200822662 九、發明說明： 【發明所屬之技術領域】 本發明係有關一種用於保密通訊之超渾沌系統與方 法，尤指一種用於數位保密通訊之強健式超渾沌加密解密之 系統與方法。 【先前技術】 著電腦與網際網路廣泛的使用，通訊之安全性益趨重 要然而於一般之負料數位通訊，大多數皆無加密與解密之 功月t ’亦即無數位保密通訊之功能。 此外，Pic著渾ί屯科技之發展，越來越多的研究開始聚焦 於由非線性祕所產生之渾_制於保密通訊之可能 性。由於非線縣統產生之渾域道具有無規律性 、無週期 陡不可預測、相當靈敏地依賴初始條件等特性，以及關於 兩個非線性純間之渾制步化技術之發展，渾㈣統確可 應用於保密通訊上。 於-潭祕密通訊中，渾洗訊號可用作為掩蔽流來攜帶 貝Α然後藉由發送端與接收端間渾洗同步化性態，可將該 200822662 Μ »孔回復然而，早先大多數對渾洗保密通訊之研究主要係 針對類比峨方面。僅有少數研究聚焦於數位峨之保密通 訊上。 關於數位保密通訊的研究方面，雖然發現利用邏輯映射 之一渾料、統的確可以產生具不可預測性之相；然而，由 於欠缺精準度’齡統僅具有少量之整體狀態，因此容易遭 受藉由對雜、魏。料，岐該純可糊左循環 函數與參數回饋迴路來加贿密之強度。令人遺韻是，於 選擇明文之假定下，該種系統仍容易遭受攻擊。另一方面， 許夕研究聚t、於對科絲軌之攻紅；結絲示，該系 統將可被以輸出序列描繪之映射攻擊；其原因在於每單一渾 洗系統具有其鱗之映射麵’藉此將胁分辨不同的渾洗 系統並重建其方程式。 為解決此問崎，大多數提出之研究聚焦於如何增強輸出 序列之複雜。_研究大致可料三類1-類··為使初 〜K號不可糊，便制另—渾触射來產生初始訊號至一 此先映射。第二類：使用數個渾触射；於任何時間，使用 特疋之映射，其係依據—絲定義順序或是—使用者定義 機制第—類係為前兩類之結合型。需注意的是，此三類 7 200822662 方法仍使用僅有-個Lyapun〇v正指數之一維系統 ，如此仍 然侷限了渾沌動力學之複雜性。 此外，參數值之可用區域為一不連續渾洗同步化系統之 缺點所在。系統之秋性_視其參數而定。然而令人遺憾 的疋亚非所有的錄皆為钱，其巾—些參數將會導致「空 由J匕處之i由」係定義為一非線性系統之渾綠道於 電腦上以湖性模式顯現^此時，因參數空聰小，所以剩 餘的參數空間可能易於遭受蠻力計數法之攻擊。 一傳統邏輯映射L可定義為·· «i+υ = L (r，x(i)) =rx(i) (1_x⑴），x⑴e似] 其中r為-參數且〇卞4。於上述之方程式，當3 57 < γ = 4時’所產生的序列係為非週期性與非收斂性的。然而， 於:.57 <r = 4下造成該方程式「空窗」之參數r係為開放 且密集。此外，混沌吸子並未分佈於於〇與丨範圍之間，且 長度小於1。於此情況下，藉由測量混沌吸子的長度，將十 分各易探知r值。而於該方程式中唯一可行的情況為當 之時，當是時渾沌吸子均勻分佈於0與1的範圍間。由此觀 之，r數值之選取係極為有限。 8 200822662 【發明内容】 本發明之一目的在於提供用於保密通訊之一強健式超 渾沌加密解密系統，該系統具有較大之參數空間，得以避免 蠻力計數法之攻擊，且無法運用現今運算科技重建該系統。 本發明之另一目的在於提供用於保密通訊之一強健式 超渾沌加密解密系統，其針對同一明文訊息，可藉由不同初 始向量之輸入而相應產生不同之超渾沌密文，藉此提高保密 層級。 本發明之再一目的在於提供用於保密通訊之一強健式 超渾>屯加密解密祕，該系統可產生不完全_帶映射來傳 送於公共通道之中，藉此，即使在選擇明文攻擊的假設狀態 下，亦難以重建該映射。 為達到上述目的，本發明提供之強健式超渾沌加密解密 系統，其包括—發送端與—接收端。其中該發送端包括一超 渾/屯訊號產生$，其可將—明文訊息攜人為超渾⑨訊號之一 掩蔽序W巾’與—發送端參數調整裝置，用於調整該超渾洗 訊號產生11之參數，藉此該超渾織號產生n可將明文訊息 與掩蔽序_為—轉祕文。該密文储由該超渾洗產生 裔傳达至該接收端。哺接收端包括—超渾航制步接收 9 200822662 器’其用於產生為超渾沌訊號之一去掩蔽序列，且將超渾沌 密文與去掩蔽序列轉變為一解密明文訊息；一接收端參數調 整裝置，用以調整該超渾沌訊號同步接受器之參數，使其於 接收超渾沌密文後，得以藉由與發送端之掩蔽序列達成超渾 沌同步而產生一為超渾沌訊號之去掩蔽序列。 此外’本發明之強健式超渾沌加密解密方法，包括一加 密與一解密過程。該加密過程包含下列步驟：首先，將明文 訊息解構至-{#)丨序列，而後藉互斥運算將該序職入一為 超渾沌訊號之掩蔽序列中，產生一超渾沌密文；而解密過程 貝J包括下列步驟··於接收端接收該密文後，藉由與發送端之 掩蔽序列達成超渾沌同步而產生一為超渾沌訊號之去掩蔽 序列，而後藉互斥運算將該欲文轉變為解密明文訊息。該掩 蔽序列較佳依照輸入之初始向量與參數而產生，而該去 掩蔽序列較佳依輸入之初始向量y⑼與參數而產生；藉此， 針對同一明文訊息若使用不同之初始向量，將可產生不同的 密文。而該初始向量X(〇)較佳於該發送端隨機產生，然後被 y(())取代後傳送至該接收端，再於該接收端由义⑼代換之，·藉 此，該掩蔽序列將與該去掩蔽序列相當，而密文將得以正確 地被解密。 10 200822662 實作―瞭解’， 【實施方式】 如第1圖所示’於-般保密通訊方案中，資訊在經過訊 破源編媽、加密、通道編碼與簡後，由魏方賴道輸送。 接收端則藉由顛倒上述步驟來回復資訊。而於本發明中，輸 入項相對應來自於訊龍編碼步驟，而輪出酬相對應送至 通道編碼與調變之步驟。 第2圖所不’根縣發明之—強健式超科加密解密 …括發送端10與一接收端6〇。其中該發送端忉包括 超Hfl號產生器20與一發送端參數調整裝置3〇。該設 置於該發送端H)之超科訊號產生器2㈣崎—明文訊息 22載入為超渾洗訊號之_掩蔽序列24中該掩蔽序列㈣ 由該超渾⑨峨產生H 2Q所產生。而該發送端參數調整裝 置30則用於調整該超渾輪號產生器2q之參數，藉此使得 以超Hfl號產生$ 2〇得以將該明文訊息22與該掩蔽序列 24轉變為-超渾洗密文5〇。該超渾洗密文5〇係藉由該超渾 tfl號產生g 2〇由發送端1Q傳送至接㈣⑼。義接收端 200822662 60則包括-超渾洗訊號同步接收器7〇與一接收端參數調整 裝置別。該接收端參數調整裝置8G肋調整該超渾洗訊號 同步接收H 7G之參數’藉此，該超渾舰朗步接收器7〇 於接收該超渾_文5〇後’得以藉與該發送端1()之掩蔽序 列24達成料朗麵產生—為超料峨之去掩蔽序列 76。此外’該超渾舰制步接㈣7{)亦將該超軍絲文 5〇與該錢蔽序列76經互斥運算轉變為-解密明文訊息 90 〇 此外，該強健式超渾洗加密解密系統係使用兩個強健式 超渾洗工具’其巾每—健健式超渾駐具由概個強健式 邏輯映射、-個攜帶映射與數個隱匿映射組成。其中該強健 式邏輯映射為-均勻分佈之映射’具有—較大之參數空間， 其使用一強健式邏輯函數定義如下： L(r，x)= 7 xu-x; (modi) x(l-x) (modi) (r/4)(modl) ，x e lim [7 其中 U E (〇，l)\Iint，jnt=[y7i V2l，Γ ，77 2= 1/2十 i/4——Vr^\ · Jixb mi ^ 松 1 γ 5 /、τ [·]為一等於或小於ω 之最大整數。 根據上述該強健式邏輯錄之方程式，7值之範圍可延 200822662 伸超過4。當[(r，x)大於i時’上述之第一個方程式可將大 於1之映射值轉至(T1之範圍内，其中模組式單運算得使X 值不變地保持於_。然而，當x值在Iint範圍時，該映射將 會不均勻分佈，而造成該映射之「空窗」。因此，冑 小於1時’上述第二個方程式可將該健比例轉至i細 内。藉由該模組式運算與比例式運#，可使該映射均句分佈 於範圍内。 該超渾沌訊號產生器20之作用係利用一第一強健式超 渾沌工具，其可定義為： Χ(1) = := CJL(r，x(m )，其中㊇忖 Xi(i),，BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a hyperchaotic system and method for secure communication, and more particularly to a system and method for robust hyperchaotic encryption and decryption for digital secure communication. [Prior Art] With the widespread use of computers and the Internet, the security of communication is becoming more important. However, in general, digital communication with negative data, most of which have no function of encryption and decryption, that is, the function of digital security. In addition, with the development of the technology, more and more research has begun to focus on the possibility of secret