TW201643816A - Contour encryption and decryption - Google Patents

Contour encryption and decryption Download PDF

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TW201643816A
TW201643816A TW104118936A TW104118936A TW201643816A TW 201643816 A TW201643816 A TW 201643816A TW 104118936 A TW104118936 A TW 104118936A TW 104118936 A TW104118936 A TW 104118936A TW 201643816 A TW201643816 A TW 201643816A
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curve
bit
closed
closed curve
arc
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TW104118936A
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菲丹H 坦恩
明華 梁
勞倫斯 鐘
詹姆士A 哈華德
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Apdn維京群島公司
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Abstract

A method of encrypting information includes converting an information sequence represented as a strings of bits into a curvilinear coding system, where each element of the curvilinear coding system corresponds to a sub-sequence of successive same-valued bits, converting said curvilinear coding system into a at least one closed curve, and embedding said at least one closed curve in a 2-dimensional pattern. A method for decrypting information includes extracting at least one closed curve from a digitized 2-dimensional pattern, and converting the at least one closed curve into an information sequence represented as a string of bits.

Description

輪廓加密及解密技術 Contour encryption and decryption technology

本發明涉及在嵌入例如迷彩圖案之二維曲線中編碼及解碼資訊的方法。 The present invention relates to a method of encoding and decoding information in a two-dimensional curve embedded in, for example, a camouflage pattern.

一種鑑別商品的方法係將識別標誌貼附在商品上,例如能辨識商品的來源的商標、條碼、或二維條碼(QR code)。然而這些識別標誌可從商品上拆下,且仿冒商品可加上一識別碼,該識別碼可將仿冒商品不實地標示成特定製造商或來源,無異常地透過該特定辨識碼辨識出來。 One method of identifying a product is to attach an identification mark to the item, such as a trademark, barcode, or QR code that identifies the source of the item. However, these identification marks can be detached from the product, and the counterfeit goods can be added with an identification code, which can falsely mark the counterfeit goods as a specific manufacturer or source, and can be identified through the specific identification code without abnormality.

在此所述之本發明構思的範例實施例基本上包含在二維曲線中編碼及解碼資訊的系統及方法。可被編碼成位元串(string of bits)即可數位化的任何形式資訊也可編碼於二維曲線中。透過本發明構思的實施例,可編碼至二維曲線、並具有商業重要性的非限制碼(non-limiting code)之兩範例為一維產品條碼及二維條碼。數位化二維曲線可嵌入二維圖案中,以隱藏二維曲線的存在,且二維圖案可印在商品上,或成為商品中物件例如衣服、DVD或積體電路的一部分,或可為產品標誌的全部或一部分。 Example embodiments of the inventive concepts described herein basically comprise systems and methods for encoding and decoding information in a two-dimensional curve. Any form of information that can be encoded into a string of bits to be digitized can also be encoded in a two-dimensional curve. Through the embodiments of the inventive concept, two examples of non-limiting codes that can be encoded into a two-dimensional curve and have commercial importance are one-dimensional product barcodes and two-dimensional barcodes. The digitized two-dimensional curve can be embedded in the two-dimensional pattern to hide the existence of the two-dimensional curve, and the two-dimensional pattern can be printed on the commodity, or become part of the article in the commodity such as clothing, DVD or integrated circuit, or can be a product All or part of the logo.

根據本發明構思的一實施例,係提供一種加密資訊的方法,包括將表示為一位元串的一資訊序列轉換成一曲線編碼系統,以提供至少一封閉曲線;以及將該至少一封閉曲線嵌入至二維圖案中。 According to an embodiment of the inventive concept, a method for encrypting information includes converting a sequence of information represented as a one-bit string into a curve coding system to provide at least one closed curve; and embedding the at least one closed curve In the two-dimensional pattern.

根據本發明構思的另一實施例,該方法包括將該位元串中之連續同值位元的每個子字串轉換成一弧線,其中每個弧線的半徑對應於每個子序列中的位元數量,且對應於高值位元的序列的一弧線具有與對應於低值位元的序列的一弧線相反的一輪廓特徵(signature);以及藉由將該弧線序列的終點連接至該弧線序列的起點,將該弧線序列轉換成一封閉曲線。 According to another embodiment of the inventive concept, the method includes converting each substring of consecutive equi-valued bits in the bit string into an arc, wherein the radius of each arc corresponds to the number of bits in each subsequence And an arc corresponding to the sequence of high value bits has a contour signature opposite to an arc corresponding to the sequence of low value bits; and by connecting the end point of the arc sequence to the arc sequence The starting point, which converts the sequence of arcs into a closed curve.

根據本發明構思的另一實施例,該方法包括將該位元串轉換成複數個封閉曲線,並將該等封閉曲線的每一個嵌入至該二維圖案中。 According to another embodiment of the inventive concept, the method includes converting the bit string into a plurality of closed curves, and embedding each of the closed curves into the two-dimensional pattern.

根據本發明構思的另一實施例,將嵌入於該二維圖案中的該等封閉曲線的其中之一係為一參考曲線,該參考曲線包含剩餘的該等封閉曲線的編碼資訊,該編碼資訊包含每個封閉曲線中的起點/終點之其一或兩者以及該等封閉曲線的一遍歷順序(traversal order)。 According to another embodiment of the inventive concept, one of the closed curves embedded in the two-dimensional pattern is a reference curve, and the reference curve includes coding information of the remaining closed curves, and the coding information One or both of the start/end points in each closed curve and a traversal order of the closed curves are included.

根據本發明構思的另一實施例,該二維圖案係具有複數種顏色深淺的一迷彩圖案。根據本發明構思的另一實施例,該至少一封閉曲線係一簡單封閉曲線。根據本發明構思的另一實施例,該位元串表示成一二維條碼(QR Code)。 According to another embodiment of the inventive concept, the two-dimensional pattern has a camouflage pattern of a plurality of color shades. According to another embodiment of the inventive concept, the at least one closed curve is a simple closed curve. According to another embodiment of the inventive concept, the bit string is represented as a QR Code.

根據本發明構思的另一實施例,該方法包括接收一參考點,從該位元串中的同值位元的一子字串產生一弧線;其中同值位元的該子字串的長度對應於該弧線上一選擇點至該參考點的距離,且在同值位元的該子字串中的位元值在該選擇點上相對於該參考點對應於該封閉曲線的一輪廓特徵;從該參考點至相對一預設方向的該選擇點保存一向量的角度;以及重複產生一弧線與保存一角度的步驟,直到該位元串全部轉換成一系列的弧線。根據本發明構思的另一實施例,該方法包括當該等弧線有一個或多個不連接時,在相鄰的多對不連接的弧線之間產生連接弧線,以產生至少一封閉曲線。 According to another embodiment of the inventive concept, the method includes receiving a reference point, generating an arc from a substring of the same value bit in the bit string; wherein the length of the substring of the same value bit Corresponding to a distance from a selected point to the reference point on the arc, and a bit value in the substring of the same value bit corresponds to a contour feature of the closed curve with respect to the reference point at the selected point The selection point from the reference point to a predetermined direction stores an angle of a vector; and the step of repeatedly generating an arc and saving an angle until the bit string is completely converted into a series of arcs. According to another embodiment of the inventive concept, the method includes generating a connecting arc between adjacent pairs of unconnected arcs when one or more of the arcs are not connected to generate at least one closed curve.

根據本發明構思的另一實施例,該方法包括接收一封閉邊界曲線與一參考點;在該封閉邊界曲線內部,從該位元串 中同值位元的一子字串產生一弧線,其中同值位元的該子字串的長度對應於該弧線相對於該封閉曲線上的一偏移,且在同值位元的該子字串的位元值對應於該弧線的一輪廓特徵;從該弧線上的一選擇點到該參考點保存一向量的長度及相對於一預設方向該向量的一角度偏移;以及重複產生一弧線以及保存一長度與一偏移角度的步驟,直到該位元串全部轉換成一系列的弧線。 According to another embodiment of the inventive concept, the method includes receiving a closed boundary curve and a reference point; and within the closed boundary curve, from the bit string A substring of the same value bit generates an arc, wherein the length of the substring of the same value bit corresponds to an offset of the arc relative to the closed curve, and the sub-bit of the same value bit The bit value of the string corresponds to a contour feature of the arc; from a selected point on the arc to the reference point, the length of a vector and an angular offset of the vector relative to a predetermined direction are saved; and the generation is repeated An arc and a step of saving a length and an offset angle until the bit string is all converted into a series of arcs.

根據本發明構思的另一實施例,該方法包括當從該封閉邊界曲線在相同的偏移的一個或多個該弧線不連接時,在相鄰的多對不連接的弧線之間產生連線弧線,以在表示一等值線圖之該封閉邊界曲線內產生複數個巢狀曲線。 According to another embodiment of the inventive concept, the method includes generating a connection between adjacent pairs of unconnected arcs when one or more of the arcs of the same offset from the closed boundary curve are not connected An arc produces a plurality of nested curves in the closed boundary curve representing a contour map.

