure 5
Figure 5. Figure 5: Difference between four fonts in printed Hanzis. C. Matching behaviors of Hanzi-graphs 1) Dui-lians, also, Chinese couplets: In Chinese culture, a sentence, called “Shang-lian”, has its own matching sentence, named as “Xia-lian”, and two sentences Shang-lian and Xia￾lian form a Chinese couplet, refereed as “Dui-lian” in Chinese. The sentence (a) of Fig.6 is a Shang-lian, and the sentence (b) of Fig.6 is a … view at source ↗
Figure 3
Figure 3. Figure 3: Left is a simplified Chinese character, and Right is a traditional Chinese character in each of equations above. Some Hanzis are no distinguishing about traditional Chinese characters and simplified Chinese characters [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Three Chinese characters with more strokes, Left has 64 strokes, Middle has 56 strokes. B. Different fonts of Hanzis There are four fonts in printed Hanzis. In Fig.5, we give four basic fonts: Songti, Fangsong, Heiti and Kaiti. Clearly, there are differences in some printed Hanzis. These differences will be important for us when we build up mathematical models of Hanzis [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 8
Figure 8. Figure 8: The same Hanzis in a couplet. 云长啊云长 打一成语 英国人说再见，中国人行个礼 打一字 悟空扣门八戒开 打俗语五字 会吃没有嘴，会走没有腿，杀马不流血，过河没有 水 打一游戏 性格温柔又坚定，为使错误能改正，刮层皮也高兴 打一物 有钱没人借 打一字 横三竖四，蜿蜒不直 打一字 门人聚会 打一字 岁末 打一字 遇见皇后 打一字 招手告别捎一言 打一字 微风轻吹雨声响 打一字 [PITH_FULL_IMAGE:figures/full_fig_p005_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Twelves Chinese conundrums. Chinese character, the usage of some traditional Chinese characters, also, is not unique, such examples are shown in Fig.21. 13) Configuration in Hanzis: ∗ Symmetry means that Hanzis posses horizontal sym￾metrical structures, or vertical symmetrical structures, or two directional symmetries. We select some Hanzis having sym￾metrical structures in Fig.22 (a), (b), (c) and (f). ∗ … view at source ↗
Figure 12
Figure 12. Figure 12: Private keys obtained by homonyms, or understanding by insight. 同音 同偏旁 ：亻 [PITH_FULL_IMAGE:figures/full_fig_p006_12.png] view at source ↗
Figure 10
Figure 10. Figure 10: Some Xie-hou-yus in Chinese. 打南边来了一个喇嘛，手里提着五斤鳎 蚂，打 北边来了一个哑巴，腰里别着一个喇叭。提搂鳎蚂的 喇嘛要拿鳎蚂去换别着喇叭的哑巴的喇叭，别着喇叭 的哑巴不愿意拿喇叭去换提搂鳎蚂的喇嘛的鳎蚂。提 搂鳎蚂的喇嘛抡起鳎蚂就给了别着喇叭的哑巴一鳎 蚂，别着喇叭的哑巴抽出喇叭就给了提搂鳎蚂的喇嘛 一喇叭，也不知是提搂鳎蚂的喇嘛打了别着喇叭的哑 巴，还是别着喇叭的哑巴打了提搂鳎蚂的喇嘛。喇嘛 回家炖鳎蚂，哑巴回家滴滴答答吹喇叭。 上一山，下一山，跑了三里三米三，登了一座大高 山，山高海拔三百三。上了山，大声喊：我比山高三 尺三。 黑化黑灰化肥灰会挥发发灰黑讳为黑灰花会回飞； 灰化灰黑化肥会会挥发发黑灰为讳飞花回化为灰。 [PITH_FULL_IMAGE:figures/full_fig_p006_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Three Chinese tongue twisters. nese characters” [42]S, which is constituted by 0, 1, 2, . . . , 8, 9 (see Fig.23(c)). Clearly, the above three ways are not possible for making passwords with bytes as long as desired. We introduce the fourth way, named as Topsnut-gpw, see an example shown in Fig.1(c). As known, Hanzi-graphs are saved in computer by popular matrices, see a Hanzi-graph T4706 shown in Fig.1 (… view at source ↗
Figure 14
Figure 14. Figure 14: All Hanzia have the same pronunciation “ji”. 爸爸= 爸比,老爸,阿爸,老爹,阿爹,爹哋, 爷,老子,老窦,老头,达达,多桑,老爷子,大, 老汉(儿),拔,巴拔,耶,大,爷,大大,掉掉,叭叭, 阿呆,阿爷,阿噶吧,阿噶呆,阿噶爷,阿噶伯,达, 巴巴,哒,哒哒,大,大大,阿爹,答答,把吧 [PITH_FULL_IMAGE:figures/full_fig_p007_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Father, daddy in Chinese dialects. Rule-4 No odd-cycles. We restrict our Hanzi-graphs have no odd-cycles for the guarantee of set-ordered graceful la￾bellings (see Fig.30). There are over 6763 Hanzis in [42], and we have 3500 Hanzis in frequently used. So it is not an easy job to realize the set-ordered gracefulness of the Hanzi-graphs in [42]. Clearly, the 0-rotatable gracefulness of the Hanzi￾graphs in … view at source ↗
Figure 17
Figure 17. Figure 17: (a) Split a word into several words; (b) building words by a group of words obtained from splitting a given word. E(G), and g(uv)+|g(u)−g(v)| = k with a constant k for each edge uv ∈ E(G). Moreover, g is super if max g(E(G)) < min g(V (G)) (or max g(V (G)) < min g(E(G))). ✷ In Definition 4 we restate several known labellings that can be found in [11], [31], [48], [49] and [23]. We write f(V (G)) = {f(u) :… view at source ↗
Figure 18
Figure 18. Figure 18: Explaining words. 白日依山尽，黄河入海流。 欲穷千里目，更上一层楼。 春眠不觉晓，处处闻啼鸟。 夜来风雨声，花落知多少。 独在异乡为异客，每逢佳节倍思亲。 遥知兄弟登高处，遍插茱萸少一人。 柳庭风静人眠昼，昼眠人静风庭柳。 香汗薄衫凉，凉衫薄汗香。 手红冰碗藕，藕碗冰红手。 郎笑藕丝长，长丝藕笑郎。 [PITH_FULL_IMAGE:figures/full_fig_p008_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Tang poems. the induced edge labels are defined as θ(xy) = |θ(x) − θ(y)|. Write θ(V (G)) = {θ(u) : u ∈ V (G)}, θ(E(G)) = {θ(xy) : xy ∈ E(G)}. There are the following constraints: (a) |θ(V (G))| = p. (b) |θ(E(G))| = q. (c) θ(V (G)) ⊆ [0, q], min θ(V (G)) = 0. (d) θ(V (G)) ⊂ [0, 2q − 1], min θ(V (G)) = 0. (e) θ(E(G)) = {θ(xy) : xy ∈ E(G)} = [1, q]. (f) θ(E(G)) = {θ(xy) : xy ∈ E(G)} = {1, 3, 5, . . . , 2q − … view at source ↗
Figure 24
Figure 24. Figure 24: Three substituted expressions of eight Hanzis. 人人好公 则天下太平 人好人公 则天下太平 人人好 则天下太公平 人好人则公 太平天下 公则天下 人好人太平 天下公 则人好人太平 太平天下 则人好人公 人人好公 则太平天下 天下太平 则人人好公 人好则公 天下人太平 人公则好 天下人太平 天下人公 人好则太平 好人则公 天下人太平 人人公 天下好则太平 公平天下人 则人太好 天下公平 则人人太好 [PITH_FULL_IMAGE:figures/full_fig_p009_24.png] view at source ↗
Figure 23
Figure 23. Figure 23: Four expressions of a Hanzi H4043 (= man). x, y ∈ V (G) and {f(u) + f(v) : uv ∈ E(G)} = Sk,d. (7) [11] A harmonious labelling f of G holds f(V (G)) ⊆ [0, q−1], min f(V (G)) = 0 and f(E(G)) = {f(uv) = f(u)+ f(v) (mod q) : uv ∈ E(G)} = [0, q − 1] such that (i) if G is not a tree, f(x) 6= f(y) for distinct x, y ∈ V (G); (ii) if G is a tree, f(x) 6= f(y) for distinct x, y ∈ V (G) \ {w}, and f(w) = f(x0) for s… view at source ↗
Figure 26
Figure 26. Figure 26: Hanzi-graphs with one stroke, in which Hanzi-graphs (b), (c) and (d) can be considered as one from the topology of view. So, (a) and (e) are the same Hanzi-graph [PITH_FULL_IMAGE:figures/full_fig_p010_26.png] view at source ↗
Figure 29
