A facile encryption way was successfully applied to the holographic optical encryption system with high speed,multidimensionality,and high capacity,which provided a better security solution for underwater communicatio...A facile encryption way was successfully applied to the holographic optical encryption system with high speed,multidimensionality,and high capacity,which provided a better security solution for underwater communication.The reconstructed optical security system for information transmission was based on wavelengthλand focal length f that were keys to encryption and decryption.To finish the secure data transmission(λ,f)between sender and receiver,an extended Rivest-Shamir-Adleman(ERSA)algorithm for the encryption was achieved based on three-dimension quaternion function.Therein,the Pollard’s rho method was used for the evaluation and comparison of RSA and ERSA algorithms.The results demonstrate that the message encrypted by the ERSA algorithm has better security than that by RSA algorithm in the face of unpredictability and complexity of information transmission on the unsecure acoustic channel.展开更多
In this paper, we discuss the expected number of steps in solving multi-discrete logarithm problems over a group of elliptic curves with prime order by using Pollard＇s rho method and parallel collision search algorit...In this paper, we discuss the expected number of steps in solving multi-discrete logarithm problems over a group of elliptic curves with prime order by using Pollard＇s rho method and parallel collision search algorithm. We prove that when using these algorithms to compute discrete logarithms, the knowledge gained through computing many logarithms does not make it easier for finding other logarithms. Hence in an elliptic cryptosystem, it is safe for many users to share the same curve, with different private keys.展开更多
The discrete logarithm problem(DLP)is to find a solution n such that g^n=h in a finite cyclic group G=,where h∈G.The DLP is the security foundation of many cryptosystems,such as RSA.We propose a method to improve Pol...The discrete logarithm problem(DLP)is to find a solution n such that g^n=h in a finite cyclic group G=,where h∈G.The DLP is the security foundation of many cryptosystems,such as RSA.We propose a method to improve Pollard’s kangaroo algorithm,which is the classic algorithm for solving the DLP.In the proposed algorithm,the large integer multiplications are reduced by controlling whether to perform large integer multiplication.To control the process,the tools of expanding factor and jumping distance are introduced.The expanding factor is an indicator used to measure the probability of collision.Large integer multiplication is performed if the value of the expanding factor is greater than the given bound.The improved algorithm requires an average of(1.633+o(1))q(1/2)times of the large integer multiplications.In experiments,the average large integer multiplication times is approximately(1.5+o(1))q(1/2).展开更多
基金supported by Young Academic Leaders Program of Taiyuan Institute of Technology(No.2022XS06)Scientific Research Funding Project of Taiyuan Institute of Technology(Nos.2022LJ028,2022KJ103).
文摘A facile encryption way was successfully applied to the holographic optical encryption system with high speed,multidimensionality,and high capacity,which provided a better security solution for underwater communication.The reconstructed optical security system for information transmission was based on wavelengthλand focal length f that were keys to encryption and decryption.To finish the secure data transmission(λ,f)between sender and receiver,an extended Rivest-Shamir-Adleman(ERSA)algorithm for the encryption was achieved based on three-dimension quaternion function.Therein,the Pollard’s rho method was used for the evaluation and comparison of RSA and ERSA algorithms.The results demonstrate that the message encrypted by the ERSA algorithm has better security than that by RSA algorithm in the face of unpredictability and complexity of information transmission on the unsecure acoustic channel.
基金NNSF of China.No.90304012973 Project,No.2004CB318000
文摘In this paper, we discuss the expected number of steps in solving multi-discrete logarithm problems over a group of elliptic curves with prime order by using Pollard＇s rho method and parallel collision search algorithm. We prove that when using these algorithms to compute discrete logarithms, the knowledge gained through computing many logarithms does not make it easier for finding other logarithms. Hence in an elliptic cryptosystem, it is safe for many users to share the same curve, with different private keys.
基金partially supported by National Key R&D Program of China(no.2017YFB0802500)The 13th Five-Year National Cryptographic Development Foundation(no.MMJJ20180208)+1 种基金Beijing Science and Technology Commission(no.2181100002718001)NSF(no.61272039).
文摘The discrete logarithm problem(DLP)is to find a solution n such that g^n=h in a finite cyclic group G=,where h∈G.The DLP is the security foundation of many cryptosystems,such as RSA.We propose a method to improve Pollard’s kangaroo algorithm,which is the classic algorithm for solving the DLP.In the proposed algorithm,the large integer multiplications are reduced by controlling whether to perform large integer multiplication.To control the process,the tools of expanding factor and jumping distance are introduced.The expanding factor is an indicator used to measure the probability of collision.Large integer multiplication is performed if the value of the expanding factor is greater than the given bound.The improved algorithm requires an average of(1.633+o(1))q(1/2)times of the large integer multiplications.In experiments,the average large integer multiplication times is approximately(1.5+o(1))q(1/2).