根據本發明構思的另一實施例,該方法包括產生該等封閉曲線,其中該等封閉曲線的其中之一係為一參考曲線,且其他該等封閉曲線的每一個透過一仿射變換由該參考曲線衍生出,其中該等仿射變換的每一個是選自平移、反射、旋轉、縮放變換、位似變換(homothetic transformation)、剪切映射(shear mapping)中至少兩種變換的組合,其中將該位元串轉換成該等封閉曲線的步驟包含將每個同值位元的子字串轉換成該等封閉曲線的其中之一,其中該同值位元的數量對應於該至少兩種變換的其中之一,且該同值位元的位元值對應於該至少兩種變換中的其他變換。 According to another embodiment of the inventive concept, the method includes generating the closed curves, wherein one of the closed curves is a reference curve, and each of the other closed curves is passed through an affine transformation The reference curve is derived, wherein each of the affine transformations is a combination of at least two transformations selected from the group consisting of translation, reflection, rotation, scaling transformation, homothetic transformation, and shear mapping, wherein Converting the bit string into the closed curve includes converting a substring of each equi-valued bit into one of the closed curves, wherein the number of the same-valued bits corresponds to the at least two One of the transforms, and the bit values of the equi-valued bits correspond to other transforms in the at least two transforms.

根據本發明構思的另一實施例,該方法包括將同值位元的每個子字串轉換成在該至少一封閉曲線內部的一子區域,每個子區域透過一對平行線段為界,其中該對平行線段具有延伸通過至少一封閉曲線內部和一對曲線線段的一預定分隔,其中每個該子區域的面積對應於同值位元的一對應子字串的長度,且該同值位元的位元值對應於劃界該子區域的該至少一對曲線線段的一輪廓特徵;以及沿著相鄰的多對平行線段附加連續的子區域,其中該等對曲線線段形成至少一封閉曲線。 According to another embodiment of the inventive concept, the method includes converting each substring of the same value bit into a sub-region inside the at least one closed curve, each sub-region being bounded by a pair of parallel line segments, wherein The parallel line segment has a predetermined separation extending through at least one of the closed curve interior and the pair of curved line segments, wherein an area of each of the sub-regions corresponds to a length of a corresponding sub-string of the same-valued bit, and the same-valued bit a bit value corresponding to a contour feature of the at least one pair of curved line segments delimiting the sub-region; and a continuous sub-region along a plurality of adjacent pairs of parallel line segments, wherein the pair of curved line segments form at least one closed curve .

根據本發明構思的另一實施例,提供一種非暫存的用電腦可讀取程式儲存裝置,有形地收錄有由該電腦處理的指令 程式以執行用於解密資訊的方法步驟。該方法包括從一數位化的二維圖案,提取至少一封閉曲線;以及將該至少一封閉曲線轉換成表示為一位元串的一資訊序列。 According to another embodiment of the inventive concept, a non-temporary computer readable program storage device is provided, tangibly including instructions processed by the computer The program executes the method steps for decrypting the information. The method includes extracting at least one closed curve from a digitized two-dimensional pattern; and converting the at least one closed curve into a sequence of information represented as a one-bit string.

根據本發明構思的另一實施例,該方法包括將該至少一封閉曲線拆開成一序列的弧線,且決定每個弧線的一輪廓特徵與一半徑;以及將該序列的弧線轉換成該位元串,其中連續同值位元的每個子序列對應於一弧線,其中該每個子序列的長度對應於每個弧線的半徑,且每個子序列的位元值對應於每個弧線的一輪廓特徵。根據本發明構思的另一實施例,該二維圖案係為一具有複數種灰階的迷彩圖案。 According to another embodiment of the inventive concept, the method includes splitting the at least one closed curve into a sequence of arcs, and determining a contour feature and a radius of each arc; and converting the arc of the sequence into the bit A string, wherein each subsequence of consecutive equivalence bits corresponds to an arc, wherein the length of each subsequence corresponds to the radius of each arc, and the bit value of each subsequence corresponds to a contour feature of each arc. According to another embodiment of the inventive concept, the two-dimensional pattern is a camouflage pattern having a plurality of gray scales.

根據本發明構思的另一實施例,該方法包括從該二維圖案中提取該等封閉曲線,且將從該等封閉曲線的每一個衍生出的該位元串序連成表示為該資訊序列的一單一位元串。 According to another embodiment of the inventive concept, the method includes extracting the closed curves from the two-dimensional pattern, and concatenating the bit sequences derived from each of the closed curves into the information sequence a single bit string.

根據本發明構思的另一實施例,從該二維圖案所提取的該等封閉曲線的其中之一係為一參考曲線,該參考曲線包含剩餘的該封閉曲線的解碼資訊,該解碼資訊包含每個封閉曲線中的起點/終點之其一或兩者以及該等封閉曲線的一遍歷順序(traversal order)。根據本發明構思的另一實施例,該至少一封閉曲線為一簡單封閉曲線。根據本發明構思的另一實施例,該位元串表示成一二維條碼(QR Code)。 According to another embodiment of the inventive concept, one of the closed curves extracted from the two-dimensional pattern is a reference curve, and the reference curve includes remaining decoding information of the closed curve, and the decoding information includes each One or both of the start/end points in the closed curve and a traversal order of the closed curves. According to another embodiment of the inventive concept, the at least one closed curve is a simple closed curve. According to another embodiment of the inventive concept, the bit string is represented as a QR Code.

根據本發明構思的另一實施例,該方法包括在該封閉曲線上,從一參考點延伸一向量到一選擇點;其中從該參考點到該選擇點的一向量的長度對應於在該位元串的子字串的同值位元的數量,且同值位元的該子字串中的該位元值是由該封閉曲線在該選擇點的一輪廓特徵決定。 According to another embodiment of the inventive concept, the method includes extending a vector from a reference point to a selection point on the closed curve; wherein a length of the vector from the reference point to the selection point corresponds to the bit The number of equi-valued bits of the substring of the metastring, and the bit value in the substring of the equivalence bit is determined by a contour feature of the closed curve at the selected point.

根據本發明構思的另一實施例,該方法包括接收一參考點及相對一預設方向的一起始角度,在該封閉曲線上,從該起始角度之該參考點延伸一向量到一選擇點;透過一預設角度偏移來偏移該向量,以從該參考點延伸另一向量到該封閉曲線上的另一點;以及重複透過一預設角度偏移來偏移該向量,以從該參 考點延伸另一向量到該封閉曲線上的另一點的步驟,直到該封閉曲線已經遍歷,其中該向量的長度對應於在一子字串中同值位元的數量,且在同值位元的該子字串中的該位元值是由該封閉曲線在該點的一輪廓特徵決定,其中該至少一封閉曲線被轉換成表示為一位元串的一資訊序列。 According to another embodiment of the inventive concept, the method includes receiving a reference point and a starting angle relative to a preset direction, and extending a vector from the starting point to a selection point on the closed curve Offseting the vector by a predetermined angular offset to extend another vector from the reference point to another point on the closed curve; and repeatedly shifting the vector by a predetermined angular offset to Reference The step of extending another vector to another point on the closed curve until the closed curve has been traversed, wherein the length of the vector corresponds to the number of identical bits in a substring and is in the same value bit The bit value in the substring is determined by a contour feature of the closed curve at the point, wherein the at least one closed curve is converted into a sequence of information represented as a one-bit string.

根據本發明構思的另一實施例,該至少一封閉曲線包含複數個以一等值線圖表示的巢狀封閉曲線,其中將該至少一封閉曲線轉換成一位元串包含接收一參考點與相對一預設方向的一起始角度;以及藉由從該參考點以該起始角度的一預設距離延伸一向量到該等巢狀封閉曲線的其中之一的一點,且藉由連續偏移該向量一預設角度偏移,將該等巢狀封閉曲線轉換成該位元串,其中從該等巢狀封閉曲線一外部等值線之該等巢狀封閉曲線該其中之一的一偏移對應於在該位元串中的子字串的同值位元的數量,且在同值位元的該子字串中的位元值是由該等巢狀封閉曲線的該其中之一在該點的一輪廓特徵決定。 According to another embodiment of the inventive concept, the at least one closed curve includes a plurality of nested closed curves represented by a contour map, wherein converting the at least one closed curve into a one-dimensional string comprises receiving a reference point and a relative a starting angle of a predetermined direction; and extending a vector from the reference point to a point of one of the nested closed curves by a predetermined distance of the starting angle, and by continuously offsetting a predetermined angle offset, the nested closed curve being converted into the bit string, wherein an offset of one of the nested closed curves from the outer contour of the nested closed curve Corresponding to the number of equi-valued bits of the sub-string in the bit string, and the bit value in the sub-string of the same-valued bit is one of the nested closed curves A contour feature of the point is determined.

根據本發明構思的另一實施例,從該數位化的二維圖案中提取該等封閉曲線,其中該等封閉曲線的其中之一係為一參考曲線,且其他的每一該等封閉曲線透過一仿射變換從該參考曲線衍生出,其中每一該等仿射變換是選自平移、反射、旋轉、縮放變換、位似變換、剪切映射中兩種或更多種轉換的組合;以及其中將該等封閉曲線轉換成一位元串包含將每一該等封閉曲線轉換成同值位元的子字串,其中同值位元的數量對應於該二種或更多種變換的其中之一,且該同值位元的位元值對應於兩種或更多種變換的其他變換。 According to another embodiment of the inventive concept, the closed curves are extracted from the digitized two-dimensional pattern, wherein one of the closed curves is a reference curve, and each of the other closed curves passes through An affine transform is derived from the reference curve, wherein each of the affine transforms is a combination of two or more transforms selected from the group consisting of: translation, reflection, rotation, scale transformation, bit transformation, and shear mapping; Converting the closed curves into a one-bit string comprises converting the each closed curve into a substring of the same value bit, wherein the number of the same value bits corresponds to the two or more transformations One, and the bit values of the equi-valued bits correspond to other transforms of two or more transforms.