Figure 29. Figure 29: First group of mathematical models of Hanzis components and radicals. (p, q)-graph G, and let Fum(G, f) = X uv∈E(G) [f(u) + f(v) (mod q + 1)], we call f a felicitous-sum labelling. Find two extremum maxf Fum(G, f) and minf Fum(G, f) over all felicitous-sum labellings of G. ✷ Motivated from Definition 12 and Definition 13, we design: Definition 14. ∗ A connected (p, q)-graph G admits a labelling f : V (G)∪… view at source ↗
Figure 30
Figure 30. Figure 30: Second group of mathematical models of Hanzis components and radicals. 4043 4043 2635 2511 5282 4476 4734 4411 3829 [PITH_FULL_IMAGE:figures/full_fig_p011_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: The topological structure (Hanzi-graphs) of Hanzis shown in Fig.24. Find these six extremum minf Fve(G, f), maxf Fve(G, f), minf F|ve|(G, f), maxf F|ve|(G, f), minf Fmagic(G, f) and maxf Fmagic(G, f) over all ϕ-labellings of G, where ϕ ∈ {ve-sum-difference, ve-difference, k-edge-average}. Definition 15. [47] Let (X, Y ) be the bipartition of a bipartite (p, q)-graph G. If G admits a felicitous labelling f… view at source ↗
Figure 32
Figure 32. Figure 32: Each connected Hanzi-graph of a Hanzi-graph group T shown in Fig.31 admits a set-ordered graceful labelling. so we get a Hanzi-gpw group H as follows H = H gpw1 4043 H gpw2 4043 H gpw 2635H gpw 2511H gpw 5282H gpw 4476H gpw 4734H gpw 4411H gpw 3829. Join them by edges for producing a connected graph T ∗ = T + E∗ , and then Fig.34 shows us a set-ordered graceful labelling f ∗ of T ∗ by the set-ordered grac… view at source ↗
Figure 33
Figure 33. Figure 33: A Hanzi-graph group T shown in Fig.32 admits a flawed set-ordered graceful labelling. 70 51 37 42 40 2 29 20 11 9 26 80 86 44 60 63 47 57 18 13 19 17 16 12 34 38 35 15 14 37 36 51 53 50 52 4 8 7 6 48 47 42 40 41 5 46 3 43 10 39 49 1 44 45 21 22 23 25 24 55 54 33 56 31 32 30 31 28 27 59 57 34 62 36 26 35 61 27 33 60 32 28 29 30 58 38 39 49 48 50 69 19 68 20 24 63 25 41 64 23 45 46 67 21 66 43 65 22 89 91 9… view at source ↗
Figure 34
Figure 34. Figure 34: A connected graph T + E ∗ a based on Fig.33 admits a set￾ordered graceful labelling. In general, we have a result shown in the following: Theorem 2. Let G1, G2, . . . , Gm be disjoint connected graphs, and E∗ be an edge set such that each edge uv of E∗ has one end u in some Gi and another end v is in some Gj with i 6= j, and E∗ joins G1, G2, . . . , Gm together to form a connected graph H, denoted as H = … view at source ↗
Figure 36
Figure 36. Figure 36: (a) and (b) do not admit 0-rso-graceful systems, but (a-1), (a-2), (b-1) and (b-2) admit 0-rso-graceful systems. Lemma 8. If a tree T admits a 0-rotatable system of (odd- )graceful labellings, then its symmetric tree T T 0 admits a 0-rotatable set-ordered system of (odd-)graceful labellings. Proof. Let f be a graceful labelling of a tree T having p vertices, and (X, Y ) be the bipartition of vertex set of… view at source ↗
Figure 37
Figure 37. Figure 37: Two trees T1, T2 shown in (a) and (b) admit 0-rotatable system of graceful labellings, but set-ordered. A tree T1 T2 admits a 0-rotatable system of graceful labellings. Seq-1. A vertex mapping f : V (G) → AM such that f(u) 6= f(v) for distinct vertices u, v ∈ V (G). Seq-2. A total mapping g : V (G)∪E(G) → AM ∪Bq such that g(x) 6= g(y) for distinct elements x, y ∈ V (G) ∪ E(G). Seq-3. An induced edge label… view at source ↗
Figure 38
Figure 38. Figure 38: A scheme for a half-edge split operation from left to right, and a half-edge coincident operation from right to left. Definition 33. Let xw be an edge of a (p, q)-graph G, such that N(x) = {w, u1, u2, . . . , ui , v1, v2, . . . , vj} and N(w) = {x, w1, w2, . . . , wm}, and xw ∈ E(G). Op-1. A half-edge split operation is defined by deleting the edge xw, and then splitting the vertex x into two vertices x 0… view at source ↗
Figure 40
Figure 40. Figure 40: (a) An edge-subdivided graph G.w obtained by subdividing a vertex w = (x, y) into an edge xy from (b) to (a); (b) an edge￾contracted graph G / xy obtained by contracting an edge xy to a vertex (x, y) from (a) to (b). 1 u 2 u 1,1 v 2,1 v 1,2 v 2,2 v uk  k 1, v ik v , 1  uk n u n 2, k 1,1 v ,in v v ik v  ,1 i v ,1 i v ,2 1 u 2 u 1,1 v 2,1 v i1,1v 1 ,1 m v 1,2 v 2,2 v i1,2 v 2 ,2 m v k u k 1, v ik … view at source ↗
Figure 39
Figure 39. Figure 39: (a) A vertex-coincident graph G(x 0 x 00) obtained by a vertex-coincident operation from (b) to (a); (b) a vertex-split graph G∧x obtained by a vertex-split operation from (a) to (b); (c) an edge￾coincident graph G(x 0w 0 x 00w 00) obtained by an edge-coincident operation from (d) to (c); (d) an edge-split graph G ∧ xw obtained by an edge-split operation from (c) to (d). as G(x 0 x 00), called a vertex-co… view at source ↗
Figure 41
Figure 41. Figure 41: (a) A path P = u1u2 · · · un in black, and a cycle C = P + u1un in black and blue; (b) two cycles C 0 = P 0 + u 0 1u 0 n and C 00 = P 00 + u 00 1 u 00 n obtained by a series of half-edge split operations. Theorem 11. Any simple graph G can be decomposed into Hanzi-graphs G1, G2, . . . , Gm with G = Sm i=1 Gi , E(G) = Sm i=1 E(Gi) and E(Gi) ∩ E(Gj ) = ∅ if i 6= j. Let DHg(G) be the smallest number of Hanzi… view at source ↗
Figure 42
Figure 42. Figure 42: An example for illustrating the half-edge split operation. G H T [PITH_FULL_IMAGE:figures/full_fig_p018_42.png] view at source ↗
Figure 44
Figure 44. Figure 44: A scheme for illustrating the procedure of finding a flawed set-ordered graceful labelling of the (78, 55)-Hanzi-graph G shown in Fig.43. Our split operations can be used to decompose graphs and form new colorings/labellings. In [40] and [39], the authors investigate the v-split and e-split connectivity of graphs/networks. They define two new connectivities as fol￾lows: The v-divided connectivity. A v-div… view at source ↗
Figure 43
