为了解决Shamir(t, n)门限方案在秘密共享时,未能充分利用多项式系数和共享份额的问题,本文设计了一种独立高容量半色调图像信息隐藏算法。利用多项式的常数项和一次项系数隐藏秘密图像,共享份额隐藏份额编号或者用户信息等单个共享份...为了解决Shamir(t, n)门限方案在秘密共享时,未能充分利用多项式系数和共享份额的问题,本文设计了一种独立高容量半色调图像信息隐藏算法。利用多项式的常数项和一次项系数隐藏秘密图像,共享份额隐藏份额编号或者用户信息等单个共享份额信息。利用二次项系数隐藏版权信息或者防伪信息。单个共享份额和达到门限数量的多个共享份额都可以进行认证。实验表明,该算法可分离秘密图像和多个共享份额的信息,实现多种信息的可逆隐藏,并且利用单个份额隐藏单个份额的特有信息。该算法增加了信息的种类和嵌入容量。对于Shamir(3, 5)门限共享,嵌入率可以达到3.5 bpp。In order to solve the problem of Shamir(t, n) threshold scheme not fully utilizing polynomial coefficients and shared shares during secret sharing, an independent high-capacity halftone image information hiding algorithm was designed in this paper. Using the constant term and first-order coefficient of polynomials to hide secret images, sharing shares to hide individual shared share information, such as share numbers or user information. Using quadratic coefficients to hide copyright or anti-counterfeiting information. Single shared shares and multiple shared shares that reach the threshold can be authenticated. Experiments have shown that this algorithm can separate secret images and information from multiple shared shares, achieve reversible hiding of multiple types of information, and utilize a single share to hide unique information of a single share. This algorithm increases the variety and embedding capacity of information. For Shamir(3, 5) threshold sharing, the embedding rate can reach 3.5 bpp.展开更多
With the advent of quantum computing,numerous efforts have been made to standardize post-quantum cryptosystems with the intention of(eventually)replacing Elliptic Curve Cryptography(ECC)and Rivets-Shamir-Adelman(RSA)....With the advent of quantum computing,numerous efforts have been made to standardize post-quantum cryptosystems with the intention of(eventually)replacing Elliptic Curve Cryptography(ECC)and Rivets-Shamir-Adelman(RSA).A modified version of the traditional N-Th Degree Truncated Polynomial Ring(NTRU)cryptosystem called NTRU Prime has been developed to reduce the attack surface.In this paper,the Signcryption scheme was proposed,and it is most efficient than others since it reduces the complexity and runs the time of the code execution,and at the same time,provides a better security degree since it ensures the integrity of the sent message,confidentiality of the data,forward secrecy when using refreshed parameters for each session.Unforgeability to prevent the man-in-the-middle attack from being active or passive,and non-repudiation when the sender can’t deny the recently sent message.This study aims to create a novel NTRU cryptography algorithm system that takes advantage of the security features of curve fitting operations and the valuable characteristics of chaotic systems.The proposed algorithm combines the(NTRU Prime)and Shamir’s Secret Sharing(SSS)features to improve the security of the NTRU encryption and key generation stages that rely on robust polynomial generation.Based on experimental results and a comparison of the time required for crucial exchange between NTRU-SSS and the original NTRU,this study shows a rise in complexity with a decrease in execution time in the case when compared to the original NTRU.It’s encouraging to see signs that the suggested changes to the NTRU work to increase accuracy and efficiency.展开更多
In Shamir’s(t,n) threshold of the secret sharing scheme, a secret is divided into n shares by a dealer and is shared among n shareholders in such a way that (a) the secret can be reconstructed when there are t or mor...In Shamir’s(t,n) threshold of the secret sharing scheme, a secret is divided into n shares by a dealer and is shared among n shareholders in such a way that (a) the secret can be reconstructed when there are t or more than t shares;and (b) the secret cannot be obtained when there are fewer than t shares. In the secret reconstruction, participating users can be either legitimate shareholders or attackers. Shamir’s scheme only considers the situation when all participating users are legitimate shareholders. In this paper, we show that when there are more than t users participating and shares are released asynchronously in the secret reconstruction, an attacker can always release his share last. In such a way, after knowing t valid shares of legitimate shareholders, the attacker can obtain the secret and therefore, can successfully impersonate to be a legitimate shareholder without being detected. We propose a simple modification of Shamir’s scheme to fix this security problem. Threshold cryptography is a research of group-oriented applications based on the secret sharing scheme. We show that a similar security problem also exists in threshold cryptographic applications. We propose a modified scheme to fix this security problem as well.展开更多
