CN113992326B - Non-interactive image editing validity detection method based on aggregation algorithm - Google Patents
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Abstract
本发明涉及基于聚合算法的图像编辑检测方法,其包括:公钥密码学的基础上,对密码学中的聚合器进行优化,实现了可审计聚合器,并与数字签名技术相结合,通过对图像基于编辑规则进行预处理和哈希,生成哈希集,再对哈希集结合用户公钥进行聚合,生成针对图像用户的编辑许可证书。图像用户持有编辑许可证书后,编辑图像并利用用户私钥为编辑后的图像计算附加证据,验证方收到新图像后,依据编辑许可证书和附加证据验证新图像编辑行为是否经合法授权,采用以上技术方案可以同时检测编辑用户的操作合法性和身份合法性,不但能保证图像应用的安全性,而且运算高效便捷,有利于图像接收方快速验证所收到的图像是否涉及侵权。
The invention relates to an image editing detection method based on an aggregation algorithm, which includes: on the basis of public key cryptography, optimize the aggregator in cryptography, realize an auditable aggregator, and combine it with digital signature technology, through the The image is preprocessed and hashed based on the editing rules to generate a hash set, and then the hash set is aggregated with the user's public key to generate an editing license for the image user. After the image user holds the editing license, he edits the image and uses the user's private key to calculate additional evidence for the edited image. After receiving the new image, the verifier verifies whether the editing of the new image is legally authorized according to the editing license and additional evidence. Using the above technical solutions can simultaneously detect the legality of the editing user's operation and identity, which not only ensures the security of the image application, but also makes the operation efficient and convenient, which is helpful for the image receiver to quickly verify whether the received image involves infringement.
Description
技术领域technical field
本发明涉及多媒体信息安全领域,特别是支持图像验证方对图像编辑的合法性进行验证,具体涉及了基于聚合算法的非交互图像编辑合法性检测方法。The invention relates to the field of multimedia information security, in particular supports an image verification party to verify the legality of image editing, and specifically relates to a non-interactive image editing legality detection method based on an aggregation algorithm.
背景技术Background technique
图像版权是指图像在被创建时自动分配给创作者的一种专属权利,该权利赋予图像版权人(或称创作者)决定如何使用和处理该图像。知识产权法明文规定,任何人未经版权人许可,不得盗窃、复制或出售其他人作品。侵权行为一旦发生并被公信机构认定,被侵权人可以通过法律手段主张自己的权利,并要求侵权人做出相应的经济赔偿。虽然有立法保护,侵权行为还是屡禁不止,其最主要的原因在于:侵权行为认定过程复杂,取证时间长、代价大,被侵权人主张权利过程不易。Image copyright refers to an exclusive right that is automatically assigned to the creator when the image is created, and this right empowers the image copyright owner (or creator) to decide how to use and process the image. The Intellectual Property Law expressly stipulates that no one may steal, copy or sell other people's works without the permission of the copyright owner. Once an infringement occurs and is identified by a trustworthy institution, the infringed can claim his rights through legal means and request the infringer to make corresponding economic compensation. Although there is legislative protection, infringements are still repeatedly prohibited. The main reason is that the process of identifying infringements is complicated, the time for obtaining evidence is long and the cost is high, and the process of claiming rights is not easy for the infringed.
理想情况下,图像用户在使用他人创作的作品时,需要得到图像版权人的授权许可。图像用户可通过多种途径向图像版权人申请图像的使用权或购买版权。图像用户申请付费使用图像时,付费完成后,图像版权人会通过图像使用协议,向特定图像用户对图像使用进行授权。该协议由双方共同签署,协议中规定被授权人在何种情况下如何使用该图像(包括如何编辑、向谁传播等)。然而,在实际使用过程中,仅仅通过协议,很难界定图像用户是否诚实遵守协议使用图像,常常需要与配合一定的技术方法,例如,数字水印、感知哈希等图像取证技术,以鉴定并检测图像编辑的合法性。这些技术方法难以同时检测图像编辑行为和用户身份的合法性,检测功能上存在局限性。Ideally, image users need to obtain permission from the image copyright owner when using works created by others. Image users can apply to image copyright holders for the right to use images or purchase copyrights through various channels. When an image user applies for a payment to use an image, after the payment is completed, the image copyright owner will authorize the specific image user to use the image through an image usage agreement. The agreement is signed by both parties, and the agreement stipulates how the licensee uses the image under what circumstances (including how to edit, to whom, etc.). However, in actual use, it is difficult to determine whether the image user is honestly following the agreement to use the image only through the agreement. It often needs to cooperate with certain technical methods, such as image forensics technologies such as digital watermarking and perceptual hashing, to identify and detect Legality of image editing. These technical methods are difficult to detect the legality of image editing behavior and user identity at the same time, and there are limitations in the detection function.