communication caused by nonlinear secrets. Due to the irregularity of the non-line county, the unpredictable period without periodicity, the sensitivity to rely on the initial conditions, and the development of the two-dimensional pure inter-step technology, 浑(四) Can be applied to secure communications. In the secret communication of Yutan, the scrubbing signal can be used as a masking stream to carry the bellows and then the synchronization state can be washed between the transmitting end and the receiving end, and the 200822662 Μ» hole can be recovered. However, most of the previous washing The study of confidential communications is mainly aimed at analogy. Only a few studies have focused on digital security communications. Regarding the research on digital secure communication, although it is found that the use of one of the logical mappings can indeed produce an unpredictable phase; however, due to the lack of precision, the age system has only a small overall state, so it is vulnerable to Miscellaneous, Wei. Material, 纯 This pure pasteable left cycle function and parameter feedback loop to increase the strength of bribery. The hallmark is that the system is still vulnerable to attack under the assumption of clear text. On the other hand, Xu Xi studies poly, and attacks on the silk track; the knot shows that the system can be attacked by the mapping of the output sequence; the reason is that each single wash system has its scale mapping 'This will distinguish the different wash systems and reconstruct their equations. To solve this problem, most of the research proposed focuses on how to enhance the complexity of the output sequence. _ Research can roughly predict three types of 1-class · · In order to make the initial ~ K number can not be pasted, then another - 浑 shot to generate the initial signal to a map. The second category: the use of several strontium shots; at any time, the use of special maps, which are based on the silk definition order or the -user-defined mechanism - the first two types of combinations. It should be noted that these three types of 7 200822662 methods still use a one-dimensional system with only one Lyapun〇v positive exponent, which still limits the complexity of chaotic dynamics. In addition, the available area of the parameter value is a disadvantage of a discontinuous wash synchronization system. The autumn nature of the system depends on its parameters. However, it is regrettable that all the records in Asia and Africa are money, and the parameters of the towel will lead to the definition of "empty by J", which is defined as a nonlinear system. Mode appears ^ At this time, because the parameters are small, the remaining parameter space may be vulnerable to brute force counting. A conventional logic map L can be defined as «i+υ = L (r, x(i)) = rx(i) (1_x(1)), x(1)e is like] where r is the - parameter and 〇卞4. In the above equation, the sequence produced when 3 57 < γ = 4 is non-periodic and non-convergent. However, at: .57 <r = 4, the parameter r of the equation "empty window" is open and dense. In addition, the chaotic attractors are not distributed between the 〇 and 丨 ranges, and the length is less than 1. In this case, by measuring the length of the chaotic attractor, it is easy to detect the r value. The only feasible case in this equation is that when it is, the chaotic attractors are evenly distributed between the range of 0 and 1. From this point of view, the selection of r values is extremely limited. 