（k, n） halftone visual cryptography （HVC） is proposed based on Shamir＇ s secret sharing （HVCSSS）, and through this method a binary secret image can be hided into n halftone images, and the secret image can be r...（k, n） halftone visual cryptography （HVC） is proposed based on Shamir＇ s secret sharing （HVCSSS）, and through this method a binary secret image can be hided into n halftone images, and the secret image can be revealed from any k halftone images. Firstly, using Shamir＇ s secret sharing, a binary secret image can be shared into n meaningless shares; secondly, hiding n shares into n halftone images through self-hiding method; and then n extracted shares can be obtained from n halftone images through self-decrypt method; finally, picking any k shares from n extracted shares, the secret image can be revealed by using Lagrange interpolation. The main contribution is that applying Shamir＇ s secret sharing to realize a （k, n） HVC, and this method neither requires code book nor suffers from pixel expansion. Experimental results show HVCSSS can realize a （k, n） HVC in gray-scale and color halftone images, and correct decoding rate （CDR） of revealed secret image can be guaranteed.展开更多
Massive data covert transmission scheme based on Shamir threshold is proposed in this paper. This method applies Shamir threshold scheme to divide data, uses information hiding technology to cover shadows, and realize...Massive data covert transmission scheme based on Shamir threshold is proposed in this paper. This method applies Shamir threshold scheme to divide data, uses information hiding technology to cover shadows, and realizes massive data covert transmission through transmitting stego-covers. Analysis proves that compared with the natural division method, this scheme not only improves the time-efficiency of transmitting but also enhances the security.展开更多
The well-known non-interactive and information-theoretic secure verifiable secret sharing scheme presented by Pedersen is over a large prime. In this paper, we construct a novel non-interactive and information-theoret...The well-known non-interactive and information-theoretic secure verifiable secret sharing scheme presented by Pedersen is over a large prime. In this paper, we construct a novel non-interactive and information-theoretic verifiable secret sharing over RSA （Rivest, Shamir, Adleman） modulus and give the rigorous security proof. It is shown how to distribute a secret among a group such that any set of k parties get no information about the secret. The presented scheme is generally applied to constructions of secure distributed multiplication and threshold or forward-secure signature protocols.展开更多
This paper proposes a(t,n)-threshold verifiable secret sharing scheme with changeable parameters based on a trapdoor one-way function.This scheme consists of a generation phase,a distribution phase,an encoding phase a...This paper proposes a(t,n)-threshold verifiable secret sharing scheme with changeable parameters based on a trapdoor one-way function.This scheme consists of a generation phase,a distribution phase,an encoding phase and a reconstruction phase.The generation and distribution phases are,respectively,based on Shamir’s and Feldman’s approaches,while the encoding phase is based on a novel trapdoor one-way function.In the reconstruction phase,the shares and reconstructed secret are validated using a cryptographic hash function.In comparison with existing schemes,the proposed scheme leaks no direct information about the secret from public information.Furthermore,unlike some existing schemes,the generation and distribution phases of the proposed scheme are both independent of the secret.This feature leads to a number of advantages over existing approaches such as the dealer’s ability to perform the following modifications without updating the shares(i)modify the secret and(ii)adjust the threshold parameters of the scheme.Furthermore,each participant receives a single share,and designated participants can be given the privilege of choosing their own shares for reconstructing a secret S.Moreover,the proposed scheme possesses a high level of security which is inherited from the schemes of Shamir and Feldman,in addition to the trapdoor one-way function and the employed cryptographic hash function.展开更多
Differently from pure data encryption,secret image sharing(SIS)mainly focuses on image protection through generating a secret image into n shadow images(shares)distributed to n associated participants.The secret image...Differently from pure data encryption,secret image sharing(SIS)mainly focuses on image protection through generating a secret image into n shadow images(shares)distributed to n associated participants.The secret image can be reconstructed by collecting sufficient shadow images.In recent years,many SIS schemes are proposed,among which Shamir’s polynomial-based SIS scheme and visual secret sharing(VSS)also called visual cryptography scheme(VCS)are the primary branches.However,as the basic research issues,the security analysis and security level classification of SIS are rarely discussed.In this paper,based on the study of image feature and typical SIS schemes,four security levels are classified as well as the security of typical SIS schemes are analyzed.Furthermore,experiments are conducted to evaluate the efficiency of our analysis by employing illustrations and evaluation metrics.展开更多