发明内容Contents of the invention
针对现有技术的不足,本发明提供基于密码学中的聚合算法和数字签名方案,解决传统图像认证方法无法同时验证编辑用户的行为和身份的问题,并解决传统方法误检问题的基于聚合算法的非交互图像编辑合法性检测方法。Aiming at the deficiencies of the prior art, the present invention provides an aggregation algorithm and a digital signature scheme based on cryptography, which solves the problem that the traditional image authentication method cannot verify the behavior and identity of the editing user at the same time, and solves the problem of false detection by the traditional method. Based on the aggregation algorithm Non-interactive image editing legality detection method.
本发明的基于聚合算法的非交互图像编辑合法性检测方法,采用以下技术方案:其包括以下具体步骤:The non-interactive image editing legality detection method based on the aggregation algorithm of the present invention adopts the following technical scheme: it includes the following specific steps:
S1:图像版权人设置安全参数,用群生成方法生成对称结构的双线性群,再运用哈希算法设置公开参数;S1: The image copyright owner sets security parameters, uses the group generation method to generate a bilinear group with a symmetrical structure, and then uses the hash algorithm to set public parameters;
S2:图像版权人基于安全参数调用密钥生成算法生成版权人公钥和版权人私钥;图像用户从双线性群中的正整数乘法群获得用户私钥,并计算用户公钥;所述版权人公钥和用户公钥公开发布,所述版权人私钥和用户私钥各自私有保存;S2: The image copyright owner calls the key generation algorithm based on the security parameters to generate the copyright owner's public key and the copyright owner's private key; the image user obtains the user's private key from the positive integer multiplication group in the bilinear group, and calculates the user's public key; The public key of the copyright owner and the public key of the user are publicly released, and the private key of the copyright owner and the private key of the user are kept privately;
S3:图像版权人制定图像编辑规则,并结合用户公钥生成图像针对该图像用户的编辑许可证书;S3: The image copyright owner formulates image editing rules, and combines the user's public key to generate an image editing license for the image user;
S4:图像用户依据编辑许可证书编辑图像并为编辑后的新图像生成附加证据;S4: The image user edits the image according to the editing license and generates additional evidence for the edited new image;
S5:验证方收到图像和新图像后,依据编辑许可证书和附加证据验证新图像编辑行为是否经合法授权。S5: After receiving the image and the new image, the verifying party verifies whether the editing of the new image is legally authorized according to the editing license and additional evidence.
进一步,所述步骤S1包括:Further, the step S1 includes:
S1-1:设置安全参数λ,λ为常数,用群生成方法生成对称结构的双线性群BP=(G1,G1,G2,e,p),其中p为大素数且p>2λ,G1,G2均是阶为p的乘法循环群,g为群G1的生成元素,e为对称双线性运算e:G1×G1→G2;S1-1: Set the safety parameter λ, λ is a constant, and use the group generation method to generate a bilinear group BP=(G 1 ,G 1 ,G 2 ,e,p) with a symmetrical structure, where p is a large prime number and p> 2 λ , G 1 , G 2 are all multiplicative cyclic groups with order p, g is the generating element of group G 1 , and e is the symmetric bilinear operation e: G 1 ×G 1 →G 2 ;
S1-2:建立哈希函数H1:{0,1}*→Zp *,H2:{0,1}*→G1,其中,{0,1}*为任意字符串,Zp *为模p运算的正整数乘法群;S1-2: Establish hash function H 1 : {0,1} * → Z p * , H 2 : {0,1} * → G 1 , where {0,1} * is any string, Z p * is the positive integer multiplication group of modulo p operation;
S1-3:设置公开参数为param={g,H1,H2,BP}。S1-3: Set the public parameters as param={g, H 1 , H 2 , BP}.