8 200822662 SUMMARY OF THE INVENTION One object of the present invention is to provide a robust hyperchaotic encryption and decryption system for secure communication, which has a large parameter space to avoid brute force counting attacks and cannot use current computing. Technology rebuilds the system. Another object of the present invention is to provide a robust hyperchaotic encryption and decryption system for secure communication, which can generate different hyper-chaotic ciphertexts by inputting different initial vectors for the same plaintext message, thereby improving confidentiality. Level. It is still another object of the present invention to provide a robust over-the-spot encryption encryption decryption secret for secret communication, which system can generate incomplete_band mapping for transmission in a common channel, thereby even selecting a plaintext attack. In the hypothetical state, it is also difficult to reconstruct the mapping. To achieve the above object, the present invention provides a robust hyperchaotic encryption and decryption system including a transmitting end and a receiving end. The sending end includes a super/浑 signal generation $, which can be used to adjust the super-wash signal generation device by using the plaintext message as one of the super-9 signals. 11 parameters, whereby the super-texture generation n can be used to clear the plaintext message and the masking sequence. The ciphertext store is communicated to the receiving end by the super-washing generator. The receiving end includes - the super-snoring step receiving 9 200822662 'which is used to generate one of the super-chaotic signals to mask the sequence, and converts the hyper-hidden ciphertext and the de-masking sequence into a decrypted plaintext message; a receiving end parameter The adjusting device is configured to adjust the parameter of the super-chaotic signal synchronous receiver to generate a super-chaotic sequence of the super-chaotic signal by receiving a hyperchaotic synchronization with the masking sequence of the transmitting end after receiving the super-hidden ciphertext . Further, the robust hyperchaotic encryption and decryption method of the present invention includes an encryption and a decryption process. The encryption process comprises the following steps: first, deconstructing the plaintext message to the -{#) sequence, and then using the mutual exclusion operation to enter the sequence into a masking sequence of the super-chaotic signal to generate a hyper-hidden ciphertext; The process J includes the following steps: After receiving the ciphertext at the receiving end, a super-chaotic synchronization is generated by a masking sequence with the transmitting end to generate a de-masking sequence of the hyper-chaotic signal, and then the repulsion is performed by the mutual exclusion operation. Change to decrypt plaintext messages. The masking sequence is preferably generated according to an initial vector and a parameter of the input, and the demasking sequence is preferably generated according to the input initial vector y(9) and parameters; thereby, if different initial vectors are used for the same plaintext message, Different ciphertexts. The initial vector X(〇) is preferably randomly generated at the transmitting end, then replaced by y(()) and transmitted to the receiving end, and then replaced by the meaning (9) at the receiving end, thereby, the masking The sequence will be equivalent to the demasking sequence and the ciphertext will be decrypted correctly. 10 200822662 Implementation--Understanding, [Implementation] As shown in Figure 1, in the general security communication scheme, the information is transmitted by Weifang Laidao after the source is encrypted, encrypted, channel coded and simplified. . The receiving end responds to the information by reversing the above steps. In the present invention, the input item is correspondingly derived from the Xunlong coding step, and the round payment is correspondingly sent to the channel coding and modulation step. In the second figure, the invention is invented by the root county. The robust super-tech encryption and decryption includes the transmitting end 10 and a receiving end 6〇. The transmitting end includes an ultra Hfl number generator 20 and a transmitting end parameter adjusting device 3〇. The masking sequence (4) of the super-sigma signal generator 2 (4), which is placed at the transmitting end H), is loaded into the masking sequence 24 of the super-wash signal, and the