RSA(Rivest-Shamir-Adleman)public-key cryptosystem is widely used in the information security area such as encryption and digital signature. Based on the modified Montgomery modular multiplication algorithm, a new arch...RSA(Rivest-Shamir-Adleman)public-key cryptosystem is widely used in the information security area such as encryption and digital signature. Based on the modified Montgomery modular multiplication algorithm, a new architecture using CSA(carry save adder)was presented to implement modular multiplication. Compared with the popular modular multiplication algorithms using two CSA, the presented algorithm uses only one CSA, so it can improve the time efficiency of RSA cryptoprocessor and save about half of hardware resources for modular multiplication. With the increase of encryption data size n, the clock cycles for the encryption procedure reduce in (T(n^2),) compared with the modular multiplication algorithms using two CSA.展开更多
Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller’s randomization, he then gave a factorization algorithm. But the al...Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller’s randomization, he then gave a factorization algorithm. But the algorithm has two shortcomings, the order must be even and the output might be a trivial factor. Actually, these drawbacks can be overcome if the number is an RSA modulus. Applying the special structure of the RSA modulus, an algorithm is presented to overcome the two shortcomings. The new algorithm improves Shor’s algorithm for factoring RSA modulus. The cost of the factorization algorithm almost depends on the calculation of the order of 2 in the multiplication group.展开更多
文摘RSA(Rivest-Shamir-Adleman)public-key cryptosystem is widely used in the information security area such as encryption and digital signature. Based on the modified Montgomery modular multiplication algorithm, a new architecture using CSA(carry save adder)was presented to implement modular multiplication. Compared with the popular modular multiplication algorithms using two CSA, the presented algorithm uses only one CSA, so it can improve the time efficiency of RSA cryptoprocessor and save about half of hardware resources for modular multiplication. With the increase of encryption data size n, the clock cycles for the encryption procedure reduce in (T(n^2),) compared with the modular multiplication algorithms using two CSA.
文摘Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller’s randomization, he then gave a factorization algorithm. But the algorithm has two shortcomings, the order must be even and the output might be a trivial factor. Actually, these drawbacks can be overcome if the number is an RSA modulus. Applying the special structure of the RSA modulus, an algorithm is presented to overcome the two shortcomings. The new algorithm improves Shor’s algorithm for factoring RSA modulus. The cost of the factorization algorithm almost depends on the calculation of the order of 2 in the multiplication group.