进一步,所述步骤S2中图像版权人基于安全参数调用签名密钥设置的版权人公钥和版权人私钥包括:Further, in the step S2, the copyright owner public key and the copyright owner private key set by the image copyright owner based on the security parameter call signature key include:
S2-1:选取随机数x∈Zp *,并选取标准签名方案,基于安全参数λ调用标准签名方案的密钥生成算法DSS.KeyGen(λ),生成签名公私钥对(sks,pks);S2-1: Select a random number x∈Z p * , and select a standard signature scheme, call the key generation algorithm DSS.KeyGen(λ) of the standard signature scheme based on the security parameter λ, and generate a signature public-private key pair (sk s ,pk s );
S2-2:设置版权人私钥为skA=(x,sks);S2-2: Set the private key of the copyright owner as sk A = (x, sk s );
S2-3:对所有的i=0至n计算获得版权人公钥为pkA=({Xi|0≤i≤n},pks);S2-3: Calculate for all i=0 to n Obtaining the public key of the copyright owner is pk A = ({X i |0≤i≤n},pk s );
所述步骤S2中图像用户从双线性群中的正整数乘法群获得用户私钥,并计算用户公钥包括:In the step S2, the image user obtains the user private key from the positive integer multiplication group in the bilinear group, and calculates the user public key including:
S2-4:随机选取y∈Zp *并设置用户私钥skE=y;S2-4: Randomly select y∈Z p * and set user private key sk E =y;
S2-5:计算Y=gy并设置用户公钥pkE=Y。S2-5: Calculate Y=g y and set user public key pk E =Y.
进一步,所述步骤S3包括:Further, the step S3 includes:
S3-1:设立图像编辑规则:对所有的i=0to|P|的图像设为Mi=fi(Mi,ai);S3-1: Establish image editing rules: set M i =f i (M i ,a i ) for all images i=0to|P|;
S3-2:获得图像Mi的哈希值hi=H1(Mi),并选择随机数k∈Zp *并利用图像用户公钥pkE计算聚合值: S3-2: Obtain the hash value h i =H 1 (M i ) of the image M i , and select a random number k∈Z p * and use the image user public key pk E to calculate the aggregation value:
S3-3:通过聚合值A获得签名σ=DSS.Sign(A,sks);S3-3: Obtain the signature σ=DSS.Sign(A,sk s ) through the aggregation value A;
S3-4:获得编辑许可证书EC=(A,k,σ)。S3-4: Obtain the editing license EC=(A, k, σ).
进一步,所述步骤S4包括:Further, the step S4 includes:
S4-1:基于编辑许可证书EC编辑图像Mi生成新图像M';S4-1: Generating a new image M' based on the edited image M i edited by the editing license EC;
S4-2:获得新图像M'的哈希值hi=H1(M');S4-2: Obtain the hash value h i =H 1 (M') of the new image M';
S4-3:生成附加证据: S4-3: Generate additional evidence:
进一步,所述步骤S4还包括所述图像用户在编辑图像前验证编辑许可证书是否遭遇篡改:如果DSS.Verify(A,σ,pks)=false,停止编辑并返回空,否则进行图像编辑,并为新图像生成附加证据。Further, the step S4 also includes that the image user verifies whether the editing license has been tampered with before editing the image: if DSS.Verify(A,σ,pk s )=false, stop editing and return empty, otherwise perform image editing, And generate additional evidence for new images.
进一步,所述步骤S5中验证方依据编辑许可证书和附加证据验证新图像编辑行为是否经合法授权包括:Further, in the step S5, the verifying party verifies whether the new image editing behavior is legally authorized according to the editing license certificate and additional evidence, including:
S5-1:进行签名验证防止编辑许可证书EC遭遇篡改:如果DSS.Verify(A,σ,pks)=false,验证失败,否则进行下一步;S5-1: Perform signature verification to prevent the editing license EC from being tampered with: if DSS.Verify(A,σ,pk s )=false, the verification fails, otherwise proceed to the next step;
S5-2:验证附加证据的正确性:S5-2: Verify the correctness of additional evidence:
若则新图像编辑行为是经过合法授权,like Then the new image editing behavior is legally authorized,
否则,新图像编辑行为未经过合法授权,侵犯图像版权人的合法权利。Otherwise, the new image editing behavior is not legally authorized, which infringes the legal rights of the image copyright owner.