Figure 43. Figure 43: An example for illustrating DHg(G) < DHg(H), since H is not a Hanzi, DHg(G) = 1, but DHg(H) ≥ 2. new edges for obtaining a caterpillar T 0 = m j=1Hj1 with the new edge set E∗ = {usut : us ∈ E(His ), ut ∈ E(Hit )}, see (b) in Fig.44; Step 3. Give a graceful set-ordered labelling of T 0 , see (c) in Fig.44; Step 4. Delete the added edges and then we get a flawed set-ordered graceful labelling of G, see (d) … view at source ↗
Figure 45
Figure 45. Figure 45: (a) A graph H with minimum degree δ(H) = 4; (b) an e-divided graph H ∧ xw with κ 0 d(H) = 1; (c) a v-divided graph H ∧ {x, w} with κd(H) = 2; (d) a v-deleted graph H − {x, w} with κ(H) = 2; (e) an e-deleted graph H − {yx, yw, yu, yv} with κ 0 (H) = 4. G hold the following inequalities [10] κ(H) ≤ κ 0 (H) ≤ δ(H) (10) true. Unfortunately, we do not have the inequalities (10) about the minimum degree δ(H), t… view at source ↗
Figure 46
Figure 46. Figure 46: A derivative hanzi-system built on a Hanzi H4476. H gpwj 4476 admit a flawed set-ordered graceful labelling fj with j ∈ [1, 4], so fj (V (H gpwj 4476 )) = [0, 10] for j ∈ [1, 4] according to Definition 2 [PITH_FULL_IMAGE:figures/full_fig_p020_46.png] view at source ↗
Figure 47
Figure 47. Figure 47: A hz-ε-graph made by the derivative hanzi-system of a Hanzi H4476 shown in Fig.46, where ε is the graceful labelling. Clearly, our hz-ε-graphs are Hanzi-gpws too. In Fig.46, we can see the following facts: (1) Two flawed set-ordered graceful labellings in Fig.46(c) and (h) are dual to each other. Again, adding a new vertex and a new edge makes (i)= H gpw 4932; then (n)= H gpw 493 is obtained by adding 8 n… view at source ↗
Figure 49
Figure 49. Figure 49: (a) A group of three Hanzis-gpws with their seven connected components having set-ordered graceful labellings; (b)-(e) four dif￾ferent flawed set-ordered graceful labellings. Hence, we have the edge label set f(E∗ ) = {f(xiyi) = f(yi) − f(xi) : xiyi ∈ E∗} = {2, 6, 11, 20, 26, 29, 37, 40, 42, 44, 47, 51, 57, 60, 63, 70, 80, 86} with 18 = |E∗ |. Thereby, we can set: (2 + k1) − k1 = 2, (6 + k2) − k2 = 6, (11… view at source ↗
Figure 51
Figure 51. Figure 51: Two Hanzi-gpws (H4476, H4585) shown in (f) are made from (a) to (e). Definition 37. ∗ Let H = Sm i=1 Gi with subgraphs G1, G2, . . . , Gm, and let H admit a flawed set-ordered grace￾ful labelling h. If each Gi admits a flawed set-ordered graceful labelling hi induced by h, such that |hi(E(Gi)) ∩ hi+1(E(Gi+1))| = 1 for i ∈ [1, m−1], then we say h a flawed jointly set-ordered graceful labelling of H (see ex… view at source ↗
Figure 50
Figure 50. Figure 50: Paragraphs can be transformed into Hanzi-graphs having the same components with that of three Hanzis H4043, H2511 and H3829. (a) A public key; (b) possible private keys. F. Self-growable Hanzi-gpws Some Hanzi-gpws can grow to many Topsnut-gpws. An example shown in Fig.51 is just a self-growable Hanzi-gpw, in which H gpw 4476 is as a public key, H gpw 4585 is as a private key, the authentication is shown i… view at source ↗
Figure 52
Figure 52. Figure 52: Two examples for self-growing Hanzi-gpws admitting flawed set-ordered graceful labellings. for a (an odd-)graceful labelling f of G by defining f(aij ) = |f(i) − f(j)| if edge ij ∈ E(G), otherwise f(aij ) = 0 if edge ij 6∈ E(G), and f(aii) = 0. We refer to A(G, f) as an adjacency edge-value matrix of G. Motivated from the matrix expression of graphs, such as incidence matrices of graphs, we have the follo… view at source ↗
Figure 53
Figure 53. Figure 53: A Hanzi-gpw H1 ∪ H2 made by two Hanzi-gpws H gpw 4476 and H gpw2 4043 shown in Fig.34. A(H1) =   57 58 29 29 28 60 60 61 62 27 28 30 31 32 33 34 35 36 30 30 59 60 60 27 26 26 26   (18) A(H2) =   5 4 87 88 88 81 82 83 84 85 86 86 4 4 3   (19) Two matrices (18) and (19) are two Topsnut-matrices of two Hanzi-gpws H1 = H gpw 4476 and H2 = H gpw 4043 shown in Fig.53, respectively. Now, we do a column-e… view at source ↗
Figure 54
Figure 54. Figure 54: The lines in (a), (b), (c) and (d) are the basic rules for producing TB-paws; others are examples for showing there exist many 1-line TB-paws. T (c) b =303027572859603058293160273 229283326263460603526863861 6281864825483438487888885 T (d) b =57273058283029305929316028 32606033276034266135266236265 818648386878348884488853 T (e) b =888887456261606028292958572 73030283059603132602733342626 3536268681828648… view at source ↗
Figure 55
Figure 55. Figure 55: Four basic 1-line O-k with k ∈ [1, 4] used in general matrices, such as Fig.54 (a), (b), (c) and (d). ALGORITHM-I (1-line-O-1) Input: Avev(G) = (X W Y ) −1 3×q Output: TB-paws: 1-line O-1 TB-paw T O−1 b ; 1-line O￾1-r TB-paw T O−1−r b ; and 1-line O-1-i TB-paw T O−1−i b as follows: T O−1 b =x1x2 · · · xqeqeq−1 · · · e2e1y1y2 · · · yq T O−1−r b =y1y2 · · · yqeqeq−1 · · · e2e1x1x2 · · · xq T O−1−i b =xqxq−1… view at source ↗
Figure 56
Figure 56. Figure 56: A Hanzi H4043 with its Hanzi-gpw H gpw 4043 and two adjacency ve-value matrices A (1)(H4043) and A (2)(H4043). Two matrices A(1)(H4043) and A(2)(H4043) shown in Fig.56 are two ve-value matrices. We present four standard 26 [PITH_FULL_IMAGE:figures/full_fig_p026_56.png] view at source ↗
Figure 58
Figure 58. Figure 58: Examples for using four standard 1-line Vo-t with t ∈ [1, 4] shown in Fig.57. of Topsnut-matrices. Suppose that A = (aij )n×n is a popular matrix, so it has n 2 elements aij with i, j ∈ [1, n]. We can obtain (n 2 )! TB-paws with n 2 bytes from A = (aij )n×n. However, a (p, q)-graph G has many its own adjacent e-value and adjacent ve-value matrices, in which two adjacent e-value matrices (or adjacent ve-va… view at source ↗
Figure 59
Figure 59. Figure 59: Four groups of keys in keys. G. TB-paws from matrices with elements of Hanzi-GB2312-80 or Chinese code Definition 39. ∗ A Hanzi-GB2312-80 matrix Ahan(H) of a Hanzi-sentence H = hHii m i=1 made by m Hanzis H1, H2, . . . , Hm is defined as Ahan(H) =   a1 a2 · · · am b1 b2 · · · bm c1 c2 · · · cm d1 d2 · · · dm   4×m = (A B C D) −1 4×m (26) where A = (a1 a2 · · · am), B = (b1 b2 · · · bm) C = (c1 c2 … view at source ↗