根據本發明構思的另一實施例,該方法包括將該至少一封閉曲線的一內部劃分成複數個子區域,每個子區域透過一對平行線段為界,其中該對平行線段具有延伸通過至該少一封閉曲線的該內部和該曲線兩側的一對曲線線段的一預定分隔;以及將該封閉曲線轉換成表示為一位元串的一資訊序列,其中每個子區域的面積對應於該位元串的子字串的同值位元的位元數量,且 該同值位元的位元值對應於劃界該子區域的該至少一對曲線線段的一輪廓特徵。 According to another embodiment of the inventive concept, the method includes dividing an interior of the at least one closed curve into a plurality of sub-regions, each sub-region being bounded by a pair of parallel line segments, wherein the pair of parallel line segments have an extension to the less a predetermined separation of the interior of the closed curve and a pair of curved line segments on either side of the curve; and converting the closed curve into a sequence of information represented as a one-bit string, wherein the area of each sub-region corresponds to the bit The number of bits of the same value bit of the substring of the string, and The bit value of the equi-valued bit corresponds to a contour feature of the at least one pair of curved line segments delimiting the sub-region.

根據本發明構思的另一實施例,提供一種加密資訊的方法,包括藉由將一位元串中的連續同值位元的每個子字串轉換成一弧線,將表示為該位元串的一資訊序列轉換成曲線編碼系統,其中同值位元的各該子字串的長度對應於該弧線上一選擇點到一參考點的距離,且在同值位元的該子字串的一位元值對應於該弧線在該選擇點相對該參考點的一輪廓特徵;將該等弧線形連接成一封閉曲線;以及將該封閉曲線嵌入至一二維圖案中。 According to another embodiment of the inventive concept, there is provided a method of encrypting information, comprising: converting each substring of consecutive equi-valued bits in a one-bit string into an arc, representing one of the bit strings The information sequence is converted into a curve coding system, wherein the length of each substring of the same value bit corresponds to a distance from a selection point to a reference point on the arc, and one bit of the substring in the same value bit The element value corresponds to a contour feature of the arc at the selected point relative to the reference point; the arc lines are connected into a closed curve; and the closed curve is embedded in a two-dimensional pattern.

11‧‧‧區域 11‧‧‧Area

31‧‧‧圖形 31‧‧‧ graphics

32‧‧‧圖形 32‧‧‧ graphics

33‧‧‧圖形 33‧‧‧ graphics

70‧‧‧封閉曲線 70‧‧‧Closed curve

71‧‧‧參考點 71‧‧‧ reference point

72‧‧‧參考點 72‧‧‧ reference point

73‧‧‧向量 73‧‧‧ Vector

74‧‧‧向量 74‧‧‧ Vector

80‧‧‧封閉曲線 80‧‧‧Closed curve

81‧‧‧等值線圖 81‧‧‧ contour map

82‧‧‧參考點 82‧‧‧ reference point

83‧‧‧起始向量 83‧‧‧start vector

84‧‧‧點 84‧‧ points

100‧‧‧曲線 100‧‧‧ Curve

101‧‧‧子區域 101‧‧‧Sub-area

110‧‧‧曲線 110‧‧‧ Curve

111‧‧‧參考點 111‧‧‧ reference point

112‧‧‧向量 112‧‧‧ Vector

113‧‧‧向量 113‧‧‧ Vector

114‧‧‧向量 114‧‧‧Vector

115‧‧‧向量 115‧‧‧ Vector

116‧‧‧向量 116‧‧‧ Vector

117‧‧‧向量 117‧‧‧ vector

118‧‧‧向量 118‧‧‧Vector

121‧‧‧步驟 121‧‧‧Steps

122‧‧‧步驟 122‧‧‧Steps

123‧‧‧步驟 123‧‧‧Steps

131‧‧‧步驟 131‧‧‧Steps

132‧‧‧步驟 132‧‧‧Steps

133‧‧‧步驟 133‧‧‧Steps

141‧‧‧電腦系統 141‧‧‧ computer system

142‧‧‧中央處理器 142‧‧‧Central processor

143‧‧‧記憶體 143‧‧‧ memory

144‧‧‧輸入/輸出(I/O)介面 144‧‧‧Input/Output (I/O) interface

145‧‧‧顯示器 145‧‧‧ display

146‧‧‧輸入裝置 146‧‧‧ input device

147‧‧‧常用程式 147‧‧‧Common programs

148‧‧‧訊號元 148‧‧‧ signal element

第1圖係顯示根據本發明構思的實施例之具有嵌入驗證的二維條碼的迷彩圖案外套的例子;第2圖係顯示根據本發明構思的實施例,取自第1圖的迷彩圖案的放大部分;第3圖係顯示根據本發明構思的實施例,在黑色背景中嵌入來自二值化迷彩圖案的複數個白色形狀,如第3圖所示;第4圖(a)至第4圖(c)係顯示根據本發明構思的實施例,分別提取自第3圖所示的形狀之三個範例用的弧線;第5圖(a)至第5圖(c)係顯示根據本發明構思的實施例,從包含複數個不同輪廓特徵與半徑的弧線的簡單封閉曲線衍生出的位元串;第6圖係顯示根據本發明構思的實施例,從第5圖所示之位元串形成的二維條碼(QR code);第7圖係根據本發明構思的實施例,描述具有分別自兩參考點投射的向量的兩參考點的封閉曲線;第8圖(a)係根據本發明構思的實施例,描述表示等值線圖的外部邊界的封閉曲線80;第8圖(b)係根據本發明構思的實施例,描述包含藉由偏移第8圖(a)的封閉曲線而形成的複數個巢狀曲線的等值線圖、以 及參考點,向量自該參考點投射至等值線圖上的點;第9圖(a)至第9圖(c)係根據本發明構思的實施例,描述三個封閉曲線,其中第9圖(a)的曲線為參考曲線,而第9圖(b)至(c)的曲線係自參考曲線透過仿射變換來產生;第10圖係根據本發明構思的實施例,描述另一曲線,其內部劃分成多個子區域,其中每個子區域對應於同值位元的子序列;第11圖(a)至第11圖(c)係根據本發明構思的一實施例,說明將封閉曲線轉換成位元串的例子;第12圖係根據本發明構思的一實施例,加密資訊於一序列的輪廓中的方法流程圖;第13圖係根據本發明構思的一實施例,將加密於一序列的輪廓中的資訊解密的方法流程圖;以及第14圖係根據本發明構思的一實施例的一範例電腦系統的方塊圖,用於實施在二維曲線中編碼與解碼資訊的方法。 1 is a diagram showing an example of a camouflage pattern jacket having a two-dimensional barcode embedded in a verification according to an embodiment of the inventive concept; and FIG. 2 is an enlarged view showing a camouflage pattern taken from FIG. 1 according to an embodiment of the inventive concept. Part 3; FIG. 3 shows a plurality of white shapes embedded in a binary camouflage pattern in a black background, as shown in FIG. 3; FIG. 4(a) to FIG. 4 (in FIG. 4) c) showing an arc for three examples of the shapes shown in FIG. 3, respectively, according to an embodiment of the inventive concept; FIGS. 5(a) to 5(c) are diagrams showing the concept according to the present invention. Embodiments, a bit string derived from a simple closed curve comprising a plurality of arcs of different contour features and radii; FIG. 6 shows a bit string formed from the bit string shown in FIG. 5 according to an embodiment of the inventive concept A QR code; a seventh diagram is a closed curve describing two reference points having vectors respectively projected from two reference points, in accordance with an embodiment of the inventive concept; FIG. 8(a) is a diagram according to the inventive concept Embodiment, describing the outer boundary of the contour map Closed curve 80; FIG. 8 (b) based concepts according to an embodiment of the present invention, is described comprising a contour map of a plurality of nested curves offset by FIG. 8 (a) to form a closed curve to And a reference point from which the vector is projected onto a point on the contour map; FIGS. 9(a) through 9(c) depict three closed curves, ninth, in accordance with an embodiment of the inventive concept The curve of FIG. (a) is a reference curve, and the curves of FIGS. 9(b) to (c) are generated from the reference curve by affine transformation; FIG. 10 is another curve according to an embodiment of the inventive concept. Internally divided into a plurality of sub-regions, wherein each sub-region corresponds to a sub-sequence of the same-valued bit; FIGS. 11(a) to 11(c) illustrate a closed curve according to an embodiment of the inventive concept An example of conversion to a bit string; FIG. 12 is a flowchart of a method of encrypting information in a sequence of outlines according to an embodiment of the inventive concept; FIG. 13 is an embodiment of the present invention, encrypted according to an embodiment of the inventive concept A flowchart of a method for decrypting information in a sequence of profiles; and a block diagram of an exemplary computer system for implementing encoding and decoding of information in a two-dimensional curve, in accordance with an embodiment of the inventive concept.

在此所敘述的本發明構思的範例實施例基本上包含在二維曲線中編碼及解碼資訊的方法。因此本發明構思可有多種修飾及替代形式,透過圖示中的範例來顯示此處的具體實施例,並將在此作詳盡的敘述。本領域技術人員應理解上述實施例並未用來限制本發明構思於特定公開的形式,相反地,本發明的構思係涵蓋落入本發明構思的精神及範圍內之所有的修飾、等同物、以及改變。 Example embodiments of the inventive concepts described herein basically comprise a method of encoding and decoding information in a two-dimensional curve. The present invention may be embodied in various modifications and alternative forms. It should be understood that the above-described embodiments are not intended to limit the scope of the embodiments of the present invention. And change.

