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An Optimal Signed Binary Fast Computation Method and Elliptic Curve Scalar Multiplication

A fast calculation, elliptic curve technology, applied in the direction of calculation, instrument, electrical and digital data processing, etc., can solve the problems of low time consumption and high speed, and achieve the effect of low operation cost and speed up operation.

Active Publication Date: 2022-08-02
YUNNAN UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0014] The purpose of the present invention is to: aim at the above existing problems, provide an optimal signed binary fast calculation method and elliptic curve scalar multiplication, through the optimal signed binary fast calculation method, select the signed binary expression with the least amount of calculation The formula solves the optimization problem of large integer binary, and at the same time, in the algebraic system of the group, especially in the elliptic curve scalar multiplication on the additive group, within O(n) time complexity and O(1) space complexity, Find the optimal and fastest calculated signed binary expression, so that the operation of signed binary elliptic curve scalar multiplication takes the least time and is the fastest

Method used

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  • An Optimal Signed Binary Fast Computation Method and Elliptic Curve Scalar Multiplication
  • An Optimal Signed Binary Fast Computation Method and Elliptic Curve Scalar Multiplication
  • An Optimal Signed Binary Fast Computation Method and Elliptic Curve Scalar Multiplication

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Embodiment 1

[0050] A kind of optimal signed binary fast calculation method of the present invention comprises the following steps:

[0051] S1: Represent the value S as binary (s n ,s n-1 ,...,s 0 ) 2 , Use r=(s, cost(s, i)) to record the calculation cost value of s scanning from 0 to the i-th bit, and use the set R to store the r record, and the set T is initialized to be empty for temporary storage;

[0052] S2: Initialize R={r=(s, cost(s, -1))};

[0053] S3: start from 0, scan every s i , until i is equal to n and ends; (at most one carry is generated)

[0054] S31: Take out each record r from the set R until all the elements in the set R are taken out;

[0055] S311: Put each retrieved record r into T;

[0056] S312: Check whether s[i] in the r record is equal to 1, if it is not equal to 1, return to S31; if it is equal to 1, perform convert() transformation at the current bit, that is, add 1 to form a carry, and add -1 to restore the value come back, and add the transformed...

Embodiment 2

[0068] In this embodiment, an optimal signed binary fast calculation method on a group is disclosed: in mathematics, a group represents an algebraic structure with binary operations satisfying closure, associativity, identity elements, and inverse elements . An element in the group is called a scalar, and multiple group operations are performed on this scalar. For example, in this example, P is an element in the set, and "+" is the only binary operation defined by this set. At this time, if you do P+P+...+P (adding S pieces of P), it can be written as SP, and then SP can be calculated using algorithms 1.1 and 1.2. The present invention can convert S into original binary value; use the optimal signed binary fast calculation method in the first embodiment to find the optimal signed binary expression, and bring the optimal signed binary expression into algorithms 1.3 and 1.4 The operation yields the result of SP.

Embodiment 3

[0070] In this embodiment, an elliptic curve scalar multiplication based on an optimal signed binary fast calculation method is disclosed, including the following steps:

[0071] Step 1: Calculate the operation cost of point addition operation ECADD, point double operation ECDBL and point inverse operation ECINV on the elliptic curve respectively;

[0072] Step 2: According to the operation cost value, the optimal signed binary fast calculation method in the first embodiment is used to obtain the optimal signed binary expression S'=(s' of the scalar factor S. n ,s′ n-1 ,...,s′ 0 ) BSD ,

[0073] Step 3: Obtain the operation result by calculating the scalar multiplication Q=S'P on the elliptic curve.

[0074] In step 1, according to the current system, the operation cost of the three basic operation points plus operation ECADD, double point operation ECDBL and point inverse operation ECINV is measured, and the specific values ​​are measured experimentally.

[0075] Bef...

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Abstract

The invention discloses an optimal signed binary fast calculation method, a group optimization algorithm based on the calculation method and an elliptic curve scalar multiplication optimization algorithm on an addition group; the optimal signed binary fast calculation method can solve the signed binary The optimization problem of the algorithm, including the optimization algorithm on the group, in which the optimization algorithm of the elliptic curve scalar multiplication on the additive group is based on the three basic operation points on the elliptic curve of the target system. The operation of adding ECADD, multiplying point ECDBL and point inverse ECINV cost, optimized for a scalar factor S, from all (3 / 2) of S n Among the signed binary expressions, under O(n) time complexity and O(1) space complexity, the signed binary expression with the least amount of computation is output, and the operation is obtained by calculating the scalar multiplication on the elliptic curve. result.

Description

technical field [0001] The invention relates to the field of group algorithms, in particular to the addition group, in particular to an optimal signed binary fast calculation method and elliptic curve scalar multiplication. Background technique [0002] In many algorithms, large integer scalar multiplication is often encountered, and direct calculation is time-consuming. Generally, it is converted into original binary and calculated by binary algorithm, but the converted original binary is still relatively large and needs to be optimized. This problem also exists in operations on additive groups, especially scalar multiplication as additive groups. [0003] Scalar multiplication is a classic problem in the field of computing, especially in the field of elliptic curve cryptography. When calculating the scalar multiplication on the elliptic curve (Scalar Multiplication) Q=SP, P(x 1 ,y 1 ) and Q(x 2 ,y 2 ) are two points on an elliptic curve where x 1 ,y 1 , x 2 ,y 2 an...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F7/483
CPCG06F7/483
Inventor 杨维忠
Owner YUNNAN UNIV
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