An Overview of Cryptanalysis of RSA Public key System

Berlin, Konstantin; S.S, Dhenakaran

doi:10.21817/ijet/2017/v9i5/170905312

Cited by 6 publications

(2 citation statements)

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“…To be specifc, the ME(a) operation can be decomposed into a series of controlled MM(•) operations, which is the equation (2), and the windowing technique can be used to compute m ME(a) operation frst. Tat is, m x i are selected frst and the 2 m cases T i � a x ′ represented by m x i can be calculated and stored in an n-qubit register, where x ′ � 􏽐 m j�1 2 i j x i j .…”

Section: Windowing Techniquementioning

confidence: 99%

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Feasibility Analysis of Cracking RSA with Improved Quantum Circuits of the Shor’s Algorithm

Liu,

Yang,

Yang

2023

Security and Communication Networks

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Since the RSA public key cryptosystem was proposed, it has been widely used because of its strong security. Although the proposal of the Shor’s algorithm offers hope for cracking RSA, it is debatable whether the algorithm can actually pose a threat in practice. From the perspective of the quantum circuit of the Shor’s algorithm, we analyse the feasibility of cracking RSA with improved quantum circuits using an ion-trap quantum computer. We present an improved quantum circuit for the modular exponentiation of a constant, which is the most expensive operation in Shor’s algorithm for integer factorization. Whereas previous studies mostly focused on minimizing the number of qubits or the depth of the circuit, we minimize the number of CNOTs, which greatly affects the time to run the algorithm on an ion-trap quantum computer. First, we give the implementation of the basic arithmetic with the lowest known number of CNOTs and the construction of an improved modular exponentiation of a constant by accumulating intermediate data and using a windowing technique. Then, we precisely estimate the number of improved quantum circuits needed to perform the Shor’s algorithm for factoring an n -bit integer, which is 217 n 3 / log 2 n + 4 n 2 + n . We analyse the running time and feasibility of the Shor’s algorithm on an ion-trap quantum computer according to the number of CNOTs. Finally, we discussed the lower bound of the number of CNOTs needed to implement the Shor’s algorithm.

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Section: Windowing Techniquementioning

confidence: 99%

“…Te proposal of the RSA public key cryptosystem [1] has given rise to numerous scholarly discussions on this problem [2][3][4][5][6], in which security relies on the integer factorization. Te problem of integer factorization is to fnd a nontrivial factor of a given composite number.…”

Section: Introductionmentioning

confidence: 99%