確保商品可正確地進行驗證以避免錯誤驗證仿冒商品的一種方法係嵌入辨識標記於商品中,如此可讓辨識標記在一般觀察下基本上隱藏在商品中,但可透過成像技術而顯現出來。例如第1圖係顯示具有嵌入驗證二維條碼的迷彩圖案外套的例子。第2圖顯示第1圖區域11的迷彩圖案的放大圖部分,一迷彩圖案具有複數種相似的顏色,該等顏色可透過複數種顏色深淺來表 示。一位元圖案可隱藏在這樣的圖案中,例如改變最低階的二位元的位元值,這種類型的編碼方法使得位元圖案基本上無法從迷彩圖案區別出。利用特定的色鍵軟體,迷彩圖案可被二值化成黑色及白色圖像,並顯示在第3圖。第3圖顯示嵌入黑色背景中複數個白色圖形,注意選擇黑色背景僅為示範而非作為限制,且特定的色鍵軟體產生白色背景的黑色圖形。圖形及背景間的邊界可用二維的簡單封閉曲線表示,每個邊界具有定義明確的內部,即圖形的內部,以及具有明確定義的外部,即背景。一旦定義出每個曲線的起點/終點後,曲線可被拆開成連貫序列的弧線,弧線的輪廓特徵為正或者負可透過弧線向簡單封閉曲線的內部內凹,或者向外部外凸來判斷。如第4圖(a)至第4圖(c)所示,給定一組二維簡單封閉曲線,在現有的數學計算環境下,例如MathWorks的MATLAB所提供的內建功能,能夠從一曲線中提取一弧線並判斷弧線的半徑及圓心。第4圖(a)至第4圖(c)係顯示三個範例弧線分別提取自於第3圖的圖形31、32及33。因此,如第5圖(a)至第5圖(c)所示,藉由結合輪廓特徵與位元值、以及半徑與位元長度,含有複數個不同輪廓特徵與半徑的弧線的一簡單封閉曲線可被轉換成位元串。該位元串可表示全部、或者部分的一產品編碼,例如一條碼,或者如第6圖所示的二維條碼。 One way to ensure that the item is properly verified to avoid false verification of counterfeit goods is to embed the identification mark in the item so that the identification mark is substantially hidden in the item under normal viewing, but can be visualized by imaging techniques. For example, Figure 1 shows an example of a camouflage pattern jacket with an embedded verification two-dimensional barcode. Figure 2 shows an enlarged view of the camouflage pattern of the area 11 of Figure 1, a camouflage pattern having a plurality of similar colors, the colors being transparent to a plurality of colors Show. A one-bit pattern can be hidden in such a pattern, for example, changing the bit value of the lowest order two bits. This type of encoding method makes the bit pattern substantially indistinguishable from the camouflage pattern. With a specific color key software, the camouflage pattern can be binarized into black and white images and displayed in Figure 3. Figure 3 shows a plurality of white graphics embedded in a black background. Note that selecting a black background is merely an example and not a limitation, and a particular color key software produces a black background with a white background. The boundary between the graphic and the background can be represented by a two-dimensional simple closed curve, each boundary having a well-defined interior, ie the interior of the graphic, and a well-defined external, ie background. Once the start/end point of each curve is defined, the curve can be disassembled into a continuous sequence of arcs. The contour of the arc is positive or negative through the arc to the inner concave of the simple closed curve, or to the external convexity. . As shown in Figures 4(a) through 4(c), given a set of two-dimensional simple closed curves, in the existing mathematical computing environment, for example, the built-in functions provided by MathWorks' MATLAB can be derived from a curve. Extract an arc and judge the radius and center of the arc. Figures 4(a) through 4(c) show three example arcs extracted from graphs 31, 32 and 33 of Fig. 3, respectively. Thus, as shown in Figures 5(a) through 5(c), a simple closure of a plurality of arcs of different contour features and radii, by combining contour features with bit values, and radius and bit lengths The curve can be converted into a string of bits. The bit string may represent all or part of a product code, such as a code, or a two-dimensional bar code as shown in FIG.

在本發明構思的另一實施例中,複數個弧線可結合以形成複數個二維曲線,且該等曲線的陣列可嵌入迷彩圖案中。此外,在本發明構思的另一實施例中,曲線的陣列之其一可為一參考曲線,該參考曲線包含剩餘曲線的編碼資訊。編碼資訊可包含曲線的起點及終點之其一或兩者、曲線陣列的一遍歷順序、以及由曲線編碼的一類型資訊,例如曲線是否表示成一二維條碼。若曲線的陣列以一二維條碼表示,則該參考曲線可更包含二維條碼上的大小的資訊,以及二維條碼如何拆開成個別的封閉曲線。在每個曲線的起點及終點的資訊可包含例如每個曲線內部的一質心點、以及一偏移角度,該偏移角度通過質心而與曲線相交作為起點/終點。根據本發明構思的實施例,該參考曲線可在一曲線陣 列的左上方,然而,該參考曲線的位置僅為示範而非作為限制,且該參考曲線可位在該曲線陣列的任意處。 In another embodiment of the inventive concept, a plurality of arcs may be combined to form a plurality of two-dimensional curves, and an array of the curves may be embedded in the camouflage pattern. In addition, in another embodiment of the inventive concept, one of the arrays of curves may be a reference curve, and the reference curve includes coding information of the remaining curves. The encoded information may include one or both of the start and end points of the curve, a traversal sequence of the array of curves, and a type of information encoded by the curve, such as whether the curve is represented as a two-dimensional bar code. If the array of curves is represented by a two-dimensional bar code, the reference curve may further include information on the size of the two-dimensional bar code, and how the two-dimensional bar code is split into individual closed curves. The information at the start and end points of each curve may include, for example, a centroid point inside each curve, and an offset angle that intersects the curve as a start/end point through the centroid. According to an embodiment of the inventive concept, the reference curve may be in a curved array The upper left of the column, however, the position of the reference curve is merely exemplary and not limiting, and the reference curve can be located anywhere in the array of curves.

第7圖至第10圖係根據本發明構思的其他實施例,說明在輪廓中編碼資訊的其他方法。 7 through 10 illustrate other methods of encoding information in a contour, in accordance with other embodiments of the inventive concept.

第7圖係描述具有向量73、74分別自兩參考點71、72投射出的封閉曲線70。參考點72可為封閉曲線圍成區域的質心,但不限於此。在其他情況,自參考點至曲線上的一點的向量的長度對應於同值位元的長度,且曲線的輪廓特徵對應於位元值,該輪廓特徵即曲線在曲線上的一點是否為凹/凸情況。藉由自參考點前進一預先指定的角度偏移的向量來找到下一個同值位元的子序列。 Figure 7 depicts a closed curve 70 with vectors 73, 74 projected from two reference points 71, 72, respectively. The reference point 72 may be a centroid of the enclosed curve, but is not limited thereto. In other cases, the length of the vector from the reference point to a point on the curve corresponds to the length of the same-valued bit, and the contour feature of the curve corresponds to the bit value, which is whether the point of the curve on the curve is concave/ Convex situation. A subsequence of the next equivalence bit is found by advancing a vector of a pre-specified angular offset from the reference point.

第8圖(a)係描述表示等值線圖的外部邊界的封閉曲線80,同時第8圖(b)描述包含藉由偏移第8圖(a)的封閉曲線所形成的複數個巢狀曲線的等值線圖81、以及向量83投射至等值線圖81上的點84的參考點82。新的曲線可以自外邊界向內固定的增量定義出,直到一曲線自身交叉,內部曲線可定義其高度高於外部邊界。藉由自參考點82延伸起始向量83一預定的距離,可找到對應於一資訊序列的開頭的起始點,該預定的距離可在一資料庫中找到,同值位元的位元數量對應於在起始點的輪廓高度,且位元值係透過曲線於該點為凹/凸情況來給定。藉由偏移起始向量83一預定的角度增量,及藉由延伸向量一預定的距離至該等巢狀曲線其中之一的一點上來找到下一個點,該預定的角度增量也可於資料庫中找到。 Figure 8(a) depicts a closed curve 80 representing the outer boundary of the contour map, while Figure 8(b) depicts a plurality of nests formed by offsetting the closed curve of Figure 8(a). The contour map 81 of the curve, and the vector 83 are projected to the reference point 82 of the point 84 on the contour map 81. The new curve can be defined from the inward fixed increment of the outer boundary until a curve crosses itself, and the inner curve can define its height above the outer boundary. By extending the starting vector 83 from the reference point 82 by a predetermined distance, a starting point corresponding to the beginning of a sequence of information can be found, which can be found in a database, the number of bits of the same value bit. Corresponds to the contour height at the starting point, and the bit value is given by the curve being concave/convex at that point. The predetermined angle increment is also obtained by offsetting the start vector 83 by a predetermined angular increment and by extending the vector by a predetermined distance to a point of one of the nested curves. Found in the database.

