To provide a high-security guaran- tee to network coding and lower the comput- ing complexity induced by signature scheme, we take full advantage of homomorphic prop- erty to build lattice signature schemes and sec- u...To provide a high-security guaran- tee to network coding and lower the comput- ing complexity induced by signature scheme, we take full advantage of homomorphic prop- erty to build lattice signature schemes and sec- ure network coding algorithms. Firstly, by means of the distance between the message and its sig- nature in a lattice, we propose a Distance-bas- ed Secure Network Coding （DSNC） algorithm and stipulate its security to a new hard problem Fixed Length Vector Problem （FLVP）, which is harder than Shortest Vector Problem （SVP） on lattices. Secondly, considering the bound- ary on the distance between the message and its signature, we further propose an efficient Bo- undary-based Secure Network Coding （BSNC） algorithm to reduce the computing complexity induced by square calculation in DSNC. Sim- ulation results and security analysis show that the proposed signature schemes have stronger unforgeability due to the natural property of lattices than traditional Rivest-Shamir-Adleman （RSA）-based signature scheme. DSNC algo- rithm is more secure and BSNC algorithm greatly reduces the time cost on computation.展开更多
Under the assumption that the wiretapper can get at most r(r < n) independent messages, Cai et al. showed that any rate n multicast code can be modified to another secure network code with transmitting rate n- r by...Under the assumption that the wiretapper can get at most r(r < n) independent messages, Cai et al. showed that any rate n multicast code can be modified to another secure network code with transmitting rate n- r by a properly chosen matrix Q^(-1). They also gave the construction for searching such an n × n nonsingular matrix Q. In this paper, we find that their method implies an efficient construction of Q. That is to say, Q can be taken as a special block lower triangular matrix with diagonal subblocks being the(n- r) ×(n- r)and r × r identity matrices, respectively. Moreover, complexity analysis is made to show the efficiency of the specific construction.展开更多
基金ACKNOWLEDGEMENT This work was partially supported by the National Basic Research Program of China under Grant No. 2012CB315905 the National Natural Sci- ence Foundation of China under Grants No. 61272501, No. 61173154, No. 61370190 and the Beijing Natural Science Foundation under Grant No. 4132056.
文摘To provide a high-security guaran- tee to network coding and lower the comput- ing complexity induced by signature scheme, we take full advantage of homomorphic prop- erty to build lattice signature schemes and sec- ure network coding algorithms. Firstly, by means of the distance between the message and its sig- nature in a lattice, we propose a Distance-bas- ed Secure Network Coding （DSNC） algorithm and stipulate its security to a new hard problem Fixed Length Vector Problem （FLVP）, which is harder than Shortest Vector Problem （SVP） on lattices. Secondly, considering the bound- ary on the distance between the message and its signature, we further propose an efficient Bo- undary-based Secure Network Coding （BSNC） algorithm to reduce the computing complexity induced by square calculation in DSNC. Sim- ulation results and security analysis show that the proposed signature schemes have stronger unforgeability due to the natural property of lattices than traditional Rivest-Shamir-Adleman （RSA）-based signature scheme. DSNC algo- rithm is more secure and BSNC algorithm greatly reduces the time cost on computation.
基金Supported by the National Natural Science Foundation of China(61201253)
文摘Under the assumption that the wiretapper can get at most r(r < n) independent messages, Cai et al. showed that any rate n multicast code can be modified to another secure network code with transmitting rate n- r by a properly chosen matrix Q^(-1). They also gave the construction for searching such an n × n nonsingular matrix Q. In this paper, we find that their method implies an efficient construction of Q. That is to say, Q can be taken as a special block lower triangular matrix with diagonal subblocks being the(n- r) ×(n- r)and r × r identity matrices, respectively. Moreover, complexity analysis is made to show the efficiency of the specific construction.