masking sequence (4) is generated by the generating of the H 2Q. The transmitting end parameter adjusting device 30 is configured to adjust the parameter of the super wheel number generator 2q, thereby causing the clear text message 22 and the masking sequence 24 to be converted into a super-浑 by generating a $2〇 with the super Hfl number. Wash the ciphertext 5 〇. The super-small ciphertext 5 is transmitted from the transmitting end 1Q to the fourth (9) (9) by generating the g 2 该 by the super 浑 tfl number. The receiving end 200822662 60 includes a super-washing signal synchronous receiver 7〇 and a receiving end parameter adjusting device. The receiving end parameter adjusting device 8G rib adjusts the parameter of the super-washing signal synchronous receiving H 7G. Thereby, the super-small stalking receiver 7 is able to borrow the sending after receiving the super-浑 文 5文The masking sequence 24 of the end 1 () achieves the production of the surface - a masking sequence 76 for the excess. In addition, the super-snake ship step (4) 7{) also converts the super-milk file 5〇 and the money cover sequence 76 into a deciphering plaintext message 90. In addition, the robust ultra-washing encryption and decryption system The use of two robust super-washing tools 'the towel per-health-type super-station consists of a robust logical mapping, a carrying map and several hidden mappings. Where the robust logical mapping is a - uniformly distributed mapping 'has a larger parameter space, which is defined using a robust logical function as follows: L(r, x) = 7 xu-x; (modi) x(lx) (modi) (r/4)(modl) ,xe lim [7 where UE (〇,l)\Iint,jnt=[y7i V2l,Γ ,77 2= 1/2 十 i/4——Vr^\ Jixb mi ^ loose 1 γ 5 /, τ [·] is a maximum integer equal to or smaller than ω. According to the above equation of the robust logic record, the range of 7 values can be extended to more than 4 in 200822662. When [(r,x) is greater than i, the first equation above can transfer the mapped value greater than 1 to (T1), where the modular single operation keeps the X value unchanged at _. When the value of x is in the range of Iint, the mapping will be unevenly distributed, resulting in an "empty window" of the mapping. Therefore, when 胄 is less than 1, the second equation above can be used to shift the ratio to i. The mapping average sentence can be distributed within the range by the modular operation and the proportional operation. The super-chaotic signal generator 20 functions as a first robust hyperchaotic tool, which can be defined as: (1) = := CJL(r,x(m ), where gossip Xi(i),,
Xn(i)]T ’ 他 x(’[L(r i，Xl ㈣）’…’ L(Tn， 中尤(r，x)為一強健式邏輯函數，已於上述提及，且 r^\\ C12 ... cln^ C= c”，….〜Xn(i)]T 'he x('[L(ri,Xl (4))'...' L(Tn, 中尤(r,x) is a robust logic function, mentioned above, and r^\ \ C12 ... cln^ C= c",....~
Cn2 · · · Cnn 其為一正隨機耦合矩陣，其中所有元素係為OsCijSi，且 Σ(Ι^=1 f〇rij= ΐ”··，η。 此外，該掩蔽序列24可定義為z(i) = Xl(〇，係由發送端 10之該超渾池訊说產生器20依照輸入之初始向量與袁數所 13 200822662 產生，其中該初始向量可定義為· /〇、[ Μ⑼，，χ (0>^其 中沪ΕΚ〇，1)\{1/2}};而該參數包括 Χη 八 π仃η列之隨機矩 陣 C = [(¾]，其中 〇< q <i、i j=i θ IJ ，J ，·..，η，以及—渾沌參數向 量r = [ri ’ …，rJT，其中？1 = 4、i=1 „ 而該超渾舰號同步接收器70之作用係利用一第二強 健式超渾沌工具，可定義為： γω = G(rsy^)：=CiL(r,x^)，y^[yi(i), ^ ,yn(i)]X ^ i>o。 而該去掩蔽序列76可定義為·· z(i) e yi (i)，係由接收端 60之解舰朗步触n 7G健獻之初始㈣y⑼％ 數而產生。 於此需要注意的是’該第—強㈣超渾紅具與第二強 健式超渾洗工具分別屬於x①與#，且具有相同參數c和犷。 此外’根據本發明之-強健式超渾洗加密解密方法則包 括-城與-觸雜，其巾該加㈣程為：將明文訊息解 構至-相，藉互斥運算_序_人—鱗紐號之掩蔽 序列中，產生-超浑死密文;解密過程則為：於接收端接收該 密文後，藉由與發送端之掩蔽序列達成超渾沌同步而產生一 為渾洗訊狀去減序列，藉互斥運算將密讀為解密明文 14 200822662 訊息。 當該明文訊息22進人發送端10後，將被解構為-{ρ(π} : 序列。若將該第—_式超渾紅具之實數位元表示為m， 丨 而令每一 p(i)之長度為4，則其關係可表示為：d = m—〖eN， 卜1。於此條件下，於該發送端進行之該加密程序定義為： ^吃〜①丄， cw= Ζω0ρ(1)，其中0代表互斥運算，而 代表自X脫落最初《數位。 而於接收端進行之該解密過程可定義為：#= Ly/j £， p(1)= zd)©^1)，其中ρω為—解密明文訊息。 須注意的是，該初始向量X (0)係由該發送端隨機產生， 然後由y(G)取代後傳送至該接收端，再於該接收端由代 % 換之；經上述步驟，ζ〇)== ζ (1)、1 > 〇。而由於該第一強健 式超渾沌工具與第二強健式超渾沌工具具有相同初始向 量，且z(i)= z(i)，是故該密文50可被正確地解密，亦即， P (i) = P(i)。 此外，藉由於通訊中隱匿ί個最重要之數位，亦即，將 這些ί個數位脫落不使用於加密中，藉此，掩蔽序列24之 隨機性可被加強。隱匿越多位元，該密文5〇將越難被分析。 15 200822662 然而，保密性之增加是以犧牲其運算資源為代價，而隱匿二 數位即可得到良好的隨機性。 