Shamir proposed a classic polynomial-based secret sharing(SS)scheme,which is also widely applied in secret image sharing(SIS).However,the following researchers paid more attention to the development of properties,such...Shamir proposed a classic polynomial-based secret sharing(SS)scheme,which is also widely applied in secret image sharing(SIS).However,the following researchers paid more attention to the development of properties,such as lossless recovery,rather than the principle of Shamir’s polynomial-based SS scheme.In this paper,we introduce matrix theory to analyze Shamir’s polynomial-based scheme as well as propose a general(k,n)threshold SIS construction based on matrix theory.Besides,it is proved that Shamir’s polynomial-based SS scheme is a special case of our construction method.Both experimental results and analyses are given to demonstrate the effectiveness of the proposed construction method.展开更多
文摘为了解决Shamir(t, n)门限方案在秘密共享时,未能充分利用多项式系数和共享份额的问题,本文设计了一种独立高容量半色调图像信息隐藏算法。利用多项式的常数项和一次项系数隐藏秘密图像,共享份额隐藏份额编号或者用户信息等单个共享份额信息。利用二次项系数隐藏版权信息或者防伪信息。单个共享份额和达到门限数量的多个共享份额都可以进行认证。实验表明,该算法可分离秘密图像和多个共享份额的信息,实现多种信息的可逆隐藏,并且利用单个份额隐藏单个份额的特有信息。该算法增加了信息的种类和嵌入容量。对于Shamir(3, 5)门限共享,嵌入率可以达到3.5 bpp。In order to solve the problem of Shamir(t, n) threshold scheme not fully utilizing polynomial coefficients and shared shares during secret sharing, an independent high-capacity halftone image information hiding algorithm was designed in this paper. Using the constant term and first-order coefficient of polynomials to hide secret images, sharing shares to hide individual shared share information, such as share numbers or user information. Using quadratic coefficients to hide copyright or anti-counterfeiting information. Single shared shares and multiple shared shares that reach the threshold can be authenticated. Experiments have shown that this algorithm can separate secret images and information from multiple shared shares, achieve reversible hiding of multiple types of information, and utilize a single share to hide unique information of a single share. This algorithm increases the variety and embedding capacity of information. For Shamir(3, 5) threshold sharing, the embedding rate can reach 3.5 bpp.
文摘With the advent of quantum computing,numerous efforts have been made to standardize post-quantum cryptosystems with the intention of(eventually)replacing Elliptic Curve Cryptography(ECC)and Rivets-Shamir-Adelman(RSA).A modified version of the traditional N-Th Degree Truncated Polynomial Ring(NTRU)cryptosystem called NTRU Prime has been developed to reduce the attack surface.In this paper,the Signcryption scheme was proposed,and it is most efficient than others since it reduces the complexity and runs the time of the code execution,and at the same time,provides a better security degree since it ensures the integrity of the sent message,confidentiality of the data,forward secrecy when using refreshed parameters for each session.Unforgeability to prevent the man-in-the-middle attack from being active or passive,and non-repudiation when the sender can’t deny the recently sent message.This study aims to create a novel NTRU cryptography algorithm system that takes advantage of the security features of curve fitting operations and the valuable characteristics of chaotic systems.The proposed algorithm combines the(NTRU Prime)and Shamir’s Secret Sharing(SSS)features to improve the security of the NTRU encryption and key generation stages that rely on robust polynomial generation.Based on experimental results and a comparison of the time required for crucial exchange between NTRU-SSS and the original NTRU,this study shows a rise in complexity with a decrease in execution time in the case when compared to the original NTRU.It’s encouraging to see signs that the suggested changes to the NTRU work to increase accuracy and efficiency.
文摘In Shamir’s(t,n) threshold of the secret sharing scheme, a secret is divided into n shares by a dealer and is shared among n shareholders in such a way that (a) the secret can be reconstructed when there are t or more than t shares;and (b) the secret cannot be obtained when there are fewer than t shares. In the secret reconstruction, participating users can be either legitimate shareholders or attackers. Shamir’s scheme only considers the situation when all participating users are legitimate shareholders. In this paper, we show that when there are more than t users participating and shares are released asynchronously in the secret reconstruction, an attacker can always release his share last. In such a way, after knowing t valid shares of legitimate shareholders, the attacker can obtain the secret and therefore, can successfully impersonate to be a legitimate shareholder without being detected. We propose a simple modification of Shamir’s scheme to fix this security problem. Threshold cryptography is a research of group-oriented applications based on the secret sharing scheme. We show that a similar security problem also exists in threshold cryptographic applications. We propose a modified scheme to fix this security problem as well.