第9圖(a)至第9圖(c)係描述三個封閉曲線,其中第9圖(a)的曲線可視為一參考曲線,其它如第9圖(b)至第9圖(c)所示的曲線可由參考線透過一仿射變換來產生,其中每個連續曲線皆與一同值位元的連串子字串結合在一起,該仿射變換可為平移、反射、旋轉、縮放變換、位似變換、剪切映射中兩種或更多種的組合。舉例來說,平移的距離、縮放的程度、因為剪切而產生的傾斜幅度等可對應於資訊序列中同值位元的位元數量,同時反射或 者旋轉的角度偏移對應於位元值,例如一實施例中,非限制位元值編碼可將第一n度角偏移表示為1,第二n度角標示為0,第三n度角表示為1等。需要注意的是用來將旋轉偏移量制定成位元值的前述方法中也可使用平移、縮放或剪切,編碼方案可從該資料庫中來判斷。 Figures 9(a) to 9(c) depict three closed curves, wherein the curve of Fig. 9(a) can be regarded as a reference curve, and the others are as shown in Fig. 9(b) to Fig. 9(c). The illustrated curve can be generated by a reference line through an affine transformation, wherein each successive curve is combined with a series of substrings of the same value bit, which can be translation, reflection, rotation, scaling, A combination of two or more of a bit-like transform, a cut map. For example, the distance of translation, the degree of scaling, the magnitude of the tilt due to clipping, etc. may correspond to the number of bits of the same value bit in the information sequence, while reflecting or The angular offset of the rotation corresponds to the bit value. For example, in an embodiment, the non-restricted bit value encoding may represent the first n-degree angular offset as 1, and the second n-degree angle as 0, the third n-degree. The angle is expressed as 1 or the like. It should be noted that translation, scaling or cropping can also be used in the aforementioned method for formulating the rotational offset into a bit value, from which the coding scheme can be judged.

第10圖係描述另一個曲線100,其內部分劃分成子區域101,其中每個子區域對應於一同值位元的子序列,需要注意的是,為了清楚表示,僅在圖中指出一些的子區域101。每個子區域的面積可對應同值位元的數量,同時位元值可以由邊界曲線兩端的凹/凸來決定。舉例來說,一內凹的上曲線可為0,任意其他組合可為1,允許有其它結合的定義。 Figure 10 depicts another curve 100 in which the inner portion is divided into sub-regions 101, where each sub-region corresponds to a sub-sequence of a same-valued bit, and it should be noted that for clarity, only some sub-regions are indicated in the figure. 101. The area of each sub-area may correspond to the number of identical-valued bits, and the value of the bit may be determined by the concave/convex at both ends of the boundary curve. For example, a concave upper curve can be 0, any other combination can be 1, allowing for other combinations of definitions.

在本發明構思的其它實施例,一物品可具有例如星星的一標記,該標記含有金鑰的機密資料庫,其含有用於讀取輪廓編碼的所有資訊,例如定義垂直線、參考點的位置、以及另一個曲線上的點的角度偏移等。 In other embodiments of the inventive concept, an item may have a mark such as a star, the mark containing a key database of keys containing all information for reading the outline code, such as defining a vertical line, a position of a reference point And the angular offset of the point on the other curve.

第11圖(a)至第11圖(c)係根據本發明構思的一實施例,說明將封閉曲線轉換成位元串的例子。第11圖(a)係描述嵌入迷彩圖案中的曲線110,而第11圖(b)係描述自迷彩圖案中提取的曲線110。第11圖(b)進一步描述參考點111以及自參考點延伸至曲線110的複數個向量112、113、114、115、116、117及118。參考點111的位置以及向量112至118之每一個的角度偏移量可自上述的機密資料庫中讀取。一組範例中,向量112、113、114、115、116、117及118的非限制角度偏移量可分別為0°、40°、53°、54°、48°、44°以及62°,需要注意的是在本範例中,角度偏移量為連續向量之間的角度。透過向量與曲線交叉的弧線的輪廓特徵,可判讀出與每個向量連結的位元子字串的位元值。在本範例中,位元值0或黑色與向外凸的一弧線連結,而位元值1或白色與向內凹陷的一弧線連接,此外同值位元的數量對應於相關向量的長度。在一組範例中,向量112、113、114、115、116、117及118的非限制位元長度分別可為7黑、2白、1黑、1白、2黑、1白及7黑,需要注意的是,顯示 於第11圖(b)中向量112至118的顯示長度並非必然地對應於所連結的位元數。第11圖(c)係描述自曲線110衍生出的位元串,其中同值位元的每個子字串的參考數量對應於第11圖(b)中相關的向量。 11(a) to 11(c) illustrate an example of converting a closed curve into a bit string, according to an embodiment of the inventive concept. Fig. 11(a) depicts a curve 110 embedded in a camouflage pattern, and Fig. 11(b) depicts a curve 110 extracted from a camouflage pattern. Figure 11 (b) further depicts reference point 111 and a plurality of vectors 112, 113, 114, 115, 116, 117 and 118 extending from reference point to curve 110. The position of the reference point 111 and the angular offset of each of the vectors 112 to 118 can be read from the above-described confidential database. In one example, the unrestricted angular offsets of the vectors 112, 113, 114, 115, 116, 117, and 118 may be 0°, 40°, 53°, 54°, 48°, 44°, and 62°, respectively. It should be noted that in this example, the angular offset is the angle between successive vectors. By reading the contour features of the arc intersecting the curve, it is possible to determine the bit value of the bit substring connected to each vector. In this example, the bit value 0 or black is concatenated with an outwardly convex arc, and the bit value 1 or white is connected to an inwardly recessed arc, and the number of homomorphic bits corresponds to the length of the correlation vector. In one set of examples, the unrestricted bit lengths of vectors 112, 113, 114, 115, 116, 117, and 118 can be 7 black, 2 white, 1 black, 1 white, 2 black, 1 white, and 7 black, respectively. Need to pay attention to, the display The display length of the vectors 112 to 118 in Fig. 11(b) does not necessarily correspond to the number of connected bits. Figure 11 (c) depicts a bit string derived from curve 110, wherein the reference number of each substring of the same value bit corresponds to the vector associated with Fig. 11(b).

第12圖係根據本發明構思的一實施例,將表示為位元串的資訊序列轉換成曲線編碼系統,以提供至少一封閉曲線的方法流程圖。一資訊序列可以表示一位元串,其中每個位元皆含有一低值及一高值,一般分別以0及1表示,位元串例如可為全部或部分產品條碼或二維條碼的代表,位元串包含連續0位元及1位元的子序列。現參考第12圖,方法從步驟121開始,係將資訊序列轉換成一曲線編碼系統,一範例中,非限制曲線編碼系統為一序列的弧線,其中非限制曲線編碼系統的每一碼元為係對應於連續同值位元之一子序列的一弧線。每個弧線的半徑對應於每個子序列中的位元數量,且對應於高值位元的序列的一弧線具有與對應於低值位元的序列的一弧線相反的一輪廓特徵。例如根據本發明構思的一實施例,對應於0位元串的弧線半徑可與對應於1位元串的弧線半徑指向不同的方向。由於一位元串可包含複數個連續1位元的子序列及連續0位元的子序列,因而可產生出複數個弧線。 Figure 12 is a flow diagram of a method of converting a sequence of information represented as a bit string into a curve coding system to provide at least one closed curve, in accordance with an embodiment of the inventive concept. A sequence of information may represent a string of bits, each of which contains a low value and a high value, generally represented by 0 and 1, respectively, and the bit string may be, for example, a representation of all or part of a product barcode or a two-dimensional barcode. The bit string contains consecutive 0-bit and 1-bit subsequences. Referring now to Figure 12, the method begins with step 121 by converting the information sequence into a curve coding system. In an example, the unconstrained curve coding system is a sequence of arcs, wherein each symbol of the unconstrained curve coding system is a system. An arc corresponding to a subsequence of consecutive identical value bits. The radius of each arc corresponds to the number of bits in each subsequence, and an arc of the sequence corresponding to the high value bit has a contour feature that is opposite to an arc of the sequence corresponding to the low value bit. For example, according to an embodiment of the inventive concept, an arc radius corresponding to a 0-bit string may point in a different direction from an arc radius corresponding to a 1-bit string. Since a one-bit string can contain a plurality of consecutive 1-bit subsequences and consecutive 0-bit sub-sequences, a plurality of arcs can be generated.

在步驟122中,藉由將弧線序列的起點連接至終點,以一序列的弧線表示的曲線編碼系統被轉換成一封閉曲線。根據本發明構思的一實施例,該封閉曲線可為平面的簡單封閉曲線。一平面曲線係嵌入一相對於一曲面的平面中,且一簡單封閉曲線本身不會產生交叉。一簡單封閉曲線的習知特徵為該簡單封閉曲線將一平面分成兩個不相交的兩個區域,即曲線的內部區域及外部區域。根據本發明構思的一實施例,終點可連接至起點使得具有0位元子序列的弧線特徵為向封閉曲線向內凹陷,且具有1位元子序列的弧線特徵為向封閉曲線向外凸。或者根據本發明構思的另一實施例,終點可連接至起點使得具有0位元子序列的弧線特徵為向封閉曲線向外凸,且具有1位元子序列的弧線特徵為向封閉曲線向內凹陷。 In step 122, the curve coding system represented by a sequence of arcs is converted into a closed curve by connecting the start of the sequence of arcs to the end point. According to an embodiment of the inventive concept, the closed curve may be a simple closed curve of a plane. A plane curve is embedded in a plane relative to a curved surface, and a simple closed curve itself does not intersect. A conventional feature of a simple closed curve is that the simple closed curve divides a plane into two regions that are not intersecting, namely the inner and outer regions of the curve. According to an embodiment of the inventive concept, the end point may be connected to the starting point such that the arc feature having the 0 bit subsequence is inwardly recessed toward the closed curve, and the arc feature having the 1-bit subsequence is convex toward the closed curve. Or according to another embodiment of the inventive concept, the end point may be connected to the starting point such that the arc feature having the 0 bit subsequence is convex toward the closed curve, and the arc characteristic having the 1-bit subsequence is inward toward the closed curve Depression.