上述該第一強健式超渾沌工具與第二強健式超渾沌工 具係由複數個耦合強健式邏輯映射所組成（耦合邏輯映射之 數目為η)，其中每一強健式邏輯映射擁有其各自之Lyapun〇v 才曰數為了解疋否於该工具維數下其正指數數 里疋否確實增加，我們將利用數值法分析該強健式超渾沌工 具。#該工具具有越高之維數，其將擁有更多之Lyapunov 正才曰數。藉此，輸出掩蔽序列24之性態將更趨複雜。下例 中，耦合強健式邏輯映射數目設為2(亦即n=2)。於此情形 下，此二耦合強健式邏輯映射具有兩參數^丨與/?。在第 3A圖中，兩_合強健式邏輯映射之兩個Lyap_v指數在 7 1 〇至16、1/3〇比例以及7 2為一定值29· 6668情況下繪 回〆、、、°果顯不，當7 1值大於或等於4時，兩個Lyapunov 數白為正值，也就是說，該工具確實為超渾洗且無「空 同樣地’當n等於3’4及1G時，其中在1 < i “ ^ 1為固定值，且r 1之範圍為〇至16，Lyapunov指數之 數目分別顯示於第3B〜_中。由此可知，當η值增大時， I^p_V 增加’且無「空窗」出現， 16 200822662 而該工具中所有r!值皆大於4。 以下將對__式超科岭職祕進行密碼分 析’將以-例說明’例中其精準度為48位元，且具有兩個 輕合強健式映射。當n=2時(n為_式邏輯映射之數目）， 該第一強健式超渾沌工具可表示為： ί X1(1) = cnU?bXi(H)+(l-cn)L(?2,x2(i-i)) χ20) - ^c2Mh^l)) 於此例中，有四個參數C11、C22、n與Y2，而參數可選擇 的總數目則為24x48= 2192個。其提供了一較大的參數空間。此 外，由於該掩蔽序列24之產生相當靈敏性地依賴參數，藉 此攻擊者將十分不易發現參數與其相對應之掩蔽序列24之 間的關連。 以下將以一實驗來顯示此一特性。首先，以上述第一強 健式超渾沌工具之方程式中為例。其次，選取一組(：與1^參 數並以其為基礎來產生一基準掩蔽序列Sbase。然後，以變動 最少基準71的重要位元來產生200個。以不同的rl與 相同的r 2與C，產生200個掩蔽序列Sbase—dx，8，其中用 d= 1 ’…1 〇 〇來標示該掩蔽序列。最後，我們計算Sbase與Sbase— 間的位元錯誤率。由第4圖可知，即使在一個參數2x2-48的 17 200822662 微小改變下，產生之序列確實有所不同。 此外，攻擊者可能藉由分析一個渾、;屯映射之輸出序列來 繪製映射。對該工具進行展開為一種用來計算未知參數值之 方法。仍以上述工具之方程式為例，當i=1時，方程式有五 個未知的變數，即r i、r 2,、Cu、⑶與Χ2(1}。將該方程式展 開至i=4時，攻擊者將有八個方程式來解額外的三個變數， 即X2 、X2(〉與X2(4l整體來說，給予之八個方程式可解該 八個未知數。然而，於強健式超渾沌工具中，攻擊者將無法 罪展開法來重建映射，其原因歸功於以下兩個特色。第一， 掩蔽序列z(i)24為第一強健式超渾沌工具之一不完整輸出序 列，其中最重要的：個數位皆被脫漏，也就是說，掩蔽序列 z(1)24不等於〜⑴。若方程式中有四個χιω，每一個z⑴脫落 j位元，四個Χι山可能的組合為（2〇4。第二，於強健式邏輯 射中使用組態式單運算來計算映射函數。片斷非線性映射並 非為一對一映射。一已知之L映射之輸出，其輸入可能性 為7/4 x2個。在此例中，需要解決八個^映射。可能的 組合為（7 /4 x2)8。假設r小於2, 〇48，且j=8，攻擊者 將總共需要嚐試(28)4χ1，〇248次可能的方程式組合來解決具 有上述兩特點之未知變數。如果我們使用為ΠΗζ中央處理 18 200822662 單元之電腦，其每秒可處理1〇12彳 王AU個可能組合，若用於計算上 例之組合’财要將近-百料柯重建該第—_式超渾 洗工具。現今運算科技_無法銳該第-賊式超浑 沌工具。 而為顯示該第—強健式鱗缸具之效能，以下將示範 其於硬想内細之航。該工具_之·如下所述：強健 式邏輯映射數目為二，工具之實際數位表示為m=12數位， 而隱匿數位數，即ί =2。然後，於十六進位表示（一數位為 四位元），該工具係以49位元運算（一位元代表一符號位 元）。一個掩蔽訊號流長度為40位元，且有兩個隱匿數位。 藉此，該明文訊息22將分割成40位元長的片段。 第5圖係顯示於該超渾沌訊號產生器内之該第一強健式 超渾沌工具之資料流。於此資料流中，每產生一個掩蔽序列 z(i) ’需要八次乘法運算。將49位元的X!❽、χ2ω、r i、r 2、 cii與c22輸入乘法運算中。seal與sca2分別標記兩個用於 常態化運算的比例因子，即 1^1 二 (Ύ i/4)(modl)與(7 i/4)(modl)。而 V 1= 1/2— /ι/4— [Τ ι/4] , 7? 2= 1/2+^/4— [7 ι/4], / -fT ^ ~~ΤΤ 19 200822662 7? 3= 1/2 —” 4 = 分別標示四種狀況來決定是否使用一組態式運算或是比例 式運算。由於Π、r2係由使用者決定、且於運算過程中保 持不變，所以77广心、心、^、叫與叫為輸入向量。 當〜< X广1 < ?? 2 ( 77 3 < # < 77 4)時，scai _2)被選來依比例 調整映射值。否則，則乘以常數1。 第6圖為該第一強健式超渾沌工具於硬體中應用之方塊 圖。為了區域與表現效能之緣故，則使用一二級管線流通乘 法器。因此，需要八回合來產生一個掩蔽序列。除了該49 位元的二級乘法器，本系統更有兩個用於暫存資料的仙位 凡之暫存器，即「暫存器A」與「暫存器B」，以及四個加減 器。方塊「職」用來計算NEG(X)=1—X，而方塊「㈤⑶純」 用來檢查該輸入是否於Iint範圍中。回路以veril〇g形式安 置且經TSMC · 13um轉合成。第7圖為該模擬結果。於本 示範中，依照閘位網路連線表之準模擬，該第一強健式超渾 死工具之加密速率可達每秒500千位元。 當n=2時，該第一強健式超渾沌工具將使用以下參數值 來示範： 20 200822662Cn2 · · · Cnn This is a positive random coupling matrix in which all elements are OsCijSi and Σ(Ι^=1 f〇rij= ΐ”··, η. Furthermore, the masking sequence 24 can be defined as z(i = Xl (〇) is generated by the super-cell signal generator 20 of the transmitting end 10 according to the initial vector of the input and the number of the number 13 200822662, wherein the initial vector can be defined as · / 〇, [ Μ (9), χ (0>^where ΕΚ〇,1)\{1/2}}; and this parameter includes the random matrix C [ [(3⁄4], where 〇< q <i, ij= i θ IJ , J ,·.., η, and — chaotic parameter vector r = [ri ' ..., rJT, where ?1 = 4, i = 1 „ and the role of the supersonic synchronous receiver 70 is utilized A second robust hyperchaotic tool can be defined as: γω = G(rsy^):=CiL(r,x^),y^[yi(i), ^ ,yn(i)]X ^ i>o The demasking sequence 76 can be defined as ·· z(i) e yi (i), which is generated by the initial (four) y (9)% of the N7G contribution of the receiving end 60. It is 'the first-strong (four) super 浑 red and the second strong super-washing tool belong to x1 #, and have the same parameters c and 犷. In addition, according to the present invention - the robust ultra-washing encryption and decryption method includes - city and - touch, the towel plus (four) is: deconstruct the plaintext message to - phase, In the masking sequence of the mutual exclusion operation _ sequence _ human-scale new number, the 浑 浑 浑 cipher text is generated; the decryption process is: after receiving the ciphertext at the receiving end, the hyper-chaos is achieved by the