RSA public key decomposition and decryption method and system

Abstract

The invention discloses an RSA public key decomposition and decryption method and system, wherein the RSA public key decomposition method comprises the following steps: (1) acquiring an RSA public keyn; (2) acquiring a prime factor pair (p, q) less than or equal to n / 3, forming a corresponding two-dimensional Hermitian matrix according to the prime factor pair (p, q) and the public key n, meanwhile controlling an external electromagnetic field of a quantum system, so that the Hamiltonian of the quantum system is the two-dimensional Hermitian matrix, measuring an energy spectrum of the quantumsystem to check whether an eigenvalue of the two-dimensional Hermitian matrix is at x=0, if not, judging other prime factor pairs (p, q), and if yes, judging the prime factor pair (p, q) as two primefactor obtained by decomposing the RSA public key n, and performing output. According to the RSA public key decomposition and decryption method and system disclosed by the invention, the calculationtime is short, a small number of storage bits are required, the algorithm efficiency is high, and the stability is good.

Description

technical field

[0001] The invention relates to the field of information security, in particular to an RSA public key decomposition method and system, and a decryption method and system based on RSA public key decomposition. Background technique

[0002] The RSA public key encryption system is an important infrastructure for information security in the modern information society. The system was proposed by Ron Rivest, Adi Shamir and Leonard Adleman in 1978 [1]. It is an asymmetric key encryption system. As shown in Table 1, the basic principle is to randomly select two large prime numbers p, q, and calculate n=pq. Then choose a small odd number e that is coprime with (p-1)(q-1), and use (e, n) as the public key subject to release to the outside world. At the same time, the inverse element d of e is calculated in the (p-1)(q-1) multiplication group, and (d, n) is kept privately as the private key subject. The pair of keys can perform two-way encryption and decryption. Un...

Examples

Embodiment 1

[0060] This embodiment provides a method for decomposing an RSA public key, such as figure 1 shown, including the following steps:

[0061] (1) Get the RSA public key n;

[0062] (2) Obtain a prime factor pair less than or equal to n / 3, and form a corresponding two-dimensional Hermitian matrix according to the prime factor pair and the public key n, and control the external quantum system Electromagnetic field, make the Hamiltonian of the quantum system be the two-dimensional Hermitian matrix, and measure the energy spectrum of the quantum system to see whether the eigenvalue of the two-dimensional Hermitian matrix is ​​at x=0 (experimentally, there is a The maximum value of the resonance peak appears), if not, judge other prime factor pairs , if yes, then judge that the prime factor pair is obtained by decomposing the RSA public key n The two prime factors of are output. This step specifically includes:

[0063] (2.1) Set the initial value of the prime factor pair to ...

Embodiment 2

[0084] This embodiment discloses a kind of RSA public key decomposition system, comprising:

[0085] The public key acquisition module is used to obtain the RSA public key n;

[0086] The public key decomposition module is used to obtain a prime factor pair less than or equal to n / 3, and form a corresponding two-dimensional Hermitian matrix according to the prime factor pair and the public key n, while controlling The external electromagnetic field of the quantum system makes the Hamiltonian of the quantum system be the two-dimensional Hermitian matrix, and measure the energy spectrum of the quantum system to see whether the eigenvalue of the two-dimensional Hermitian matrix is ​​at x=0, if not, then the Other prime factor pairs are judged, and if they are, then the prime factor pair is judged to be two prime factors obtained by decomposing the RSA public key n, and output.

[0087] Wherein, the public key decomposition module specifically includes:

[0088] The initial va...

Embodiment 3

[0098] This embodiment provides a kind of RSA decryption method, comprising:

[0099] (1) adopt the RSA public key decomposition method of embodiment 1 to decompose the RSA public key n, obtain two prime factors p, q;

[0100] (2) Calculate the private key d according to the prime factors p and q in the following way:

[0101] d=e -1 (mod(p-1)(q-1))

[0102] In the formula, e is an odd number that is relatively prime to (p-1)(q-1);

[0103] (3) Obtain the ciphertext data C to be decrypted, and use the following formula to decrypt the ciphertext data C into plaintext data M:

[0104] M=C d modn.

technical field

[0001] The invention relates to the field of information security, in particular to an RSA public key decomposition method and system, and a decryption method and system based on RSA public key decomposition. Background technique

[0002] The RSA public key encryption system is an important infrastructure for information security in the modern information society. The system was proposed by Ron Rivest, Adi Shamir and Leonard Adleman in 1978 [1]. It is an asymmetric key encryption system. As shown in Table 1, the basic principle is to randomly select two large prime numbers p, q, and calculate n=pq. Then choose a small odd number e that is coprime with (p-1)(q-1), and use (e, n) as the public key subject to release to the outside world. At the same time, the inverse element d of e is calculated in the (p-1)(q-1) multiplication group, and (d, n) is kept privately as the private key subject. The pair of keys can perform two-way encryption and decryption. Un...

Examples

Embodiment 1

[0060] This embodiment provides a method for decomposing an RSA public key, such as figure 1 shown, including the following steps:

[0061] (1) Get the RSA public key n;

[0062] (2) Obtain a prime factor pair less than or equal to n / 3, and form a corresponding two-dimensional Hermitian matrix according to the prime factor pair and the public key n, and control the external quantum system Electromagnetic field, make the Hamiltonian of the quantum system be the two-dimensional Hermitian matrix, and measure the energy spectrum of the quantum system to see whether the eigenvalue of the two-dimensional Hermitian matrix is ​​at x=0 (experimentally, there is a The maximum value of the resonance peak appears), if not, judge other prime factor pairs , if yes, then judge that the prime factor pair is obtained by decomposing the RSA public key n The two prime factors of are output. This step specifically includes:

[0063] (2.1) Set the initial value of the prime factor pair to ...

Embodiment 2

[0084] This embodiment discloses a kind of RSA public key decomposition system, comprising:

[0085] The public key acquisition module is used to obtain the RSA public key n;

[0086] The public key decomposition module is used to obtain a prime factor pair less than or equal to n / 3, and form a corresponding two-dimensional Hermitian matrix according to the prime factor pair and the public key n, while controlling The external electromagnetic field of the quantum system makes the Hamiltonian of the quantum system be the two-dimensional Hermitian matrix, and measure the energy spectrum of the quantum system to see whether the eigenvalue of the two-dimensional Hermitian matrix is ​​at x=0, if not, then the Other prime factor pairs are judged, and if they are, then the prime factor pair is judged to be two prime factors obtained by decomposing the RSA public key n, and output.

[0087] Wherein, the public key decomposition module specifically includes:

[0088] The initial va...

Embodiment 3

[0098] This embodiment provides a kind of RSA decryption method, comprising:

[0099] (1) adopt the RSA public key decomposition method of embodiment 1 to decompose the RSA public key n, obtain two prime factors p, q;

[0100] (2) Calculate the private key d according to the prime factors p and q in the following way:

[0101] d=e -1 (mod(p-1)(q-1))

[0102] In the formula, e is an odd number that is relatively prime to (p-1)(q-1);

[0103] (3) Obtain the ciphertext data C to be decrypted, and use the following formula to decrypt the ciphertext data C into plaintext data M:

[0104] M=C d modn.

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