By Song Y. Yan

ISBN-10: 144197721X

ISBN-13: 9781441977212

ISBN-10: 1441977228

ISBN-13: 9781441977229

На английском:

The cryptosystems in accordance with the Integer Factorization challenge (IFP), the Discrete Logarithm challenge (DLP) and the Elliptic Curve Discrete Logarithm challenge (ECDLP) are primarily the single 3 varieties of functional public-key cryptosystems in use. the protection of those cryptosystems is predicated seriously on those 3 infeasible difficulties, as no polynomial-time algorithms exist for them up to now. besides the fact that, polynomial-time quantum algorithms for IFP, DLP and ECDLP do exist, only if a realistic quantum desktop exists.

Quantum assaults on Public-Key Cryptosystems presemts just about all identified quantum computing established assaults on public-key cryptosystems, with an emphasis on quantum algorithms for IFP, DLP, and ECDLP. It additionally discusses a few quantum resistant cryptosystems to interchange the IFP, DLP and ECDLP established cryptosystems.

This e-book is meant for use both as a graduate textual content in computing, communications and arithmetic, or as a easy reference within the box.

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На английском: The cryptosystems according to the Integer Factorization challenge (IFP), the Discrete Logarithm challenge (DLP) and the Elliptic Curve Discrete Logarithm challenge (ECDLP) are primarily the one 3 kinds of useful public-key cryptosystems in use. the protection of those cryptosystems is predicated seriously on those 3 infeasible difficulties, as no polynomial-time algorithms exist for them to date.

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**Extra resources for Quantum Attacks on Public-Key Cryptosystems**

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Williams, Explorations in Quantum Computation, 2nd edn. S. A. Mannucci, Quantum Computing for Computer Scientists (Cambridge University Press, Cambridge, 2008) [51] A. Yao, Classical physics and the Church Turing thesis. J. ACM 50(1), 100– 105 (2003) 2. Quantum Attacks on IFP-Based Cryptosystems If you don’t work on important problems, it’s not likely that you’ll do important work. Richard Hamming (1915–1998) The 1968 Turing Award Recipient In this chapter we shall ﬁrst study the integer factorization problem (IFP) and the classical solutions to IFP, then we shall discuss the IFP-based cryptography whose security relies on the infeasibility of the IFP problem, and ﬁnally, we shall introduce some quantum algorithms for attacking both IFP and IFP-based cryptography.

845 “ 5 ¨ 132 .. 5488 “ 24 ¨ 73 .. ´118, 11 .. 14045 “ 5 ¨ 532 .. 3072 “ 210 ¨ 3 .. 218, 59 .. 51005 “ 5 ¨ 1012 .. 17328 “ 24 ¨ 3 ¨ 192 .. Clearly, ´38 ` i and ´22 ` 19i can produce a product square, since p´38 ` iqp´22 ` 19iq “ p31 ´ 12iq2 , f p31 ´ 12iq “ 31 ´ 12m “ ´3449 Ñ x, “ p23 ¨ 3 ¨ 72 q2 “ 11762, 252 ¨ 5488 Ñ y “ 1176, gcdpx ˘ y, nq “ gcdp´3449 ˘ 1176, 84101q “ p2273, 37q. In fact, 84101 “ 2273 ˆ 37. Note that ´118 ` 11i and 218 ` 59i can also produce a product square, since 42 2.

1 p| 0y ´ i | 1yq. 2 Which pairs of expressions for quantum states represent the same state? 1 p´ | 0y ` i | 1yq. 1 e´iπ{4 | 0y ` | 1y . 2 2 6. 1 | `y ` eiγ | ´y . 2 ? ¯ ´ ? (b) 12 | 0y ´ 23 | 1y and eiγ 21 | 0y ´ 23 | 1y . 4 Quantum Computability and Complexity In this section, we shall give a brief introduction to some basic concepts of quantum computability and complexity within the theoretical framework of QTMs. The ﬁrst true QTM was proposed in 1985 by Deutsch [15]. A QTM is a quantum mechanical generalization of a PTM, in which each cell on the tape can hold a qubit (quantum bit) whose state is represented as an arrow contained in a sphere (see Fig.

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