Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 11 Sayı: 2, 78 - 83, 31.12.2019

Öz

Kaynakça

  • Bach, E., {\em Toward a theory of Pollard's rho method}, Information and Computation, \textbf{90}(1991), 139--155.
  • Dash, A., Sarmah, D., Behera, B.K., Panigrahi, P.K., \textit{Exact search algorithm to factorize large biprimes and a triprime on IBM quantum computer}, 2018.
  • Dattani, N.S., Bryans, N., {\em Quantum factorization of 56153 with only 4 qubits}. arXiv:1411.6758 [quant-ph], 2014.
  • Diffie, W., Hellman, M., {\em New Directions in Cryptography}, IEEE Transactions on Information Theory, \textbf{22(6)}(1976), 644--654.
  • Gerver, J., {\em Factoring large numbers with a quadratic sieve}, Mathematics of Computation, \textbf{41}(1983), 287--294.
  • Jiang, S., Britt, K.A., McCaskey, A.J., Humble, T.S., Kais, S, {\em Quantum annealing for prime factorization}, Scientific Reports, \textbf{8}(2018).
  • Kute S., Desai C.G., \textit{Quantum Cryptography: A Review}, Indian Jour. of Scien. and Techn., \textbf{10(3)}(2017).
  • Li, Z., Dattani, N.S., Chen, X., Liu, X., Wang, H., Tanburn, R., Chen, H., Peng, X., Du, J., {\em High-fidelity adiabatic quantum computation using the intrinsic Hamiltonian of a spin system: Application to the experimental factorization of 291311}, (2017).
  • Martin-Lopez, E., Laing, A., Lawson, T., Alvarez, R., Zhou, X., O'Brien, J.L., {\em Experimental realization of Shor's quantum factoring algorithm using qubit recycling}, Nature Photonics, 6 \textbf{11}(2012), 773--776.
  • Pal, S., Moitra, S., Anjusha, V.S., Kumar, A., Mahesh, T.S., {\em Hybrid scheme for factorization: Factoring 551 using a 3-qubit NMR quantum adiabatic processor}, (2016).
  • Pollard, J.M., {\em Theorems on factorization and primality testing}, Proceedings of the Cambridge Philosophical Society, \textbf{76}(1974), 521--528.
  • Pomerance, C., \textit{A tale of two sieves}, The Notices of the Amer. Math. Soc., \textbf{43}(1996), 1473--1485.
  • Rabin, M., \textit{Digitalized signatures and public-key functions as intractable as factorization}, MIT Laboratory for Computer Science, January 1979.
  • Rivest, R., Shamir, A., Adleman, L., {\em A method for obtaining digital signatures and public-key cryptosystems}, Communications of the ACM 21, \textbf{2}(1978), 120--126.
  • Shor, P.W., {\em Algorithms for quantum computation: discrete logarithms and factoring}, Proceedings 35th Annual Symposium on Foundations of Computer Science. IEEE Comput. Soc., 1994.
  • Silverman, R.D., Wagstaff JR., S.S., {\em A practical analysis of the elliptic curve factoring algorithm}, Mathematics of Computation, \textbf{61}(1993), 445--462.
  • Strubell, E., An Introduction to Quantum Algorithms, COS498, Chawathe, 2011.
  • Valle, C., Shor's Algorithm and Grover's Algorithm in Quantum Computing, Master's thesis, University of Kansas, 2011.
  • Vandersypen, L.M., Steffen, M., Breyta, G., Yannoni, C.S., Sherwood, M.H. , Chuang, I.L., {\em Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance}, Nature, \textbf{414}(2001), 883--887.
  • Xu, N., Zhu, J., Lu, D., Zhou, X., Peng, X., Du, J., {\em Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system}, Physical Review Letters, 108 \textbf{13}(2012).

Fundamental Structure of Shor's Quantum Algorithm for Factoring Integers

Yıl 2019, Cilt: 11 Sayı: 2, 78 - 83, 31.12.2019

Öz

One of the most well known mathematically hard problems in number theory is the integer factorization problem, roughly stated that decomposition of a composite number into its prime factors. In modern cryptography, RSA encryption algorithm whose security is based on integer factorization problem is highly practical, widespread and up to date no classical algorithm having polynomial running time for the factorization of large numbers is known. In 1994, Peter Shor proposed an efficient algorithm on quantum computer. In this paper, we  mention about the fundamentals of  Shor's quantum algorithm illustrating a concrete example.