Figure 60
Figure 60. Figure 60: Two Hanzi-gpws having variable labellings. We show an example of Hanzi-gpws with variable labellings in Fig.60. By the writing stroke order of Hanzis, we have Tb(H4476; n, k) = n(n − k)k(n − k − 1)(n − 1)(k + 1) (n − k − 3)(n − 2)(n − k − 4)(k + 2)k(n − k − 2) (n − 2)(n − k − 5)(k + 3)(n − k − 6)(n − 3)(n − 5) (n − k − 9)(k + 4)(n − k − 8)(n − 4) 28 [PITH_FULL_IMAGE:figures/full_fig_p028_60.png] view at source ↗
Figure 62
Figure 62. Figure 62: A Hanzi-graph T4585 in xOy-plane and its analytic Hanzi￾matrix. VI. SELF-SIMILAR HANZI-NETWORKS Self-similarity is common phenomena between a part of a complex system and the whole of the system. The similarity between the fine structure or property of different parts can reflect the basic characteristics of the whole. In other word, the invariance under geometric or non-linear transformation: the similar… view at source ↗
Figure 61
Figure 61. Figure 61: (a) A Hanzi-graph T4535 is expressed in xOy-plane; (b) a Hanzi-graph T8630 is expressed in xOy-plane. By Fig.62 and the 1-line O-k with k ∈ [1, 4] based on (24), we can write the following TB-paws T (1) b (T4585) =02121201111110108765432 11222111122100020, T (2) b (T4585) =0211222212123111140 111522106111070020810, T (3) b (T4585) =22121022111131212422 10501116002071110108, and T (4) b (T4585) =0211212222… view at source ↗
Figure 63
Figure 63. Figure 63: A self-similar Hanzi-network N4043(t) with first three steps t = 1, 2, 3, where N(1) = T4043. 29 [PITH_FULL_IMAGE:figures/full_fig_p029_63.png] view at source ↗
Figure 64
Figure 64. Figure 64: The self-similar Hanzi-network N4043(t) shown in Fig.63 at the forth step t = 4. B. Self-similar tree-like Hanzi-graphs In mathematics, a self-similar object is exactly or approxi￾mately similar to a part of itself (i.e. the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical prop… view at source ↗
Figure 66
Figure 66. Figure 66: A self-similar Hanzi-network N4585(t) based on a Hanzi￾graph T4585 for t = 1, 2, 3. the root of T0, and write L(T0) \ {u0} = {uj : j ∈ [1, m]}, where m = |L(T0) \ {u0}|, and assume that each leaf ui ∈ L(T0)\{u0} is adjacent to vi ∈ V (T0)\L(T0) with i ∈ [1, m]. 1) Leaf-algorithm-A: There are the copies T0,i of T0 with u0,i ∈ V (T0,i) to be the image of the root u0 with i ∈ [1, m]. Deleting each leaf ui ∈ … view at source ↗
Figure 65
Figure 65. Figure 65: (a) Hanzi-graph T4043; (b) and (c) are two non-uniformly self-similar Hanzi-graphs. We present the following constructive leaf-algorithms for building up particular self-similar tree-like networks. Let T0 be a tree on n ≥ 3 vertices and let L(T0) = {ui : i ∈ [1, m]} be the set of leaves of T0. We refer a vertex u0 ∈ V (T0) to be N N N [PITH_FULL_IMAGE:figures/full_fig_p030_65.png] view at source ↗
Figure 67
Figure 67. Figure 67: According to T0 = T4043 and Leaf-algorithm-A: (a) A Hanzi-graph T0; (b) a uniformly self-similar Hanzi-graph T1 = AhT0, {T0,i} 3 1i with the root; (c) T2 = AhT0, {T2,i} 3 1i with the root; (d) T3 = AhT0, {T3,i} 3 1i with the root. 2) Leaf-algorithm-B: We take n copies H0,1, H0,2, . . . , H0,n of a tree H0, where n = |L(H0)| is the number of leaves of H0, and do: (1) delete each leaf xi from H0, where xi i… view at source ↗
Figure 68
Figure 68. Figure 68: For illustrating the vertex-coincided algorithm-I [PITH_FULL_IMAGE:figures/full_fig_p033_68.png] view at source ↗
Figure 69
Figure 69. Figure 69: For illustrating the vertex-coincided algorithm-II. the vertex v s k of the N(k) into one vertex for j ∈ [1, nv(k)] with k ≥ 1 produces a new network N(k+1) = N(k) −→ N(k), called a uniformly vertex-split nv(k)-scaling N(0)-similar network according to Definition 40, and the unique active vertex of N(k) is defined as the unique active vertex of N(k + 1). Then, nv(k) is the scaling factor. Step 2.4. Vertex… view at source ↗
Figure 70
Figure 70. Figure 70: Self-similar Hanzi-graphs on the edge-coincided algorithm-I. Fig.70 is for illustrating the edge-coincided algorithm-I: (a) M(0) was made by a Hanzi-graph T4043 with a unique active edge u0v0; (b) M(1) = M(0)−→ M(0) with a unique active 33 [PITH_FULL_IMAGE:figures/full_fig_p033_70.png] view at source ↗
Figure 71
Figure 71. Figure 71: A self-similar Hanzi-graph with its unique active edge u2v2. The self-similar Hanzi-graph shown in Fig.71 is M(2) = M(1)−→ M(0), where M(0)=(a), M(1)=(b) shown in Fig.70. Step (2.2) Edge-coincided algorithm-II. We overlap the unique active edge x s tw s t of the sth copy Ms (t) of M(t) with the edge x s t−1 y s t−1 of the M(t − 1) into one edge for s ∈ [1, ne(t−1)] with k ≥ 1, where ne(t−1) = |E(M(t − 1))… view at source ↗
Figure 72
Figure 72. Figure 72: A self-similar Hanzi-graph made by the edge-coincided algorithm-II, where u2v2 is its unique active edge. The self-similar Hanzi-graph shown in Fig.72 is M(2) = M(0)−→ M(1), where M(0)=(a), M(1)=(b) shown in Fig.70. Step (2.3) Edge-coincided algorithm-III. Take a duplicated network of M(t), and denote as M∗ (t). We overlap the unique active edge x s tw s t of the sth copy Mj (t) of M(t) with the edge x s … view at source ↗
Figure 73
Figure 73. Figure 73: A scale-free self-similar Hanzi-tree made by two self-similar Hanzi-trees shown in Fig.68 (a)= T4043 and (b). We will apply a technique introduced in [33], since it can produce Fibonacci series trees obeying power-law k −γ with γ > 3. Let F(0) be a Hanzi-network. We present an algorithm for constructing Fibonacci self-similar Hanzi-networks having scale-free features by the following rules: Rule-1. The ve… view at source ↗
Figure 74
Figure 74. Figure 74: (a) N(1); (b) N(2); (c) N(3); (d) N(0). Fibonacci self-similar Hanzi-networks obtained by FIBONACCI-EDGE algorithm based on the edge-planting operation are denoted as N0 (t) with time step t ≥ 0. Here we omit the definition of FIBONACCI-EDGE algorithm since it is very similar with FIBONACCI-VERTEX algorithm. We will show some properties of Fibonacci self-similar Hanzi-networks N(t) made by FIBONACCI-VERTE… view at source ↗