与现有技术相比,本发明的有益效果:本发明在公钥密码学的基础上,对密码学中的聚合器进行优化,将传统聚合器中成员归属证明由公开可计算重新设计成仅指定用户可计算,实现了新密码组件——可审计聚合器(AACC,Accountable Accumulators)的设计,并将该新组件与数字签名技术相结合,实现非交互环境下的图像编辑合法性检测,在图像认证中同时实现编辑行为检测与编辑人身份验证,不但能保证图像应用的安全性,而且运算高效便捷,有利于图像接收方快速验证所收到的图像是否涉及侵权,为有效地保护图像知识产权提供关键技术支撑。Compared with the prior art, the present invention has the beneficial effect: on the basis of public key cryptography, the present invention optimizes the aggregator in cryptography, and redesigns the proof of membership in the traditional aggregator from publicly computable to only The designated user can be calculated, and the design of a new cryptographic component——Accountable Accumulators (AACC, Accountable Accumulators) is realized, and the new component is combined with digital signature technology to realize the legality detection of image editing in a non-interactive environment. In the image authentication, the editing behavior detection and the identity verification of the editor are realized at the same time, which not only ensures the security of the image application, but also has efficient and convenient operation, which is conducive to the image receiver to quickly verify whether the received image involves infringement, and to effectively protect image knowledge. Property rights provide key technical support.
附图说明Description of drawings
此处所说明的附图用来提供对本申请的进一步理解,在附图中:The accompanying drawings described here are used to provide a further understanding of the application, in the accompanying drawings:
图1为本发明系统架构图;Fig. 1 is a system architecture diagram of the present invention;
图2为本发明工作流程图;Fig. 2 is a work flow chart of the present invention;
图3为本发明工作模块图;Fig. 3 is a working block diagram of the present invention;
图4为本发明80-bit安全级别下算法运行时间对比图。Fig. 4 is a comparison chart of algorithm running time under the 80-bit security level of the present invention.
具体实施方式Detailed ways
参见图1所示,实施例基于聚合算法的非交互图像编辑合法性检测方法,采用以下技术方案:其包括以下具体步骤:Referring to shown in Fig. 1, embodiment is based on the non-interactive image editing legitimacy detection method of aggregation algorithm, adopts following technical scheme: it comprises the following specific steps:
S1:图像版权人设置安全参数,用群生成方法生成对称结构的双线性群,再运用哈希算法设置公开参数;S1: The image copyright owner sets security parameters, uses the group generation method to generate a bilinear group with a symmetrical structure, and then uses the hash algorithm to set public parameters;
S2:图像版权人基于安全参数调用密钥生成算法生成版权人公钥和版权人私钥;图像用户从双线性群中的正整数乘法群获得用户私钥,并计算用户公钥;所述版权人公钥和用户公钥公开发布,所述版权人私钥和用户私钥各自私有保存;S2: The image copyright owner calls the key generation algorithm based on the security parameters to generate the copyright owner's public key and the copyright owner's private key; the image user obtains the user's private key from the positive integer multiplication group in the bilinear group, and calculates the user's public key; The public key of the copyright owner and the public key of the user are publicly released, and the private key of the copyright owner and the private key of the user are kept privately;
S3:图像版权人制定图像编辑规则,并结合用户公钥生成图像针对该图像用户的编辑许可证书;S3: The image copyright owner formulates image editing rules, and combines the user's public key to generate an image editing license for the image user;
S4:图像用户依据编辑许可证书编辑图像并为编辑后的新图像生成附加证据;S4: The image user edits the image according to the editing license and generates additional evidence for the edited new image;
S5:验证方收到图像和新图像后,依据编辑许可证书和附加证据验证新图像编辑行为是否经合法授权。S5: After receiving the image and the new image, the verifying party verifies whether the editing of the new image is legally authorized according to the editing license and additional evidence.
进一步,所述步骤S1包括:Further, the step S1 includes:
S1-1:设置安全参数λ,λ为常数,用群生成方法生成对称结构的双线性群BP=(G1,G1,G2,e,p),其中p为大素数且p>2λ,G1,G2均是阶为p的乘法循环群,g为群G1的生成元素,e为对称双线性运算e:G1×G1→G2;S1-1: Set the safety parameter λ, λ is a constant, and use the group generation method to generate a bilinear group BP=(G 1 ,G 1 ,G 2 ,e,p) with a symmetrical structure, where p is a large prime number and p> 2 λ , G 1 , G 2 are all multiplicative cyclic groups with order p, g is the generating element of group G 1 , and e is the symmetric bilinear operation e: G 1 ×G 1 →G 2 ;
S1-2:建立哈希函数H1:{0,1}*→Zp *,H2:{0,1}*→G1,其中,{0,1}*为任意字符串,Zp *为模p运算的正整数乘法群;S1-2: Establish hash function H 1 : {0,1} * → Z p * , H 2 : {0,1} * → G 1 , where {0,1} * is any string, Z p * is the positive integer multiplication group of modulo p operation;
S1-3:设置公开参数为param={g,H1,H2,BP}。S1-3: Set the public parameters as param={g, H 1 , H 2 , BP}.