Kaynakça

  • Bach, E., {\em Toward a theory of Pollard's rho method}, Information and Computation, \textbf{90}(1991), 139--155.
  • Dash, A., Sarmah, D., Behera, B.K., Panigrahi, P.K., \textit{Exact search algorithm to factorize large biprimes and a triprime on IBM quantum computer}, 2018.
  • Dattani, N.S., Bryans, N., {\em Quantum factorization of 56153 with only 4 qubits}. arXiv:1411.6758 [quant-ph], 2014.
  • Diffie, W., Hellman, M., {\em New Directions in Cryptography}, IEEE Transactions on Information Theory, \textbf{22(6)}(1976), 644--654.
  • Gerver, J., {\em Factoring large numbers with a quadratic sieve}, Mathematics of Computation, \textbf{41}(1983), 287--294.
  • Jiang, S., Britt, K.A., McCaskey, A.J., Humble, T.S., Kais, S, {\em Quantum annealing for prime factorization}, Scientific Reports, \textbf{8}(2018).
  • Kute S., Desai C.G., \textit{Quantum Cryptography: A Review}, Indian Jour. of Scien. and Techn., \textbf{10(3)}(2017).
  • Li, Z., Dattani, N.S., Chen, X., Liu, X., Wang, H., Tanburn, R., Chen, H., Peng, X., Du, J., {\em High-fidelity adiabatic quantum computation using the intrinsic Hamiltonian of a spin system: Application to the experimental factorization of 291311}, (2017).
  • Martin-Lopez, E., Laing, A., Lawson, T., Alvarez, R., Zhou, X., O'Brien, J.L., {\em Experimental realization of Shor's quantum factoring algorithm using qubit recycling}, Nature Photonics, 6 \textbf{11}(2012), 773--776.
  • Pal, S., Moitra, S., Anjusha, V.S., Kumar, A., Mahesh, T.S., {\em Hybrid scheme for factorization: Factoring 551 using a 3-qubit NMR quantum adiabatic processor}, (2016).
  • Pollard, J.M., {\em Theorems on factorization and primality testing}, Proceedings of the Cambridge Philosophical Society, \textbf{76}(1974), 521--528.
  • Pomerance, C., \textit{A tale of two sieves}, The Notices of the Amer. Math. Soc., \textbf{43}(1996), 1473--1485.
  • Rabin, M., \textit{Digitalized signatures and public-key functions as intractable as factorization}, MIT Laboratory for Computer Science, January 1979.
  • Rivest, R., Shamir, A., Adleman, L., {\em A method for obtaining digital signatures and public-key cryptosystems}, Communications of the ACM 21, \textbf{2}(1978), 120--126.
  • Shor, P.W., {\em Algorithms for quantum computation: discrete logarithms and factoring}, Proceedings 35th Annual Symposium on Foundations of Computer Science. IEEE Comput. Soc., 1994.
  • Silverman, R.D., Wagstaff JR., S.S., {\em A practical analysis of the elliptic curve factoring algorithm}, Mathematics of Computation, \textbf{61}(1993), 445--462.
  • Strubell, E., An Introduction to Quantum Algorithms, COS498, Chawathe, 2011.
  • Valle, C., Shor's Algorithm and Grover's Algorithm in Quantum Computing, Master's thesis, University of Kansas, 2011.
  • Vandersypen, L.M., Steffen, M., Breyta, G., Yannoni, C.S., Sherwood, M.H. , Chuang, I.L., {\em Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance}, Nature, \textbf{414}(2001), 883--887.
  • Xu, N., Zhu, J., Lu, D., Zhou, X., Peng, X., Du, J., {\em Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system}, Physical Review Letters, 108 \textbf{13}(2012).
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Turgut Hanoymak 0000-0002-3822-2202

Akram Chehrazi Bu kişi benim 0000-0002-1711-7534

Yayımlanma Tarihi 31 Aralık 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 11 Sayı: 2

Kaynak Göster

APA Hanoymak, T., & Chehrazi, A. (2019). Fundamental Structure of Shor’s Quantum Algorithm for Factoring Integers. Turkish Journal of Mathematics and Computer Science, 11(2), 78-83.
AMA Hanoymak T, Chehrazi A. Fundamental Structure of Shor’s Quantum Algorithm for Factoring Integers. TJMCS. Aralık 2019;11(2):78-83.
Chicago Hanoymak, Turgut, ve Akram Chehrazi. “Fundamental Structure of Shor’s Quantum Algorithm for Factoring Integers”. Turkish Journal of Mathematics and Computer Science 11, sy. 2 (Aralık 2019): 78-83.
EndNote Hanoymak T, Chehrazi A (01 Aralık 2019) Fundamental Structure of Shor’s Quantum Algorithm for Factoring Integers. Turkish Journal of Mathematics and Computer Science 11 2 78–83.
IEEE T. Hanoymak ve A. Chehrazi, “Fundamental Structure of Shor’s Quantum Algorithm for Factoring Integers”, TJMCS, c. 11, sy. 2, ss. 78–83, 2019.
ISNAD Hanoymak, Turgut - Chehrazi, Akram. “Fundamental Structure of Shor’s Quantum Algorithm for Factoring Integers”. Turkish Journal of Mathematics and Computer Science 11/2 (Aralık 2019), 78-83.
JAMA Hanoymak T, Chehrazi A. Fundamental Structure of Shor’s Quantum Algorithm for Factoring Integers. TJMCS. 2019;11:78–83.
MLA Hanoymak, Turgut ve Akram Chehrazi. “Fundamental Structure of Shor’s Quantum Algorithm for Factoring Integers”. Turkish Journal of Mathematics and Computer Science, c. 11, sy. 2, 2019, ss. 78-83.
Vancouver Hanoymak T, Chehrazi A. Fundamental Structure of Shor’s Quantum Algorithm for Factoring Integers. TJMCS. 2019;11(2):78-83.