基金supported by the National Natural Science Foundation of China(61370188)the Scientific Research Common Program of Beijing Municipal Commission of Education(KM201610015002,KM201510015009)+2 种基金the Beijing City Board of Education Science and Technology Key Project(KZ201510015015,KZ201710015010)Project of Beijing Municipal College Improvement Plan(PXM2017_014223_000063)BIGC Project(Ec201802,Ed201803,Ea201806)
文摘（k, n） halftone visual cryptography （HVC） is proposed based on Shamir＇ s secret sharing （HVCSSS）, and through this method a binary secret image can be hided into n halftone images, and the secret image can be revealed from any k halftone images. Firstly, using Shamir＇ s secret sharing, a binary secret image can be shared into n meaningless shares; secondly, hiding n shares into n halftone images through self-hiding method; and then n extracted shares can be obtained from n halftone images through self-decrypt method; finally, picking any k shares from n extracted shares, the secret image can be revealed by using Lagrange interpolation. The main contribution is that applying Shamir＇ s secret sharing to realize a （k, n） HVC, and this method neither requires code book nor suffers from pixel expansion. Experimental results show HVCSSS can realize a （k, n） HVC in gray-scale and color halftone images, and correct decoding rate （CDR） of revealed secret image can be guaranteed.
基金Supported by the National High Technology Research and Development Program of China (863 Program) (2007AA0825)
文摘Massive data covert transmission scheme based on Shamir threshold is proposed in this paper. This method applies Shamir threshold scheme to divide data, uses information hiding technology to cover shadows, and realizes massive data covert transmission through transmitting stego-covers. Analysis proves that compared with the natural division method, this scheme not only improves the time-efficiency of transmitting but also enhances the security.
基金Supported by the National Natural Science Foun-dation of China (60403005 ,60573026)
文摘The well-known non-interactive and information-theoretic secure verifiable secret sharing scheme presented by Pedersen is over a large prime. In this paper, we construct a novel non-interactive and information-theoretic verifiable secret sharing over RSA （Rivest, Shamir, Adleman） modulus and give the rigorous security proof. It is shown how to distribute a secret among a group such that any set of k parties get no information about the secret. The presented scheme is generally applied to constructions of secure distributed multiplication and threshold or forward-secure signature protocols.
文摘This paper proposes a(t,n)-threshold verifiable secret sharing scheme with changeable parameters based on a trapdoor one-way function.This scheme consists of a generation phase,a distribution phase,an encoding phase and a reconstruction phase.The generation and distribution phases are,respectively,based on Shamir’s and Feldman’s approaches,while the encoding phase is based on a novel trapdoor one-way function.In the reconstruction phase,the shares and reconstructed secret are validated using a cryptographic hash function.In comparison with existing schemes,the proposed scheme leaks no direct information about the secret from public information.Furthermore,unlike some existing schemes,the generation and distribution phases of the proposed scheme are both independent of the secret.This feature leads to a number of advantages over existing approaches such as the dealer’s ability to perform the following modifications without updating the shares(i)modify the secret and(ii)adjust the threshold parameters of the scheme.Furthermore,each participant receives a single share,and designated participants can be given the privilege of choosing their own shares for reconstructing a secret S.Moreover,the proposed scheme possesses a high level of security which is inherited from the schemes of Shamir and Feldman,in addition to the trapdoor one-way function and the employed cryptographic hash function.
文摘Differently from pure data encryption,secret image sharing(SIS)mainly focuses on image protection through generating a secret image into n shadow images(shares)distributed to n associated participants.The secret image can be reconstructed by collecting sufficient shadow images.In recent years,many SIS schemes are proposed,among which Shamir’s polynomial-based SIS scheme and visual secret sharing(VSS)also called visual cryptography scheme(VCS)are the primary branches.However,as the basic research issues,the security analysis and security level classification of SIS are rarely discussed.In this paper,based on the study of image feature and typical SIS schemes,four security levels are classified as well as the security of typical SIS schemes are analyzed.Furthermore,experiments are conducted to evaluate the efficiency of our analysis by employing illustrations and evaluation metrics.
文摘Shamir proposed a classic polynomial-based secret sharing(SS)scheme,which is also widely applied in secret image sharing(SIS).However,the following researchers paid more attention to the development of properties,such as lossless recovery,rather than the principle of Shamir’s polynomial-based SS scheme.In this paper,we introduce matrix theory to analyze Shamir’s polynomial-based scheme as well as propose a general(k,n)threshold SIS construction based on matrix theory.Besides,it is proved that Shamir’s polynomial-based SS scheme is a special case of our construction method.Both experimental results and analyses are given to demonstrate the effectiveness of the proposed construction method.