进一步,所述步骤S2中图像版权人基于安全参数调用签名密钥设置的版权人公钥和版权人私钥包括:Further, in the step S2, the copyright owner public key and the copyright owner private key set by the image copyright owner based on the security parameter call signature key include:
S2-1:选取随机数x∈Zp *,并选取标准签名方案,基于安全参数λ调用标准签名方案的密钥生成算法DSS.KeyGen(λ),生成签名公私钥对(sks,pks);S2-1: Select a random number x∈Z p * , and select a standard signature scheme, call the key generation algorithm DSS.KeyGen(λ) of the standard signature scheme based on the security parameter λ, and generate a signature public-private key pair (sk s ,pk s );
S2-2:设置版权人私钥为skA=(x,sks);S2-2: Set the private key of the copyright owner as sk A = (x, sk s );
S2-3:对所有的i=0至n计算获得版权人公钥为pkA=({Xi|0≤i≤n},pks);S2-3: Calculate for all i=0 to n Obtaining the public key of the copyright owner is pk A = ({X i |0≤i≤n},pk s );
所述步骤S2中图像用户从双线性群中的正整数乘法群获得用户私钥,并计算用户公钥包括:In the step S2, the image user obtains the user private key from the positive integer multiplication group in the bilinear group, and calculates the user public key including:
S2-4:随机选取y∈Zp *并设置用户私钥skE=y;S2-4: Randomly select y∈Z p * and set user private key sk E =y;
S2-5:计算Y=gy并设置用户公钥pkE=Y。S2-5: Calculate Y=g y and set user public key pk E =Y.
进一步,所述步骤S3包括:Further, the step S3 includes:
S3-1:设立图像编辑规则:对所有的i=0to|P|的图像设为Mi=fi(Mi,ai);S3-1: Establish image editing rules: set M i =f i (M i ,a i ) for all images i=0to|P|;
S3-2:获得图像Mi的哈希值hi=H1(Mi),并选择随机数k∈Zp *并利用图像用户公钥pkE计算聚合值: S3-2: Obtain the hash value h i =H 1 (M i ) of the image M i , and select a random number k∈Z p * and use the image user public key pk E to calculate the aggregation value:
S3-3:通过聚合值A获得签名σ=DSS.Sign(A,sks);S3-3: Obtain the signature σ=DSS.Sign(A,sk s ) through the aggregation value A;
S3-4:获得编辑许可证书EC=(A,k,σ)。S3-4: Obtain the editing license EC=(A, k, σ).
进一步,所述步骤S4包括:Further, the step S4 includes:
S4-1:基于编辑许可证书EC编辑图像Mi生成新图像M';S4-1: Generating a new image M' based on the edited image M i edited by the editing license EC;
S4-2:获得新图像M'的哈希值hi=H1(M');S4-2: Obtain the hash value h i =H 1 (M') of the new image M';
S4-3:生成附加证据: S4-3: Generate additional evidence:
进一步,所述步骤S4还包括所述图像用户在编辑图像前验证编辑许可证书是否遭遇篡改:如果DSS.Verify(A,σ,pks)=false,停止编辑并返回空,否则进行图像编辑,并为新图像生成附加证据。Further, the step S4 also includes that the image user verifies whether the editing license has been tampered with before editing the image: if DSS.Verify(A,σ,pk s )=false, stop editing and return empty, otherwise perform image editing, And generate additional evidence for new images.
进一步,所述步骤S5中验证方依据编辑许可证书和附加证据验证新图像编辑行为是否经合法授权包括:Further, in the step S5, the verifying party verifies whether the new image editing behavior is legally authorized according to the editing license certificate and additional evidence, including:
S5-1:进行签名验证防止编辑许可证书EC遭遇篡改:如果DSS.Verify(A,σ,pks)=false,验证失败,否则进行下一步;S5-1: Perform signature verification to prevent the editing license EC from being tampered with: if DSS.Verify(A,σ,pk s )=false, the verification fails, otherwise proceed to the next step;
S5-2:验证附加证据的正确性:S5-2: Verify the correctness of additional evidence:
若则新图像编辑行为是经过合法授权,like Then the new image editing behavior is legally authorized,
否则,新图像编辑行为未经过合法授权,侵犯图像版权人的合法权利。Otherwise, the new image editing behavior is not legally authorized, which infringes the legal rights of the image copyright owner.