Figure 75
Figure 75. Figure 75: (a) N 0 (1); (b) N 0 (2); (c) N 0 (3); (d) N 0 (0). and  n 0 v (t) = α0M(t, k); n 0 e (t) = (β0 + 1)M(t, k). (53) where M(t, k) = Pt−1 k=1 Pk−1 j=0 Fk−j · |Vj |. Moreover, the formula (50) and the formula (51) give us  n 0 v (t) − nv(t) = n 0 v (t − 1) − nv(t − 1) + F • V ; n 0 e (t) − ne(t) = n 0 e (t − 1) − ne(t − 1) + F • V. (54) where the vector dot-product F • V = (F1 F2 · · · Ft) • (|Vt−1| |Vt−2| … view at source ↗
Figure 76
Figure 76. Figure 76: A Topsnut-gpw set F odd f (G). Theorem 30. If N(t) is a tree-like Hanzi-network, and an every-zero graphic group {Ff (G), ⊕} has q Topsnut-gpws such that q is not less than the number of neighbors of any vertex of N(t), then we can have a mapping F to encrypt N(t) with {Ff (G), ⊕} such that F(uv) 6= F(uw), that is, F(u) ⊕kuv F(v) 6= F(u) ⊕kuw F(w) (59) for any pair of adjacent edges uv and uw of N(t). The… view at source ↗
Figure 78
Figure 78. Figure 78: (a) A Hanzi-graph T2026 is labelled with an every-zero graphic group G 15 roup = {F odd f (G) ∪ F even f (G), ⊕k} under the zero G15; (b) a Hanzi-graph T3546 is labelled with an every-zero graphic group G 20 roup = {F odd f (G) ∪ F even f (G), ⊕k} under the zero G20. network, that is, V (N(t)) = Sk i=1 Vi , each Vi induces a subgraph Ti such that V (Ti) = Vi , let Ei,j be the set of edges in which each ed… view at source ↗
Figure 79
Figure 79. Figure 79: (c) A Hanzi-graph T2026 is labelled with an edge-every-zero graphic group G 15 roup = {F odd f (G)∪F even f (G), ⊕k} under the edge￾zero G15; (d) a Hanzi-graph T3546 is labelled with an edge-every￾zero graphic group G 20 roup = {F odd f (G) ∪ F even f (G), ⊕k} under the edge-zero G20. We take an every-zero graphic group {Ff (G), ⊕} with Ff (G) = {Gi} n 1 and G is a (p, q)-graph, such that, n ≥ k and n ≥ m… view at source ↗
Figure 80
Figure 80. Figure 80: A scheme for encrypting communities. We have n k  groups of Gi1 , Gi2 , . . . , Gik as zeros for encrypting communities T1, T2, . . . , Tk, where i1, i2, . . . , ik is a permutation of k number of 1, 2, . . . , n. Thereby, N(t) can be encrypted by at least n k  k! methods. Suppose that the graph G in an every-zero graphic group {Ff (G), ⊕} admits m labellings f (l) with l ∈ [1, m]. If these labellings f… view at source ↗
Figure 81
Figure 81. Figure 81: Six every-zero graphic groups. Let V (T4476) = X ∪ Y be the set of vertices of a Hanzi￾graph T4476 shown in Fig.82, where X = {x1, x2, x3, x4, x5, x6}, Y = {y1, y2, y3, y4, y5}; E(T4476) = {ei : i ∈ [1, 9]}. (63) 43 [PITH_FULL_IMAGE:figures/full_fig_p043_81.png] view at source ↗
Figure 82
Figure 82. Figure 82: An every-zero graphic group {FfG (G), ⊕} made by Hanzi￾graph T4476 admitting a set-ordered graceful labelling. where e1 = x1y5, e2 = x1y4, e3 = x1y3, e4 = y3x2, e5 = y3x3, e6 = y3x4, e7 = y2x4, e8 = y1x5, e9 = y1x6. The property of “set-ordered” tells us: f (j) G (xi) < f (j) G (xi+1), f (j) G (x6) < f(j) G (y1), f (j) G (yj ) < f(j) G (yj+1) for T4476 = G = G1 shown in Fig.82, and j ∈ [1, 11]. Also, we h… view at source ↗
Figure 81
Figure 81. Figure 81: Fig.81 [PITH_FULL_IMAGE:figures/full_fig_p044_81.png] view at source ↗
Figure 84
Figure 84. Figure 84: Hanzi-graph T4476 admits a set-ordered 0-rotatable system of (odd-)graceful labellings. group {FfG (G), ⊕}, can induce a TB-paw D(T4476) =D(G11)D(G4)D(G1)D(G3)D(G10) D(G2)D(G3)D(G9)D(G4)D(G3) D(G1)D(G2)D(G9)D(G5)D(G4) D(G4)D(G8)D(G5)D(G4)D(G7) D(G5)D(G6) (65) with at least 500 bytes (500 × 8 = 4000 bits). Moreover, this TB-paw D(T4476) has its own strong-rank H(D(T4476)) computed by H(D(T4476)) = L(D(T447… view at source ↗
Figure 85
Figure 85. Figure 85: A Hanzi-network T4476 is encrypted by six every-zero graphic groups shown in Fig.81, respectively. Theorem 32. If a (p, q)-graph G admits two mutually equiv￾alent labellings fa and fb, then two every-zero graphic groups {Ffa (G), ⊕} and {Ffb (G), ⊕} induced by these two labellings of G are equivalent to each other. 7) Encrypting Hanzi-networks with many restrictions: No￾tice that there are many gg-colorin… view at source ↗
Figure 86
Figure 86. Figure 86: Ha (left) is a half-directed Hanzi-gpw made by a Hanzi H4476, and Hb (right) is a directed Hanzi-gpw made by a Hanzi H4476. Here, replacing arcs by proper edges in a directed graph, or a half-directed graph produces a graph, we call this graph as the underlying graph of the directed graph, or the half-directed graph. Definition 47. ∗ Let f : V (G→) → [0, q] (resp. [0, 2q−1]) be a labelling of a half-direc… view at source ↗
Figure 87
Figure 87. Figure 87: (a) A directed tree admits a uniformly directed graceful labelling; (b) a tree admits a graceful labelling. Proposition 38. Let −→O(T) be a set of directed trees hav￾ing the same underlying tree T. If GTC-conjecture (resp. OGTC-conjecture) holds true, then −→O(T) contains at least two directed trees admitting uniformly directed (odd-)graceful labellings, and each directed tree of −→O(T) admits a directed … view at source ↗
Figure 89
Figure 89. Figure 89: Fig.89. How many Chinese sentences having real meanings [PITH_FULL_IMAGE:figures/full_fig_p049_89.png] view at source ↗
Figure 91
Figure 91. Figure 91: A digraph G labellined with Hanzis is made by six directed paths shown in (a)-(f). Problem-20. In Definition 36, it is easy to see m − 1 = min{|Ej | : j ∈ [1, n]}, we hope to determine max{|Ej | : j ∈ [1, n]} for each disconnected graph G = Sm i=1 Gi having disjoint components G1, G2, . . . , Gm. Problem-21. How to replace each triangular vertex (see Fig.92) of a public key T being a labelled graph with a… view at source ↗
Figure 90
Figure 90. Figure 90: Stars K1,j with j ∈ [3, 9] can be decomposed into Hanzi￾graphs only by the vertex-split operation defined in Definition 33. Problem-18. Since any graph can be decomposed into Hanzi-graphs, determine the smallest number of such Hanzi￾graphs from the decomposition of this graph (Ref. [24]). We may provide a public key (graph) G to ask for private keys made by some groups of Hanzi-graphs from the decompositi… view at source ↗
