This paper introduces an improvement to a currently published algorithm to compute both Lucas 'sister' sequences Vk and Uk. The proposed algorithm uses Lucas sequence properties to improve the running time by ...This paper introduces an improvement to a currently published algorithm to compute both Lucas 'sister' sequences Vk and Uk. The proposed algorithm uses Lucas sequence properties to improve the running time by about 20% over the algorithm published in [1].展开更多
In this study, we first give the definitions of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequence. By using these formulas we define (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas matrix sequences. After that we estab...In this study, we first give the definitions of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequence. By using these formulas we define (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas matrix sequences. After that we establish some sum formulas for these matrix sequences.展开更多
Investigated the properties of LUCas sequence(LUC), the paper proposed a new variant of (probabilistic) public-key encryption scheme. Security analysis of the proposed encryption schemes shows that its one-wayness is ...Investigated the properties of LUCas sequence(LUC), the paper proposed a new variant of (probabilistic) public-key encryption scheme. Security analysis of the proposed encryption schemes shows that its one-wayness is equivalent to partial LUC discrete logarithm problem in ZN, and for the proposed probabilistic encryption scheme, its semantic security is equivalent to decisional LUC Diffie-Hellman problem in ZN. At last, the efficiency of the proposed schemes is briefly analyzed.展开更多
Let a∈N.In this paper we prove that if Jacobi symbol, then the rsophantine equation y2=ax4 + x3 + 2(a - 1)x= + x + (a - 2) has no integer soutions, except a = ( is a square), x = 2,and a -2 = , x = 0, Whre 2(mod6), Q...Let a∈N.In this paper we prove that if Jacobi symbol, then the rsophantine equation y2=ax4 + x3 + 2(a - 1)x= + x + (a - 2) has no integer soutions, except a = ( is a square), x = 2,and a -2 = , x = 0, Whre 2(mod6), Qk denote Fibonacci-Lucas se-guence defined by Qn+2 = Qn+1 + Qn, Q0 = 2,Q1 =1.展开更多
文摘This paper introduces an improvement to a currently published algorithm to compute both Lucas 'sister' sequences Vk and Uk. The proposed algorithm uses Lucas sequence properties to improve the running time by about 20% over the algorithm published in [1].
文摘In this study, we first give the definitions of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequence. By using these formulas we define (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas matrix sequences. After that we establish some sum formulas for these matrix sequences.
基金Supported by the 973 State Key Project of China (No.G1999035803)the National Natural Science Foundation of China (No.69931010).
文摘Investigated the properties of LUCas sequence(LUC), the paper proposed a new variant of (probabilistic) public-key encryption scheme. Security analysis of the proposed encryption schemes shows that its one-wayness is equivalent to partial LUC discrete logarithm problem in ZN, and for the proposed probabilistic encryption scheme, its semantic security is equivalent to decisional LUC Diffie-Hellman problem in ZN. At last, the efficiency of the proposed schemes is briefly analyzed.
文摘Let a∈N.In this paper we prove that if Jacobi symbol, then the rsophantine equation y2=ax4 + x3 + 2(a - 1)x= + x + (a - 2) has no integer soutions, except a = ( is a square), x = 2,and a -2 = , x = 0, Whre 2(mod6), Qk denote Fibonacci-Lucas se-guence defined by Qn+2 = Qn+1 + Qn, Q0 = 2,Q1 =1.
