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A Shor Quantum Attack Method Against Public Key Cryptography ECC

A public-key cryptography and quantum technology, applied in the field of quantum cryptography, can solve the problems of small Qubit quantum computing attacks, which have not been solved well, and achieve the effect of strong versatility

Inactive Publication Date: 2018-07-13
SHANGHAI UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0006] However, under the limitation of the device conditions of the universal quantum computer, the problem of small Qubit quantum computing attack on the public key cryptography ECC has not been well solved.

Method used

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  • A Shor Quantum Attack Method Against Public Key Cryptography ECC
  • A Shor Quantum Attack Method Against Public Key Cryptography ECC
  • A Shor Quantum Attack Method Against Public Key Cryptography ECC

Examples

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Embodiment 1

[0036] Such as figure 1 As shown, a Shor quantum attack method against public key cryptography ECC includes the following steps:

[0037] Step 1: Select an elliptic curve on a prime field p on a binary field, and output all coordinate points (x t ,y t ), 1≤t≤N; N is the number of coordinate points on the elliptic curve; the number of executions is set to 0;

[0038] Step 2: Select point P and point Q on the elliptic curve arbitrarily, satisfy P=kQ, k is the attack private key, and the output is the same as each point on the elliptic curve (x t ,y t ) corresponding to x t P+y t Q and x t point of P;

[0039] Step 3: Construct a periodic function whose period is k:

[0040] f(a)=x a mod p (1)

[0041] Among them, x is a number smaller than p and coprime with p, and a is any natural number;

[0042] Step 4: Create two quantum registers: set the initial state of the first quantum register to means n(n=log 2 The direct product of p+1) qubits; the initial state of t...

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Abstract

The invention discloses a Shor quantum attack method for a public key password ECC, and the method comprises the following steps: selecting an elliptical curve on prime field of one binary domain, and outputting all coordinates on the elliptical curve; randomly selecting a point P and a point Q on the elliptical curve, wherein the P and Q meet a condition: P=kQ, and k is an attack private key; outputting (xP+yQ) points and xP points corresponding to all points (x, y) on the elliptical curve; constructing periodic function with a period k, building two quantum registers, and setting an initial state as a state shown in the description; enabling an Hadamard gate (shown in the description) to act on the first quantum register shown in the description; enabling a U<x, x> operator to be used for the second quantum register shown in the description; carrying out the Fourier inverse transformation if the first quantum register; measuring the eigenstate probability of the first quantum register, and obtaining an order r enabling the eigenstate probability to each the maximum value; and determining the attach private key to be r if r meets the formula: Q=rP. The method can decode the elliptical curve through a small quantum bit number, brings great threat to a current safety curve, and is higher in universality.

Description

technical field [0001] The invention relates to a Shor quantum attack method, in particular to a Shor quantum attack method for public key cryptography ECC, belonging to the technical field of quantum cryptography. Background technique [0002] The representative public key cryptography algorithms are RSA and ECC algorithms, which are widely used in the fields of e-government and e-commerce in my country. Its security basis is the NP-hard problem of large integer factorization (IFP) and elliptic curve discrete logarithm (ECDLP), respectively. In 1994, Shor of AT&T Corporation of the United States proposed a quantum algorithm that can decompose the prime factors of large integers in polynomial time, which is called the Shor algorithm. In 1997, Shor further pointed out that the Shor algorithm can be used to solve the two prime factor problems and discrete logarithm problems of large numbers N. In 2015, the U.S. Department of Defense mentioned in its "2013-2017 Five-Year Plan...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H04L9/30
Inventor 陈宇航尹宝胡风张焕国王潮
Owner SHANGHAI UNIV