利用计算机对算法的运行效率进行了详细的测试。实验设备是一台普通的联想笔记本电脑(型号:ThinkPad X390),配备3.4GHz Intel i5-7500双核中央处理器(CPU),搭载8G内存(RAM)。程序编码由C++语言结合密码专用测试库GNU Multiple PrecisionArithmetic(GMP)Library和Pairing-Based Cryptography(PBC)Library完成,程序代码由Visual Studio 2017编译并在Win10操作系统上运行。方案选取PBC中对称曲线Curve A进行了测试,数字签名方案选用基双线性映射的短签名BLS方案。The running efficiency of the algorithm is tested in detail by computer. The experimental equipment is an ordinary Lenovo laptop (model: ThinkPad X390), equipped with a 3.4GHz Intel i5-7500 dual-core central processing unit (CPU), and equipped with 8G memory (RAM). The program coding is completed by C++ language combined with GNU Multiple Precision Arithmetic (GMP) Library and Pairing-Based Cryptography (PBC) Library. The program code is compiled by Visual Studio 2017 and run on the Win10 operating system. The scheme selects the symmetric curve Curve A in PBC for testing, and the digital signature scheme selects the short signature BLS scheme based on bilinear mapping.
实验图像选取图像Lenna(分辨率256*256),利用Photoshop将原始图像编辑成400张新图像,编辑方式包括常用的锐化、去噪、压缩等。实验选取n=100~400进行测试,增长粒度100,测试数据共4组;The experimental image selects the image Lenna (resolution 256*256), and uses Photoshop to edit the original image into 400 new images. The editing methods include common sharpening, denoising, compression, etc. The experiment selects n=100~400 for testing, the growth granularity is 100, and there are 4 groups of test data;
首先根据S1和S2所述生成各实体运行需要的公私钥;First, generate the public and private keys needed for the operation of each entity according to S1 and S2;
其次,根据S3所述将图像预处理并进行哈希运算生成图像哈希集。对图像进行哈希的方法是:将图像以二进制形式读取,再利用PBC中哈希函数将图像比特流映射成群G1上的元素。此种方法进行图像哈希运算相对于其他子算法是高效的,对方案效率不会形成牵制。再将哈希集聚合后生成编辑许可证书EC。Secondly, according to S3, the image is preprocessed and a hash operation is performed to generate an image hash set. The method of hashing the image is: read the image in binary form, and then use the hash function in PBC to map the bit stream of the image into elements on the group G 1 . Compared with other sub-algorithms, this method is more efficient for image hashing, and will not hinder the efficiency of the scheme. Then the hash set is aggregated to generate the editing license EC.
然后,根据S4所述编辑图像并生成图像的附加证据SP;Then, edit the image according to S4 and generate additional evidence SP of the image;
最后,根据S5所述根据编辑许可证书EC和附加证据SP对编辑图像进行验证。Finally, the edited image is verified according to the editing license EC and the additional evidence SP as described in S5.
请参照图3和表1,在80-bit安全级别下密钥生成算法时间消耗最大并随着编辑次数n的增大呈线性增长,但由于密钥生成算法在一次授权操作中只需要运行一次,对系统效率的影响有限,而验证算法是恒定时间,与图像的授权的编辑次数无关。Please refer to Figure 3 and Table 1, the time consumption of the key generation algorithm is the largest at the 80-bit security level and increases linearly with the increase of the number of edits n, but since the key generation algorithm only needs to be run once in an authorization operation , has limited impact on system efficiency, while the verification algorithm is constant time independent of the number of authorized edits of the image.
表1 80-bit安全级别下方案各子算法运行时间Table 1 The running time of each sub-algorithm of the scheme under the 80-bit security level
尽管已经示出和描述了本发明的实施例,对于本领域的普通技术人员而言,可以理解在不脱离本发明的原理和精神的情况下可以对这些实施例进行多种变化、修改、替换和变型,本发明的范围由所附权利要求及其等同物限定。Although the embodiments of the present invention have been shown and described, those skilled in the art can understand that various changes, modifications and substitutions can be made to these embodiments without departing from the principle and spirit of the present invention. and modifications, the scope of the invention is defined by the appended claims and their equivalents.
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