Let ε ： y^2 = x3 ＋ Ax ＋ B be an elliptic curve defined over the finite field Zp（p 〉 3） and G be a rational point of prime order N on ε. Define a subset of ZN, the residue class ring modulo N, asS：={n：n∈ZN,n...Let ε ： y^2 = x3 ＋ Ax ＋ B be an elliptic curve defined over the finite field Zp（p 〉 3） and G be a rational point of prime order N on ε. Define a subset of ZN, the residue class ring modulo N, asS：={n：n∈ZN,n≠0,（X（nG）/p）=1} where X（nG） denotes the x-axis of the rational points nC and （＊/P） is the Legendre symbol. Some explicit results on quasi-randomness of S are investigated. The construction depends on the intrinsic group structures of elliptic curves and character sums along elliptic curves play an important role in the proofs.展开更多
The paper describes the concept of plaintext encryption by using the Unicode characters. In the case of elliptic curve cryptography, there is not specified rule or algorithm to specify the letters of Tifinagh as well ...The paper describes the concept of plaintext encryption by using the Unicode characters. In the case of elliptic curve cryptography, there is not specified rule or algorithm to specify the letters of Tifinagh as well as special characters. So, the paper gives the transformation of characters Tifinagh into points on elliptic curve by using the corresponding characters Latin. The obtained correspondence has been applied in Menezes-Vanstone cryptosystem based on elliptic curve. Therefore, the paper explains in detail its implementation in Maple 12.展开更多
基金Supported by the National Natural Science Foundation of China(No.61170246)the Program for New Century Excellent Talents in Fujian Province University of China(No.JK2010047)the Open Funds of State Key Laboratory of Information Security (Chinese Academy of Sciences)(No.01-01-1)
文摘Let ε ： y^2 = x3 ＋ Ax ＋ B be an elliptic curve defined over the finite field Zp（p 〉 3） and G be a rational point of prime order N on ε. Define a subset of ZN, the residue class ring modulo N, asS：={n：n∈ZN,n≠0,（X（nG）/p）=1} where X（nG） denotes the x-axis of the rational points nC and （＊/P） is the Legendre symbol. Some explicit results on quasi-randomness of S are investigated. The construction depends on the intrinsic group structures of elliptic curves and character sums along elliptic curves play an important role in the proofs.
文摘The paper describes the concept of plaintext encryption by using the Unicode characters. In the case of elliptic curve cryptography, there is not specified rule or algorithm to specify the letters of Tifinagh as well as special characters. So, the paper gives the transformation of characters Tifinagh into points on elliptic curve by using the corresponding characters Latin. The obtained correspondence has been applied in Menezes-Vanstone cryptosystem based on elliptic curve. Therefore, the paper explains in detail its implementation in Maple 12.
