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Parallel processing method and device for scalar multiplication on elliptic curve with characteristic of 2

An elliptic curve, parallel processing technology, applied in the field of information security, can solve the problem that the half-point algorithm cannot use projective coordinates and so on

Pending Publication Date: 2020-11-06
INST OF INFORMATION ENG CAS
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  • Application Information

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Problems solved by technology

[0007] Aiming at the problem that the half-point algorithm cannot use projective coordinates in the parallel algorithm proposed by Negre and Robert, the purpose of the present invention is to provide a parallel processing method and device for scalar multiplication on an elliptic curve characterized by 2

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  • Parallel processing method and device for scalar multiplication on elliptic curve with characteristic of 2
  • Parallel processing method and device for scalar multiplication on elliptic curve with characteristic of 2

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Embodiment Construction

[0059] 1. The underlying computing program and system basic parameters

[0060] Before implementing the scalar multiplication operation, it is necessary to implement addition, multiplication, squaring, inversion, square root, root operation of the quadratic equation, etc. on the characteristic 2 finite field according to the parameters of the elliptic curve. When realizing the above operation, the properties of the finite field of characteristic 2 and the modulo operation are needed. The multiplication, squaring, square root, finding the root of a quadratic equation and the inverse operation described in this patent are respectively modular multiplication, modular square, modular square root, and the root of a modular quadratic equation and the modular inverse operation. This requires the choice of irreducible polynomials in finite fields to be good enough to improve computational efficiency.

[0061] In standard FIPS 186-4, NIST recommends 10 elliptic curves over finite fiel...

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Abstract

The invention discloses a parallel processing method and device for scalar multiplication on an elliptic curve with the characteristic of 2. The method comprises the following steps: 1) an elliptic curve parameter used by cryptography and a scalar k are input into a preprocessing module; 2) the preprocessing module amplifies the scalar k by t times and transmits the scalar k to the splitting module; 3) the splitting module splits the amplified scalar k, and sends the obtained expanded part taking 2 as the substrate to a multiple point-adding module, sends the obtained expanded part taking 1 / 2as the substrate to a half point-adding module, carries out parallel calculation, sends a calculation result to a merging and adding module, carries out point-adding, and outputs the result, thereby completing scalar multiplication on an elliptic curve with the characteristic of 2 in cryptology. According to the invention, the efficiency of the algorithm is improved, the performance of the processor is more fully utilized, and simple side channel attacks can be resisted.

Description

technical field [0001] The invention relates to a new method for calculating scalar multiplication of elliptic curves on feature 2. The method adopts the idea of ​​parallel computing, and provides specific processing methods and computing units. It has important applications in elliptic curve cryptography and belongs to information field of security technology. Background technique [0002] Cryptography is both an art and a science, and it has a long history. With the emergence of computers and the advent of the information age, modern cryptography has undergone many changes and great progress compared with classical cryptography. The encryption methods of modern cryptography are mainly divided into two categories: symmetric encryption and public key encryption. Among the widely used and popular public key encryption schemes in modern times, the elliptic curve encryption scheme undoubtedly plays a pivotal role. [0003] In 1985, Koblitz and Miller independently proposed t...

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Application Information

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IPC IPC(8): G06F9/38G06F9/30G06F9/50G06F17/10H04L9/30H04L9/32
CPCG06F9/38G06F9/30112G06F9/5027G06F17/10H04L9/3066H04L9/3247
Inventor 李兴然于伟
Owner INST OF INFORMATION ENG CAS
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