Figure 92
Figure 92. Figure 92: Two public key Topsnut-gpw T1 and T2 for finding private key Topsnut-gpws. H1 2 4 17 11 20 23 5 10 9 8 18 17 11 8 9 7 16 6 10 3 15 12 1 13 14 16 15 22 21 19 18 4 23 5 3 25 14 24 13 12 7 20 19 6 22 21 26 28 27 25 24 1 26 2 28 0 27 8 3 6 23 17 11 16 15 14 21 20 8 5 6 13 19 12 7 7 17 10 9 9 18 28 27 2 1 5 4 11 16 12 13 15 26 14 25 24 1 26 25 0 28 27 20 22 21 19 18 3 22 4 24 2 23 10 H2 [PITH_FULL_IMAGE:figur… view at source ↗
Figure 93
Figure 93. Figure 93: Two private key Topsnut-gpws H1 and H2 as two solutions for the question based on two public key Topsnut-gpws T1 and T2 shown in Fig.92. graceful labelling for a graph, even for trees. Problem-23. Find graph labellings of Fibonacci self￾similar Hanzi-networks obtained by FIBONACCI-EDGE al￾gorithm or FIBONACCI-VERTEX algorithm. Problem-24. Given a disconnected graph H = Sm j=1 K j 2 having disjoint subgrap… view at source ↗
Figure 95
Figure 95. Figure 95: Prof. Xu’s pseudo Hanzis. Problem-27. We show some other type of connected pa￾rameters for further researching graph connectivity: Definition 52. Let H be a proper subgraph of a graph G. We say G to be H-connected if G − V (H) is disconnected. Particularly, we have new parameters: (1) κcycle(G) = min{m : G is Cm-connected}, where each Cm is a cycle of m vertices in G. (2) κpath(G) = min{n : G is Pn-connec… view at source ↗
Figure 98
Figure 98. Figure 98: Another graph admitting a Hanzi-idiom labelling. can be considered as a public key, so we want to find some private keys shown in Fig.50(b). Hence, for a given group of topological structures, how many paragraphs written in Chinese are there? B. Discussion H 3 84 87 7 78 85 8 76 84 10 73 83 13 67 80 14 64 78 20 55 75 21 49 70 24 45 69 36 15 51 38 8 46 42 2 44 25 40 65 26 37 63 27 28 55 33 20 53 34 18 52 2… view at source ↗
Figure 99
Figure 99. Figure 99: A disconnected graph H admitting a total labelling. 81 83 82 80 79 86 6 85 4 87 5 52 54 53 51 50 20 71 21 73 19 72 69 68 70 72 71 81 80 11 82 10 12 62 57 63 61 60 56 14 18 15 59 58 17 16 75 77 74 76 1 43 44 9 13 14 12 50 51 40 37 38 11 49 10 39 19 53 34 47 48 46 69 23 70 22 44 43 67 24 68 41 66 25 75 74 9 83 8 77 84 7 39 65 38 26 64 17 16 35 52 36 6 7 5 4 3 42 46 45 41 47 48 30 29 31 32 33 29 59 28 33 35 … view at source ↗
Figure 100
Figure 100. Figure 100: A disconnected graph G admitting a flawed graceful labelling. (1) Problem-24 can be planted into the graph labellings defined or listed here and others defined in [11]. We show some solutions for Problem Problem-24 below. Theorem 42. Given a disconnected graph H = Sm j=1 K j 2 having disjoint subgraphs K1 2 , K2 2 , . . . , Km 2 holding K j 2 ∼= K2 for j ∈ [1, m]. Assume that H admits a total labelling h… view at source ↗
Figure 97
Figure 97. Figure 97: A graph admitting a Hanzi-idiom labelling. Problem-29. A group of topological structures in Fig.50(a) [PITH_FULL_IMAGE:figures/full_fig_p052_97.png] view at source ↗
Figure 101
Figure 101. Figure 101: (a) H = K1 2 ∪ K2 2 ; (b) H0 1. … … … … [PITH_FULL_IMAGE:figures/full_fig_p053_101.png] view at source ↗
Figure 102
Figure 102. Figure 102: (a) H2; (b) G = S3 i=1 Gi. Remark 6. (1) In the proof of Theorem 42, we use stars to provide a solution. In general, assume that each tree Tk of pk vertices admits a set-ordered graceful labelling fk such that max fk(Ak) < min fk(Bk), where V (Tk) = Ak ∪ Bk, Ak = {uk,1, uk,2, . . . , uk,sk } and Bk = {wk,1, wk,2, . . . , wk,tk }, pk = |V (Tk)| = sk + tk, as well as fk(uk,iwk,j ) = fk(wk,j ) − fk(uk,i) fo… view at source ↗
Figure 105
Figure 105. Figure 105: (a) A Hanzi-gpw H gpw 4043; (b) a hollowed Hanzi-gpw with a flawed set-ordered graceful labelling based on Hanzi-graph T4043; (c) an Euler-gpw with a v-set e-proper graceful labelling. (b) A Hanzi-gpw 4 10 13 9 8 12 11 6 16 5 20 17 19 18 2 3 7 7 20 0 4 1 10 19 9 18 15 13 3 2 8 4 6 16 14 17 15 5 1 11 (a) A Hanzi H4585 and Hanzi-graph T4585 H4585 T4585 (c) An Euler-gpw with a v-set e-proper graceful labell… view at source ↗
Figure 106
Figure 106. Figure 106: (a) A Hanzi H4585 and its Hanzi-graph H4585; (b) a hollowed Hanzi-gpw with a graceful labelling based on Hanzi H4585; (c) an Euler-gpw with a v-set e-proper graceful labelling. with n ≡ 0, 3 (mod 4) admits a v-set e-proper graceful labelling. Theorem 44. [40] Every connected Euler’s graph with odd n edges admits a v-set e-proper harmonious labelling. Definition 53. ∗ A (p, q)-graph G admits a vertex labe… view at source ↗
Figure 104
Figure 104. Figure 104: H G admits an odd-graceful labelling, G = (H G) − E(H) admits a flawed odd-graceful labelling. (2) Outline Hanzis (hollow font) are popular in Chinese cultural. Some Hanzis can be obtained by cycles Cn with some labellings and Euler graphs (see Fig.105). We can split some Euler-gpws into hollowed Hanzi-gpws. Two Euler-gpws with v-set e-proper graceful labellings shown in Fig.105(c) and Fig.106(c) can be … view at source ↗
Figure 107
Figure 107. Figure 107: Each cycle (k-1) admits a v-pseudo e-proper graceful labelling for k =a,b,c,d. between printed Hanzis. Hanzis for mathematical models are based on GB2312-80. Hanzi-gpws introduced in Section 4 are constructed by two constituent parts: Hanzi-graphs in Section 2 and graph labelling/colorings in Section 3. By the disconnected property of Hanzi-gpws we define a new type of graph labellings, called flawed gra… view at source ↗
Figure 108
Figure 108. Figure 108: The word groups related with a Hanzi H4043, also H4043 =man. 58 [PITH_FULL_IMAGE:figures/full_fig_p058_108.png] view at source ↗
Figure 109
Figure 109. Figure 109: The idioms related with a Hanzi H4043. 59 [PITH_FULL_IMAGE:figures/full_fig_p059_109.png] view at source ↗
read the original abstract