masking sequence with the transmitting end Synchronously generates a scrubbing decrement sequence, which is cryptographically interpreted as a decrypted plaintext 14 200822662 message. When the plaintext message 22 enters the sender 10, it is deconstructed to -{ρ(π}: If the real number of the _-type super 浑 red is represented as m, and the length of each p(i) is 4, the relationship can be expressed as: d = m - 〖eN, 卜1. Under this condition, the encryption procedure performed at the transmitting end is defined as: ^ eat ~1丄, cw= Ζω0ρ(1), where 0 represents a mutually exclusive operation, and represents an initial "digital" from X. The decryption process performed by the receiving end can be defined as: #= Ly/j £, p(1)= zd)©^1), where ρω is - decrypt the plaintext message. Note that the initial vector X (0) is randomly generated by the transmitting end, then replaced by y (G) and then transmitted to the receiving end, and then replaced by the % at the receiving end; )== ζ (1), 1 > 〇. Since the first robust hyper-chaos tool has the same initial vector as the second robust hyper-chaos tool, and z(i)= z(i), The ciphertext 50 can be decrypted correctly, that is, P (i) = P(i). In addition, the randomness of the masking sequence 24 can be enhanced by hiding the most important digits in the communication, i.e., dropping these digits out of encryption. The more bits that are hidden, the harder it is to analyze the ciphertext. 15 200822662 However, the increase in confidentiality comes at the expense of its computing resources, and the stealth of the two digits gives good randomness. The first robust hyperchaotic tool and the second robust hyperchaotic tool are composed of a plurality of coupled robust logical mappings (the number of coupled logical mappings is η), wherein each robust logical mapping has its own Lyapun 〇v is the number to know whether it will increase in the positive index of the tool dimension. We will use the numerical method to analyze the robust hyperchaos tool. # The tool has a higher dimension, which will have more Lyapunov positive numbers. Thereby, the behavior of the output masking sequence 24 will be more complicated. In the following example, the number of coupled robust logical maps is set to 2 (that is, n=2). In this case, the two-coupling robust logic map has two parameters ^丨 and /?. In Figure 3A, the two Lyap_v indices of the two-strong robust logical mapping are plotted back to 〆, ,,° in the case of 7 1 〇 to 16, 1/3 〇 and 7 2 to a certain value of 2·6668. No, when the value of 7 1 is greater than or equal to 4, the two Lyapunov numbers are positive, that is, the tool is indeed super-washed and there is no "empty same" when n is equal to 3'4 and 1G, where When 1 < i " ^ 1 is a fixed value, and r 1 ranges from 〇 to 16, the number of Lyapunov exponents is shown in the 3B to _, respectively. It can be seen that when the value of η increases, I^p_V increases by 'and no empty window appears, 16 200822662 and all r! values in the tool are greater than 4. The following will perform a cryptanalysis of the __-type super-Kiling secret secretary, which will be described as an example. The accuracy is 48 bits and has two light and strong mappings. When n=2 (n is the number of _type logical maps), the first robust hyperchaotic tool can be expressed as: ί X1(1) = cnU?bXi(H)+(l-cn)L(?2 , x2(ii)) χ20) - ^c2Mh^l)) In this example, there are four parameters C11, C22, n and Y2, and the total number of parameters selectable is 24x48 = 2192. It provides a large parameter space. In addition, since the masking sequence 24 is relatively sensitive to parameters, the attacker will be less likely to find the correlation between the parameters and their corresponding masking sequences 24. This feature will be shown below in an experiment. First, take the equation of the first robust hyperchaotic tool described above as an example. Secondly, a set of (: and 1^ parameters are selected and used to generate a reference masking sequence Sbase. Then, 200 significant bits