在步驟123中,封閉曲線被嵌入於二維圖案中,並以 此種方式隱藏封閉曲線的存在。根據本發明構思的一實施例,圖案可為一數位化的迷彩圖案,該迷彩圖案具有複數種灰階,且封閉曲線可以編碼成至少兩個重要的位元。隱藏資料的處理為一種藏密學(Steganography)的例子,其是隱藏訊息的處理,無論訊息是否加密,使得除了傳送者及預期的接收者外,沒有人會察覺到訊息的存在。 In step 123, the closed curve is embedded in the two-dimensional pattern and This way hides the existence of a closed curve. According to an embodiment of the inventive concept, the pattern may be a digital camouflage pattern having a plurality of gray scales, and the closed curve may be encoded into at least two important bits. The processing of hidden data is an example of Steganography, which is the processing of hidden messages, regardless of whether the message is encrypted or not, so that no one will be aware of the existence of the message except for the sender and the intended recipient.

第13圖係根據本發明構思的一實施例,將編碼在一系列的輪廓線裡的資訊解密的方法流程圖,現參考第13圖,方法從步驟131開始,係從數位化的二維圖案中提取至少一封閉曲線。根據本發明構思的實施例,該二維圖案可為一迷彩圖案,且該迷彩圖案具有複數種灰階。在本發明構思的其它實施例中,可自該二維圖案中提取出複數個封閉曲線。根據本發明的實施例,每個封閉曲線可為一簡單的封閉曲線。在步驟132中,至少一(封閉)曲線可拆成一曲線編碼系統,一實施例中,非限制的曲線編碼系統為一系列的弧線,其中每個弧線表示曲線編碼系統中的碼元。接著在步驟133中,一系列的弧線中每個弧線被轉換成同值位元的子字串,每個子序列的長度對應於每個弧線的半徑,且在每個子序列中的位元值對應於每個弧線的輪廓特徵。根據本發明構思的實施例,位元串可表示成一二維條碼,再者,根據上述所揭露的內容,自二維圖案中提取的該等封閉曲線的其中之一可作為參考曲線,該參考曲線包含剩餘封閉曲線的解碼資訊。 13 is a flow chart of a method for decrypting information encoded in a series of contour lines according to an embodiment of the inventive concept. Referring now to FIG. 13, the method starts from step 131 and is performed from a digitized two-dimensional pattern. Extracting at least one closed curve. According to an embodiment of the inventive concept, the two-dimensional pattern may be a camouflage pattern, and the camouflage pattern has a plurality of gray scales. In other embodiments of the inventive concept, a plurality of closed curves may be extracted from the two-dimensional pattern. According to an embodiment of the invention, each closed curve can be a simple closed curve. In step 132, at least one (closed) curve is detachable into a curve coding system. In one embodiment, the unrestricted curve coding system is a series of arcs, wherein each arc represents a symbol in the curve coding system. Next, in step 133, each arc of the series of arcs is converted into a substring of the same value bit, the length of each subsequence corresponds to the radius of each arc, and the bit value in each subsequence corresponds to The contour features of each arc. According to an embodiment of the inventive concept, the bit string can be represented as a two-dimensional bar code. Further, according to the above disclosed content, one of the closed curves extracted from the two-dimensional pattern can be used as a reference curve. The reference curve contains decoding information for the remaining closed curves.

如上所述,任何類型的資訊可編碼成位元串,即,能夠數位化,亦可透過根據本發明構思的方法編碼在一二維的曲線中。舉兩個例子,透過本發明構思的實施例可編碼在一二維的曲線中之具商業重要性的非限制性編碼係為一維產品條碼及二維條碼。此外,如上所述,一數位化的二維曲線可嵌入二維圖案中以隱藏二維曲線的存在,且二維圖案可印在例如衣服、DVD或積體電路之商品上或者成為商品中物件的一部分,或可為一產品標誌的全部或一部分。 As described above, any type of information can be encoded into a string of bits, i.e., can be digitized, or can be encoded in a two-dimensional curve by a method in accordance with the teachings of the present invention. By way of two examples, non-limiting coding systems of commercial importance that can be encoded in a two-dimensional curve by embodiments of the inventive concept are one-dimensional product barcodes and two-dimensional barcodes. In addition, as described above, a digitized two-dimensional curve can be embedded in the two-dimensional pattern to hide the existence of the two-dimensional curve, and the two-dimensional pattern can be printed on a product such as a clothing, a DVD, or an integrated circuit or become an object in a commodity. Part of, or may be all or part of a product logo.

本領域具有通常知識者可以理解本發明構思的實施 例可藉不同的形式來實施,例如硬體、軟體、韌體、具特殊目的之製程、或其等的組合。在一實施例中,本發明構思可實施在軟體上,作為有形地收錄在一電腦可讀取程式儲存裝置上之一應用程式,該應用程式可上傳至含有一合適架構的機器,例如可為電腦工作站、桌上型電腦、筆記型電腦、智慧手機等電腦的中央處理器,並透過該機器來執行。 Those skilled in the art can understand the implementation of the inventive concept. The examples may be implemented in different forms, such as hardware, software, firmware, special purpose processes, or combinations thereof. In one embodiment, the inventive concept can be implemented on a software as an application tangibly embodied on a computer readable program storage device, the application can be uploaded to a machine containing a suitable architecture, for example The central processing unit of a computer workstation, a desktop computer, a notebook computer, a smart phone, etc., is executed by the machine.

第14圖係根據本發明一實施例的一範例電腦系統方塊圖,用於實施在二維曲線中編碼或解碼資訊的方法。現參考第14圖,用於實施本發明的電腦系統141可特別包含一中央處理器142、一記憶體143以及一輸入/輸出(I/O)介面144,該電腦系統141一般係透過輸入/輸出介面144連接至一顯示器145以及例如滑鼠及鍵盤等不同的輸入裝置146。支援電路可包含例如快取記憶體、電源供應器、時鐘電路以及通信匯流排,該記體體143可包含隨機存取記憶體(RAM)、唯讀記憶體(ROM)、磁碟機、磁帶機等,或其組合。本發明可實施為一常用程式147,其儲存於記憶體143中並透過中央處理器142來執行,以處理來自訊號元148的訊號,因此當電腦系統141執行本發明之常用程式147時,係由一台普通用途的電腦系統變成為一台特殊用途的電腦。 Figure 14 is a block diagram of an exemplary computer system for implementing a method of encoding or decoding information in a two-dimensional curve, in accordance with an embodiment of the present invention. Referring now to Figure 14, a computer system 141 for implementing the present invention may specifically include a central processing unit 142, a memory 143, and an input/output (I/O) interface 144. The computer system 141 is generally Output interface 144 is coupled to a display 145 and different input devices 146 such as a mouse and keyboard. The support circuit may include, for example, a cache memory, a power supply, a clock circuit, and a communication bus, and the body 143 may include a random access memory (RAM), a read only memory (ROM), a disk drive, and a magnetic tape. Machine, etc., or a combination thereof. The present invention can be implemented as a common program 147, which is stored in the memory 143 and executed by the central processing unit 142 to process the signal from the signal element 148. Therefore, when the computer system 141 executes the commonly used program 147 of the present invention, From a general-purpose computer system to a special-purpose computer.

電腦系統141也包含一操作系統及微指令碼,在此所述之不同的處理及功能可為部分的微指令碼或部分的應用程式(或者其兩者的組合),係透過操作系統來執行。此外,不同之其它周邊裝置例如額外的資料儲存裝置及影印裝置可連接至電腦平台。 The computer system 141 also includes an operating system and microinstruction code. The different processing and functions described herein may be part of the microinstruction code or part of the application (or a combination of the two), which is executed by the operating system. . In addition, different peripheral devices such as additional data storage devices and photocopying devices can be connected to the computer platform.

本領域具有通常知識者更應當理解到因為在圖示中描述的一些構成系統組件及方法步驟可以在軟體上實施,因此系統組件(或處理步驟)之間的實際連接會有所不同,取決於本發明所輸入的方法。鑒於本發明構思在此給予的教導,本領域具有通常知識者能夠思量本發明構思之相似的實施方法及配置。 It should be understood by those of ordinary skill in the art that since some of the constituent system components and method steps described in the figures can be implemented on software, the actual connections between system components (or processing steps) will vary, depending on The method input by the present invention. In view of the teachings of the present invention as set forth herein, those skilled in the art will be able

透過參考範例實施例詳細地描述了本發明的構思,本領具有通常知識者應當理解各種的修改及替換均在不違背附在 本發明之申請專利範圍的精神及範圍下來進行。 The concept of the present invention has been described in detail by reference to example embodiments, and those of ordinary skill in the art should understand that various modifications and substitutions are The spirit and scope of the patent application scope of the present invention proceeds.