Graphical passwords (GPWs) are in many areas of the current world. Topological graphic passwords (Topsnut-gpws) are a new type of cryptography, and they differ from the existing GPWs. A Topsnut-gpw consists of two parts: one is a topological structure (graph), and one is a set of discrete elements (a graph labelling, or coloring), the topological structure connects these discrete elements together to form an interesting "story". Our idea is to transform Chinese characters into computer and electronic equipments with touch screen by speaking, writing and keyboard for forming Hanzi-graphs and Hanzi-gpws. We will use Hanzigpws to produce text-based passwords (TB-paws). We will introduce flawed graph labellings on disconnected Hanzi-graphs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes transforming Chinese characters into Hanzi-graphs (disconnected graphs) equipped with flawed graph labellings to generate topological graphic passwords (Topsnut-gpws) that can then be converted into text-based passwords (TB-paws) for information security applications. The approach is described as using speaking, writing, and keyboard input to interface Chinese characters with touch-screen devices.

Significance. The core idea of using Chinese characters and graph labellings for password generation is conceptually novel within graphical password schemes. However, the manuscript provides no entropy estimates, attack resistance analysis, comparisons to existing schemes, or usability data, so any potential significance for the field cannot be evaluated from the current text.

major comments (1)
  1. [Abstract] Abstract: The claim that Hanzigpws will produce secure and practical TB-paws rests on the introduction of flawed graph labellings on disconnected Hanzi-graphs, yet the manuscript contains no security proofs, attack models, entropy calculations, or experimental results to support this. This absence is load-bearing for the central claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed comments. The manuscript is a conceptual proposal introducing Hanzi-graphs and flawed graph labellings for generating Topsnut-gpws convertible to TB-paws; it does not claim to deliver a fully analyzed scheme.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that Hanzigpws will produce secure and practical TB-paws rests on the introduction of flawed graph labellings on disconnected Hanzi-graphs, yet the manuscript contains no security proofs, attack models, entropy calculations, or experimental results to support this. This absence is load-bearing for the central claim.