are changed by changing the minimum reference 71. Different rls and the same r 2 C, generating 200 masking sequences Sbase_dx,8, where d=1 '...1 〇〇 is used to indicate the masking sequence. Finally, we calculate the bit error rate between Sbase and Sbase-. As can be seen from Fig. 4, Even in a slight change of the parameter 2x2-48 of 17 200822662, the resulting sequence does differ. In addition, the attacker may map the output by analyzing an output sequence of 浑, 屯 mapping. The method used to calculate the unknown parameter value. Still taking the equation of the above tool as an example, when i=1, the equation has five unknown variables, namely ri, r 2, Cu, (3) and Χ 2 (1}. When the equation is expanded to i=4, the attacker will have eight equations to solve the extra three variables, namely X2 and X2 (> and X2 (4l overall, the eight equations given can solve the eight unknowns. In the powerful hyperchaos tool, the attacker The inability to sin expansion method to reconstruct the map is attributed to the following two features. First, the masking sequence z(i)24 is one of the first robust hyperchaotic tools with an incomplete output sequence, the most important of which are: It is leaked, that is, the mask sequence z(1)24 is not equal to ~(1). If there are four χιω in the equation, each z(1) falls off j-bit, and the possible combination of four Χι mountains is (2〇4. Second, in the robust logic shot, the configuration single operation is used to calculate the mapping function. The fragment nonlinear mapping is not a one-to-one mapping. The output of a known L mapping has an input probability of 7/4 x2. In this case, we need to solve eight mappings. The possible combination is (7 / 4 x 2) 8. Assuming r is less than 2, 〇 48, and j = 8, the attacker will need to try (28) 4 χ 1, 〇 248 times in total. Possible combinations of equations to solve the unknown variables with the above two characteristics. If we use a computer that is centrally processed 18 200822662 units, it can process 1 〇 12 彳 AU possible combinations per second, if used to calculate the combination of the above example 'The wealth is close - Baike Ke rebuilds the first -_浑 工具 。 。 。 。 。 现 现 现 现 现 现 现 现 现 现 现 现 现 现 现 现 现 现 现 现 现 现 现 现 现 现 第 第 第 第 第 第 第 第 第 第 第 第 第 第 第 第 第 第 第 第· As described below: the number of robust logical maps is two, the actual digits of the tool are expressed as m=12 digits, and the number of hidden digits, ie ί = 2. Then, expressed in hexadecimal (one digit is four bits), The tool is a 49-bit operation (one bit represents a sign bit). A masked signal stream is 40 bits long and has two hidden digits. By this, the plaintext message 22 is split into 40 bits long. Fragment of. Figure 5 is a data flow of the first robust hyperchaotic tool shown in the hypertext signal generator. In this data stream, eight multiplication operations are required for each masking sequence z(i) '. The 49-bit X!❽, χ2ω, r i, r 2, cii, and c22 are input into the multiplication operation. The seal and sca2 respectively mark two scale factors for normalization, namely 1^1 2 (Ύ i/4)(modl) and (7 i/4)(modl). And V 1= 1/2— /ι/4—[Τ ι/4] , 7? 2= 1/2+^/4—[7 ι/4], / -fT ^ ~~ΤΤ 19 200822662 7? 3= 1/2 —” 4 = Indicates four conditions to determine whether to use a configuration or proportional operation. Since Π and r2 are determined by the user and remain unchanged during the operation, 77 The heart, heart, ^, call and call are input vectors. When ~<X wide 1 < ?? 2 ( 77 3 <#< 77 4), scai _2) is selected to adjust the map value proportionally Otherwise, multiply by the constant 1. Figure 6 is a block diagram of the first robust hyperchaotic tool applied to the hardware. For the sake of region and performance, a one-to-two pipeline flow multiplier is used. It takes eight rounds to generate a masking sequence. In addition to the 49-bit two-stage multiplier, the system has two more temporary registers for temporary storage of data, namely, "scratchpad A" and "temporary Saver B", and four adders and subtractors. The box "job" is used to calculate NEG(X) = 1 - X, and the box "(5) (3) pure" is used to check if the input is in the Iint range. The loop was placed in veril〇g format and synthesized by TSMC · 13um. Figure 7 shows the simulation results. In this demonstration, the first robust super-dead tool can be encrypted at a rate of up to 500 kilobits per second according to the quasi-simulation of the gate network connection table. When n=2, the first robust hyperchaotic tool will demonstrate using the following parameter values: 20 200822662