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Claims (24)

一種加密資訊的方法,包括下列步驟:將表示為一位元串的一資訊序列轉換成一曲線編碼系統,以提供至少一封閉曲線;以及將該至少一封閉曲線嵌入至一二維圖案中。 A method of encrypting information, comprising the steps of: converting a sequence of information represented as a one-bit string into a curve coding system to provide at least one closed curve; and embedding the at least one closed curve into a two-dimensional pattern. 根據申請專利範圍第1項所述之加密資訊的方法,其中將一位元串轉換成一曲線編碼系統以提供至少一封閉曲線的步驟包含:將該位元串中之連續同值位元的每個子字串轉換成一弧線,其中每個弧線的半徑對應於每個子序列中的位元數量,且對應於高值位元的序列的一弧線具有與對應於低值位元的序列的一弧線相反的一輪廓特徵;以及藉由將該弧線序列的終點連接至該弧線序列的起點,將該弧線序列轉換成一封閉曲線。 The method of encrypting information according to claim 1, wherein the step of converting a one-bit string into a curve coding system to provide at least one closed curve comprises: each of consecutive same-valued bits in the bit string The substrings are converted into an arc, wherein the radius of each arc corresponds to the number of bits in each subsequence, and an arc of the sequence corresponding to the high value bit has an arc opposite to the sequence corresponding to the low value bit a contour feature; and converting the arc sequence into a closed curve by connecting the end point of the arc sequence to the beginning of the arc sequence. 根據申請專利範圍第1項所述之加密資訊的方法,進一步包括將該位元串轉換成複數個封閉曲線,且將該等封閉曲線的每一個嵌入在該二維圖案中。 The method of encrypting information according to claim 1, further comprising converting the bit string into a plurality of closed curves, and embedding each of the closed curves in the two-dimensional pattern. 根據申請專利範圍第3項所述之加密資訊的方法,其中嵌入於該二維圖案中的該等封閉曲線的其中之一係為一參考曲線,該參考曲線包含剩餘的該等封閉曲線的編碼資訊,該編碼資訊包含每個封閉曲線的起點/終點之其一或兩者以及該等封閉曲線的一遍歷順序。 According to the method of encrypting information according to claim 3, wherein one of the closed curves embedded in the two-dimensional pattern is a reference curve, and the reference curve includes the remaining codes of the closed curves. Information, the encoded information includes one or both of the start/end points of each closed curve and a traversal sequence of the closed curves. 根據申請專利範圍第1項所述之加密資訊的方法,其中該二維圖案係具有複數種顏色深淺的一迷彩圖案。 The method of encrypting information according to claim 1, wherein the two-dimensional pattern has a camouflage pattern of a plurality of color shades. 根據申請專利範圍第1項所述之加密資訊的方法,其中該至少一封閉曲線係一簡單封閉曲線。 The method of encrypting information according to claim 1, wherein the at least one closed curve is a simple closed curve. 根據申請專利範圍第1項所述之加密資訊的方法,其中該位元串表示成一二維條碼(QR code)。 The method of encrypting information according to claim 1, wherein the bit string is represented as a QR code. 根據申請專利範圍第1項所述之加密資訊的方法,其中將一位元串轉換成一曲線編碼系統以提供至少一封閉曲線的步驟包含:接收一參考點; 從該位元串中的同值位元的一子字串產生一弧線,其中同值位元的該子字串的長度對應於該弧線上一選擇點至該參考點的距離,且同值位元的該子字串中的位元值在該選擇點上相對於該參考點對應於該封閉曲線的一輪廓特徵;從該參考點至相對於一預設方向的該選擇點保存一向量的角度;以及重複產生一弧線與保存一角度的步驟,直到該位元串全部轉換成一系列的弧線,其中當該等弧線有一個或多個不連接時,在相鄰的多對不連接的弧線之間產生連接弧線,以產生至少一封閉曲線。 The method of encrypting information according to claim 1, wherein converting the one-bit string into a curve coding system to provide at least one closed curve comprises: receiving a reference point; Generating an arc from a substring of the same value bit in the bit string, wherein the length of the substring of the same value bit corresponds to the distance from a selected point to the reference point on the arc, and the same value A bit value in the substring of the bit corresponds to a contour feature of the closed curve relative to the reference point at the selected point; a vector is saved from the reference point to the selected point relative to a predetermined direction The angle; and the step of repeatedly generating an arc and saving an angle until the bit string is all converted into a series of arcs, wherein when the one or more arcs are not connected, the adjacent pairs are not connected A connecting arc is created between the arcs to produce at least one closed curve. 根據申請專利範圍第1項所述之加密資訊的方法,其中將一位元串轉換成一曲線編碼系統以提供至少一封閉曲線的步驟包含:接收一封閉邊界曲線與一參考點;在該封閉邊界曲線內部,從該位元串中同值位元的一子字串產生一弧線,其中同值位元的該子字串的長度對應於自該封閉邊界曲線之弧線的一偏移,且在同值位元的該子字串中的位元值對應於該弧線的一輪廓特徵;從該弧線上的一選擇點至該參考點保存一向量的長度及相對於一預設方向該向量的一角度偏移;以及重複產生一弧線及保存一長度與一角度偏移的步驟,直到該位元串全部轉換成一系列的弧線,其中,當從該封閉邊界曲線在相同的偏移的一個或多個該弧線不連接時,在相鄰的多對不連接的弧線之間產生連接弧線,以在表示一等值線圖之該封閉邊界曲線內產生複數個巢狀封閉曲線。 The method of encrypting information according to claim 1, wherein converting the one-bit string into a curve coding system to provide at least one closed curve comprises: receiving a closed boundary curve and a reference point; Inside the curve, an arc is generated from a substring of the same value bit in the bit string, wherein the length of the substring of the same value bit corresponds to an offset from the arc of the closed boundary curve, and A bit value in the substring of the same value bit corresponds to a contour feature of the arc; a length of the vector is saved from a selected point on the arc to the reference point and the vector is relative to a predetermined direction An angular offset; and repeating the step of generating an arc and storing a length and an angular offset until the bit string is fully converted into a series of arcs, wherein when the closed boundary curve is at the same offset of one or When a plurality of the arcs are not connected, a connecting arc is generated between adjacent pairs of unconnected arcs to generate a plurality of nested closed curves in the closed boundary curve representing a contour map. 根據申請專利範圍第1項所述之加密資訊的方法,其中將一位元串轉換成一曲線編碼系統以提供至少一封閉曲線的步驟包含:產生該等封閉曲線,其中該等封閉曲線的其中之一係為一參考曲線,且其他該 等封閉曲線的每一個透過一仿射變換自該參考曲線衍生出,其中該等仿射變換的每一個是選自平移、反射、旋轉、縮放變換、位似變換、剪切映射中的至少兩種變換的組合,其中將該位元串轉換成該等封閉曲線的步驟包含將每個同值位元的子字串轉換成該等封閉曲線的其中之一,其中該同值位元的數量對應於該至少兩種變換的其中之一,且該同值位元的位元值對應於該至少兩種變換中的其他變換。 The method of encrypting information according to claim 1, wherein the step of converting a bit string into a curve coding system to provide at least one closed curve comprises: generating the closed curves, wherein the closed curves are One is a reference curve, and the other Each of the equal closed curves is derived from the reference curve by an affine transformation, wherein each of the affine transformations is at least two selected from the group consisting of: translation, reflection, rotation, scaling, positional transformation, and shear mapping. a combination of transformations, wherein the step of converting the bit string into the closed curves comprises converting a substring of each equivalence bit into one of the closed curves, wherein the number of the same value bits Corresponding to one of the at least two transforms, and the bit value of the equi-valued bit corresponds to other transforms in the at least two transforms. 根據申請專利範圍第1項所述之加密資訊的方法,其中將一位元串轉換成一曲線編碼系統以提供至少一封閉曲線的步驟包含:將同值位元的每個子字串轉換成在該至少一封閉曲線內部的一子區域,每個子區域透過一對平行線段為界,該對平行線段具有延伸通過該至少一封閉曲線內部和一對曲線線段的一預定分隔,其中每個該子區域的面積對應於同值位元的一對應子字串的長度,且該同值位元的位元值對應於劃界該子區域的該至少一對曲線線段的一輪廓特徵;以及沿著相鄰的多對平行線段附加連續的子區域,其中該等對曲線線段形成至少一封閉曲線。 The method of encrypting information according to claim 1, wherein converting the one-bit string into a curve coding system to provide at least one closed curve comprises: converting each sub-string of the same-valued bit into At least one sub-region inside the closed curve, each sub-region being bounded by a pair of parallel segments having a predetermined separation extending through the interior of the at least one closed curve and a pair of curved segments, wherein each of the sub-regions The area corresponds to the length of a corresponding substring of the same value bit, and the bit value of the same value bit corresponds to a contour feature of the at least one pair of curved line segments delimiting the sub-region; A plurality of adjacent parallel line segments are adjacent to successive sub-regions, wherein the pair of curved line segments form at least one closed curve. 一種非暫存的電腦可讀取程式儲存裝置,有形地收錄有由該電腦處理的指令程式以執行用於解密資訊的方法步驟,該方法包括下列步驟:從一數位化的二維圖案,提取至少一封閉曲線;以及將該至少一封閉曲線轉換成表示為一位元串的一資訊序列。 A non-temporary computer readable program storage device tangibly embodying a program program processed by the computer to perform a method step for decrypting information, the method comprising the steps of: extracting from a digitized two-dimensional pattern At least one closed curve; and converting the at least one closed curve into a sequence of information represented as a one-bit string. 根據申請專利範圍第12項所述之電腦可讀取程式儲存裝置,將該至少一封閉曲線轉換成一位元串的步驟包含:將該至少一封閉曲線拆開成一序列的弧線,且決定每個弧線的一輪廓特徵與一半徑;以及將該序列的弧線轉換成該位元串,其中連續同值位元的每 個子序列對應於一弧線,其中該每個子序列的長度對應於每個弧線的半徑,且每個子序列的該位元值對應於每個弧線的一輪廓特徵。 