    Authors: We agree the manuscript contains no security proofs, attack models, entropy calculations or experimental results. The work is an initial proposal of the Hanzi-graph construction and the use of flawed labellings on disconnected graphs; the statements about producing secure TB-paws are forward-looking rather than demonstrated. We will revise the abstract and introduction to replace 'will produce secure' phrasing with 'aim to generate' and 'potential for' and will add an explicit 'Future work' paragraph stating that entropy analysis, attack resistance and usability studies remain to be performed. revision: yes

Circularity Check

0 steps flagged

No significant circularity; conceptual proposal without derivations or self-referential claims

full rationale

The paper introduces the idea of transforming Chinese characters into Hanzi-graphs equipped with flawed graph labellings to generate text-based passwords, but presents no equations, quantitative predictions, fitted parameters, or derivation chains. No load-bearing steps reduce by construction to inputs, and the provided text contains no self-citations invoked as uniqueness theorems or ansatzes. The claims remain unsupported assertions rather than derived results, so the manuscript is self-contained with no circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

Only abstract available; the proposal rests on the untested assumption that graph labellings of Chinese characters yield usable passwords and on the authors' prior Topsnut-gpw framework.

axioms (1)
  • domain assumption Graph theory structures can model secure and memorable passwords
    Invoked when the abstract states that topological structures plus labellings form an interesting story for passwords.
invented entities (2)
  • Hanzi-graphs no independent evidence
    purpose: Represent Chinese characters as graphs for password generation
    New term introduced without independent evidence of security benefit
  • flawed graph labellings no independent evidence
    purpose: Label disconnected Hanzi-graphs to produce text passwords
    New labelling variant introduced without definition or proof of utility

pith-pipeline@v0.9.0 · 5708 in / 1167 out tokens · 24542 ms · 2026-05-24T22:47:31.371055+00:00 · methodology

discussion (0)

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Reference graph

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