Xi(0)=0.26e7bf70710c X2(〇) = 0.3cebe4e04ecb T 1 = 15.000000000 7 2=23.0000000000 Cn = 0.fe0000000000 c22 = 0.fa0000000000 第8圖為明文訊息「The Digital Encryption」之加密 結果。該明文訊息以Ascii碼格式編碼，然後資料序列藉由 掩蔽序列加密，該掩蔽序列由該第一強健式超渾沌工具依照 上述參數值所產生。結果亦顯示接收端可藉上述參數回復明 文0 依上述所揭示之說明與圖式，本發明顯可達到預 期之目的’即本發明可提供較大之參數空間，可針對同一 明文訊息，藉由不同初始向量之輸入而相應產生不同之超渾 沌密文，並可產生不完全的攜帶映射傳送於公共通道之中， 藉此達到高保密層級。 【圖式簡單說明】 第1圖係為一般保密通訊方案之方塊圖。 第2圖係為根據本發明之一強健式超渾沌加密解密系統之方 塊圖。 第3A至3D圖係為以數值法分析根據本發明之一強健式超渾 21 200822662 沌工具之結果，圖中係顯示Lyapunov指數vs. τ、 3,4,10。 第4圖係為-實驗中、與&間位元錯誤率之結果， 八,，、員示本發明之一特性：一掩蔽序列將靈敏地依照輪 入參數而產生。 第五圖係為根據本發明之—超科訊號產生騎使用之一 ^第—強健式超渾缸具之資料流示範。 "'、為根縣發明之該超渾錢號產生器所使用之該 第—強健式超渾洗工具於硬體示範之方塊圖。^ 第七圖料根據本發明之該第1健式超科工具示範之 弋=果表格’其中該第一強健式超渾洗工具之強健 式邏輯映射數目為二。 % 第八範該第一強健式超渾㈣之一加密系統之 :洗工具之強健式 軌例表，其中該第一強健式超渾 邏輯映射數目為二。 22 200822662 【主要元件符號說明】 發送端10 明文訊息22 發送端參數調整裝置30 接收端60 去掩蔽序列76 解密明文訊息90 超渾沌訊號產生器20 掩蔽序列24 超渾沌密文50 超渾沌訊號同步接收器70 接收端參數調整裝置80 23Xi(0)=0.26e7bf70710c X2(〇) = 0.3cebe4e04ecb T 1 = 15.000000000 7 2=23.0000000000 Cn = 0.fe0000000000 c22 = 0.fa0000000000 Figure 8 shows the encrypted result of the plaintext message "The Digital Encryption". The plaintext message is encoded in the Ascii code format, and then the data sequence is encrypted by a masking sequence generated by the first robust hyperchaotic tool in accordance with the parameter values. The result also shows that the receiving end can reply to the plaintext by the above parameters. According to the above description and the schema, the present invention can achieve the intended purpose. That is, the present invention can provide a larger parameter space, and can be used for the same plaintext message. The input of different initial vectors correspondingly generates different hyper-hidden ciphertexts, and may generate incomplete carrier mappings to be transmitted in the common channel, thereby achieving a high security level. [Simple description of the diagram] Figure 1 is a block diagram of a general secure communication scheme. Figure 2 is a block diagram of a robust hyperchaotic encryption and decryption system in accordance with the present invention. 3A to 3D are results of numerical analysis of a robust tool according to the present invention, which shows the Lyapunov exponent vs. τ, 3, 4, 10. Fig. 4 is a result of the experiment, and the error rate between the & bit error rate, eight, and one of the characteristics of the present invention: a masking sequence will be generated sensitively according to the rounding parameters. The fifth figure is a data flow demonstration of one of the super-technical super-cylinders according to the present invention. "', the block diagram of the first-strong super-washing tool used by the super-money generator produced by the root county in the hardware demonstration. The seventh figure is based on the first healthy super tool demonstration of the present invention. The number of robust logical maps of the first robust super-washing tool is two. % Eighth is the first strong type of super-enhanced (four) one of the encryption systems: the robust version of the washing tool, wherein the number of the first robust super-transformed logical map is two. 22 200822662 [Description of main component symbols] Transmitter 10 Clear text message 22 Transmitter parameter adjustment device 30 Receiver 60 Demasking sequence 76 Decrypting plaintext message 90 Chaos chaos signal generator 20 Masking sequence 24 Chaos ciphertext 50 Super chaotic signal synchronous reception Receiver 70 parameter adjustment device 80 23