According to the computer readable program storage device of claim 12, the step of converting the at least one closed curve into a one-bit string comprises: splitting the at least one closed curve into a sequence of arcs, and determining each a contour feature of the arc and a radius; and converting the arc of the sequence into the string of bits, wherein each of the consecutive same-valued bits The subsequences correspond to an arc, wherein the length of each subsequence corresponds to the radius of each arc, and the bit value of each subsequence corresponds to a contour feature of each arc. 根據申請專利範圍第12項所述之電腦可讀取程式儲存裝置,其中該二維圖案係為一具有複數種灰階的迷彩圖案。 The computer readable program storage device according to claim 12, wherein the two-dimensional pattern is a camouflage pattern having a plurality of gray scales. 根據申請專利範圍第12項所述之電腦可讀取程式儲存裝置,該方法進一步包括從該二維圖案中提取該等封閉曲線,且將從該等封閉曲線的每一個衍生出的該位元串序連成表示該資訊序列的一單一位元串。 The computer readable program storage device of claim 12, the method further comprising extracting the closed curves from the two-dimensional pattern, and deriving the bit from each of the closed curves The serial sequence is connected to a single bit string representing the information sequence. 根據申請專利範圍第15項所述之電腦可讀取程式儲存裝置,其中從該二維圖案提取的該等封閉曲線的其中之一係為一參考曲線,該參考曲線包含剩餘的該等封閉曲線的解碼資訊,該解碼資訊包含每個封閉曲線中的起點/終點之其一或兩者以及該等封閉曲線的一遍歷順序。 The computer readable program storage device of claim 15, wherein one of the closed curves extracted from the two-dimensional pattern is a reference curve, and the reference curve includes the remaining closed curves Decoding information that includes one or both of the start/end points in each closed curve and a traversal sequence of the closed curves. 根據申請專利範圍第12項所述之電腦可讀取程式儲存裝置,其中該至少一封閉曲線係為一簡單封閉曲線。 The computer readable program storage device of claim 12, wherein the at least one closed curve is a simple closed curve. 根據申請專利範圍第12項所述之電腦可讀取程式儲存裝置,其中該位元串表示成一二維條碼(QR Code)。 The computer readable program storage device of claim 12, wherein the bit string is represented as a QR Code. 根據申請專利範圍第12項所述之電腦可讀取程式儲存裝置,其中將該至少一封閉曲線轉換成一位元串的步驟包含:在該封閉曲線上,從一參考點延伸一向量到一選擇點;其中從該參考點到該選擇點的一向量的長度對應於在該位元串中的一子字串的同值位元的數量,且同值位元的該子字串中的該位元值是由該封閉曲線在該選擇點的一輪廓特徵決定。 The computer readable program storage device of claim 12, wherein the converting the at least one closed curve into a one-bit string comprises: extending a vector from a reference point to a selection on the closed curve a point; wherein a length of a vector from the reference point to the selection point corresponds to a number of parity bits of a substring in the bit string, and the substring in the same value bit The bit value is determined by a contour feature of the closed curve at the selected point. 根據申請專利範圍第12項所述之電腦可讀取程式儲存裝置,其中將該至少一封閉曲線轉換成一位元串的步驟包含:接收一參考點及相對於一預設方向的一起始角度;在該封閉曲線上,從該起始角度之該參考點延伸一向量到一選擇點;透過一預設角度偏移來偏移該向量,以從該參考點延伸另 一向量到該封閉曲線上的另一點;以及重複透過一預設角度偏移來偏移該向量,以從該參考點延伸另一向量到該封閉曲線上的另一點的步驟,直到該封閉曲線已經遍歷,其中該向量的長度對應於在一子字串中同值位元的數量,且在同值位元的該子字串中的該位元值是由該封閉曲線在該點的一輪廓特徵決定,其中該至少一封閉曲線被轉換成表示為一位元串的一資訊序列。 The computer readable program storage device of claim 12, wherein the converting the at least one closed curve into a one-bit string comprises: receiving a reference point and a starting angle with respect to a predetermined direction; On the closed curve, a vector is extended from the reference point of the starting angle to a selection point; the vector is offset by a predetermined angular offset to extend from the reference point a vector to another point on the closed curve; and repeating the step of shifting the vector by a predetermined angular offset to extend another vector from the reference point to another point on the closed curve until the closed curve Has been traversed, wherein the length of the vector corresponds to the number of identical bits in a substring, and the value of the bit in the substring of the same value is one of the closed curves at that point The contour feature is determined, wherein the at least one closed curve is converted into a sequence of information represented as a one-bit string. 根據申請專利範圍第12項所述之電腦可讀取程式儲存裝置,其中該至少一封閉曲線包含複數個以一等值線圖表示的巢狀封閉曲線,其中將該至少一封閉曲線轉換成一位元串的步驟包含:接收一參考點與相對於一預設方向的一起始角度;以及藉由從該參考點以該起始角度的一預設距離延伸一向量到該等巢狀封閉曲線的其中之一的一點,且藉由連續偏移該向量一預設角度偏移,將該等巢狀封閉曲線轉換成該位元串,其中從該等巢狀封閉曲線的一外部等值線之該等巢狀封閉曲線的該其中之一的一偏移對應於在該位元串的子字串中的同值位元的數量,且在同值位元的該子字串中的位元值是由該等巢狀封閉曲線的該其中之一在該點的一輪廓特徵決定。 The computer readable program storage device of claim 12, wherein the at least one closed curve comprises a plurality of nested closed curves represented by a contour map, wherein the at least one closed curve is converted into a bit The step of the string includes: receiving a reference point and a starting angle with respect to a predetermined direction; and extending a vector from the reference point to the nested closed curve by a predetermined distance from the starting angle One of the points, and by continuously offsetting the vector by a predetermined angular offset, converting the nested closed curve into the bit string, wherein an external contour from the nested closed curve An offset of one of the nested closed curves corresponds to the number of equal-valued bits in the sub-string of the bit string, and the bits in the sub-string of the same-valued bit The value is determined by a profile characteristic of one of the nested closed curves at that point. 根據申請專利範圍第12項所述之電腦可讀取程式儲存裝置,其中從該數位化的二維圖案中提取該等封閉曲線,其中該等封閉曲線的其中之一係為一參考曲線,且其他的每一該等封閉曲線透過一仿射變換從該參考曲線衍生出,其中每一該等仿射變換是選自平移、反射、旋轉、縮放變換、位似變換、剪切映射中兩種或更多種轉換的組合;以及其中將該等封閉曲線轉換成一位元串的步驟包含將每一該等封閉曲線轉換成同值位元的子字串,其中同值位元的數量對應於該二或多個變換的其中之一,且該同值位元的位元值對應於該兩種或更多種變換的其他變換。 The computer readable program storage device of claim 12, wherein the closed curves are extracted from the digitized two-dimensional pattern, wherein one of the closed curves is a reference curve, and Each of the other closed curves is derived from the reference curve by an affine transformation, wherein each of the affine transformations is selected from the group consisting of: translation, reflection, rotation, scaling transformation, bit transformation, and shear mapping. a combination of more than one transformation; and wherein the step of converting the closed curves into a one-bit string comprises converting each of the closed curves into a substring of the same value bit, wherein the number of parity bits corresponds to One of the two or more transforms, and the bit values of the equi-valued bits correspond to other transforms of the two or more transforms. 根據申請專利範圍第12項所述之電腦可讀取程式儲存裝置,其 中將該至少一封閉曲線轉換成一位元串的步驟包含:將該至少一封閉曲線的一內部劃分成複數個子區域,每個子區域透過一對平行線段為界,其中該對平行線段具有延伸通過該至少一封閉曲線的該內部和該曲線兩側的一對曲線線段的一預定分隔;以及將該封閉曲線轉換成表示為一位元串的一資訊序列,其中每個子區域的面積對應於該位元串的子字串的同值位元的位元數量,且該同值位元的位元值對應於劃界該子區域的該至少一對曲線線段的一輪廓特徵。 A computer readable program storage device according to claim 12, The step of converting the at least one closed curve into a one-bit string comprises: dividing an interior of the at least one closed curve into a plurality of sub-regions, each sub-region being bounded by a pair of parallel line segments, wherein the pair of parallel line segments have an extension a predetermined separation of the interior of the at least one closed curve and a pair of curved line segments on either side of the curve; and converting the closed curve into a sequence of information represented as a one-bit string, wherein the area of each sub-region corresponds to the The number of bits of the same-valued bit of the substring of the bit string, and the bit value of the same-valued bit corresponds to a contour feature of the at least one pair of curved line segments delimiting the sub-region. 一種加密資訊的方法,包括下列步驟:藉由將一位元串中的連續同值位元的每個子字串轉換成一弧線,將表示為該位元串的一資訊序列轉換成曲線編碼系統,其中同值位元的各該子字串的長度對應於該弧線上一選擇點到一參考點的距離,且在同值位元的該子字串的一位元值對應於該弧線在該選擇點相對於該參考點的一輪廓特徵;將該等弧線連接成一封閉曲線;以及將該封閉曲線嵌入至一二維圖案中。 A method of encrypting information, comprising the steps of: converting a sequence of information represented by the bit string into a curve coding system by converting each substring of consecutive equivalence bits in a metastring into an arc, The length of each substring of the same value bit corresponds to the distance from a selected point to a reference point on the arc, and the one-bit value of the sub-string of the same-valued bit corresponds to the arc at the Selecting a contour feature of the point relative to the reference point; connecting the arcs into a closed curve; and embedding the closed curve into a two-dimensional pattern.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112819121A (en) * 2021-01-28 2021-05-18 丁松林 Curve code generation method, curve code identification method, terminal device and readable storage medium

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112819121A (en) * 2021-01-28 2021-05-18 丁松林 Curve code generation method, curve code identification method, terminal device and readable storage medium

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