Secret key exchange or public key password encryption optimization method and system based on Meisson number

A key exchange and public key cryptography technology, which is applied in the field of key exchange based on Mersenne number or public key cryptography optimization, can solve problems such as unfavorable hardware implementation, complex circuits, complex algorithms, etc., to reduce time complexity and simplify Effect of circuit design and power consumption reduction

Pending Publication Date: 2022-04-29
SOUTH CHINA UNIV OF TECH
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0024] Although the software optimization algorithm similar to the Montgomery algorithm can increase the speed, the algorithm is more complicated and it is not conducive to hardware implementation (hardware acceleration)
Even if it is realized by hardware, it is inevitable that the circuit is complicated and the cost is high

Method used

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  • Secret key exchange or public key password encryption optimization method and system based on Meisson number
  • Secret key exchange or public key password encryption optimization method and system based on Meisson number
  • Secret key exchange or public key password encryption optimization method and system based on Meisson number

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0115] A kind of key exchange or public key cryptography optimization method based on Mersenne number, this method comprises the combination of following implementation modes:

[0116] In key exchange or public key cryptography-related calculations, the Elgamal algorithm is selected in this embodiment, and the DHM algorithm may also be selected.

[0117] In the adopted Elgamal algorithm, choose a Mersenne prime M=2 n -1 is used as the modulus of modulo operation mod, wherein n is a positive integer and can make M a prime number, such as n=1279;

[0118] In the process of corresponding modular addition, modular multiplication, and modular exponentiation, the original modulus operation mod is replaced with a specific first modulo operation mod1 without division, wherein the expression of the first modulo operation mod1 is as follows:

[0119] Modular addition: Y=A+B mod1 M=A+B mod(2 n -1),

[0120] Modular multiplication: Y=A*B mod1 M=A*B mod(2 n -1),

[0121] Modular power...

Embodiment 2

[0133] A system for implementing a Mersenne number-based key exchange or public key encryption optimization method includes one or more fast modulo operation logic circuit components C1, which can support the first modulo operation mod1;

[0134] Logic circuit assembly C1 includes the following devices (as attached image 3 shown):

[0135] n-bit register RegA (301), used for temporarily storing the input number A;

[0136] n-bit register RegB (302), used for temporarily storing the input number B;

[0137] n-bit adder ADD1 (303), used for adding two numbers, outputting an n-bit integer and a carry flag C;

[0138] n-bit multiplier MUL (304), used for multiplying two numbers and outputting 2n-bit integers;

[0139] 2n-bit register RegY0 (305), used for temporary storage of intermediate data;

[0140] N-bit adder ADD2 (306), is used for finishing fast modulus calculation, outputs n-bit integer and carry sign C;

[0141] Logic gate circuit, including n AND gates (308), 1 NO...

Embodiment 3

[0144] A method for optimizing key exchange or public key cryptography based on Mersenne numbers, comprising a combination of the following implementations:

[0145] In the key exchange or public key cryptographic calculation, this embodiment chooses to use the RSA algorithm;

[0146] In the adopted RSA algorithm, the product K of two prime numbers is constructed, and exactly K=2 n -L is used as the modulus of the modulus operation mod, where n is a positive integer, L is a small positive integer, L6 = 64;

[0147] In the process of corresponding modular addition, modular multiplication, and modular exponentiation, the original modulo operation mod is replaced with a specific fast modulo operation without division, the second modulo operation mod2, wherein the second modulo operation mod2 operation The expression is as follows:

[0148] Modular addition: Y=A+B mod2 K=A+B mod(2 n -L),

[0149] Modular multiplication: Y=A*B mod2 K=A*B mod(2 n -L),

[0150] Modular power: Y...

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Abstract

The invention discloses a key exchange or public key cryptography encryption optimization method and system based on Meisson number, and the method comprises the following steps: in an application scene of key exchange or public key cryptography calculation, selecting or constructing a modulus of modulo operation mod, and replacing the modulo operation mod with first modulo operation or second modulo operation according to the modulus; when the selected modulus is a Meisson number, or the modulus in the constructed algorithm is just the Meisson number, replacing the modulo operation mod with the first modulo operation; and when the selected or constructed modulus is a positive integer of which the form is similar to the Meisson number, replacing the modulo operation mod with a second modulo operation. According to the method, modular addition, modular multiplication and modular exponentiation operations can be optimized by utilizing the mathematical characteristics of the Meisson number, the calculation complexity is remarkably reduced, and the speed of key exchange and the speed of public key password encryption and decryption are increased.

Description

technical field [0001] The present invention relates to the technical field of information security encryption authentication, in particular to a method and system for key exchange or public key encryption optimization based on Mersenne numbers. Background technique [0002] In today's world with the rapid development of information technology, information security protection plays a pivotal role. In e-commerce, APP applications involving personal information, etc., it is often necessary to use encryption and authentication security protection methods, such as key exchange, public key encryption and decryption, etc. Examples are as follows: [0003] 1. Key exchange [0004] An example of a key exchange algorithm is the DHM (Diffie-Hellman-Merkle) algorithm (formerly known as the DH algorithm). This algorithm is based on the discrete logarithm problem and is a classic algorithm for creating public key cryptosystems. DHM key exchange does not require a complete public key ...

Claims

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Application Information

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IPC IPC(8): G06F21/60G06F7/575G06F7/501G06F7/523G06F7/72
CPCG06F21/602G06F7/722G06F7/723G06F7/72G06F7/501G06F7/523G06F7/575
Inventor 覃健诚钟宇陆以勤程喆
Owner SOUTH CHINA UNIV OF TECH
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