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Elliptic curve choosing method for bilinear pairing in security cryptography

A technology of elliptic curve and cryptographic technology, which is applied in the field of elliptic curves that select bilinear pairings in secure cryptographic technology, and can solve problems such as difficult selection of optimized elliptic curves

Inactive Publication Date: 2017-08-04
SHENZHEN OLYM INFORMATION SECURITY TECHOLOGY CO LTD
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Problems solved by technology

[0007] The present invention provides an elliptic curve method for selecting bilinear pairings in the security cryptography technology to solve the problem that the elliptic curve method for selecting bilinear pairings in the existing security cryptography technology is difficult to select an optimized ellipse while achieving the required security level. Curve technical issues

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Embodiment Construction

[0070] An elliptic curve method for selecting bilinear pairings in a secure cryptographic technique, based on the following three basic principles, 1) using the method defined in the prime field F p Curve E / F on p ; 2) Parameter selection makes the Miller cycle as short as possible in the bilinear pairing calculation process; 3) Parameter selection makes the power multiplication calculation amount in the bilinear pairing calculation process as small as possible, and the elliptic curve is selected in two cases :

[0071] 1. Select the elliptic curve according to the curve type and RSA-like security level, specifically:

[0072] 1. For the curve type is super singular elliptic curve, RSA-1536-like security level, then output:

[0073] base domain F p The p is a 768-bit prime number

[0074] p=0xC18000000300000000000000000000000000000000000031800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000D34340000346800000000000000000000000000000...

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Abstract

This invention relates to an elliptic curve choosing method for a bilinear pairing in security cryptography. According to the curve types and the RSA-class security levels, elliptic curves are chosen. The method realizes rapid calculation of the bilinear pairing, and then efficiently realizes a cryptosystem based on the bilinear pairing. The technical problem that the optimized elliptic curve is difficult to choose while the existing elliptic curve choosing method for a bilinear pairing in security cryptography reaches the required security level is solved.

Description

technical field [0001] The invention relates to an elliptic curve method for selecting bilinear pairings in safe encryption technology. Background technique [0002] As a key operation in identity cryptography, bilinear pairing has aroused extensive interest of researchers in the past few years. A bilinear pairing is defined as follows: Let and are three cyclic groups, and The orders of all are prime numbers N, P 1 yes Generator of P 2 yes The generator of the bilinear pair e is The mapping satisfies the following conditions: [0003] a) Bilinearity: for any a, There is e([a]P,[b]Q)=e(P,Q) ab ; [0004] b) Non-degenerate: [0005] c) Computability: for any Efficient algorithms exist to compute e(P,Q). [0006] The existing bilinear pairings are defined on the elliptic curve point group, and the main applicable ones are: Weil pair, Tate pair, Ate pair, optimized Ate pair, R-ate pair, etc. The calculation of these bilinear pairings all need to ch...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H04L9/30
CPCH04L9/3066
Inventor 程朝辉周枭淳
Owner SHENZHEN OLYM INFORMATION SECURITY TECHOLOGY CO LTD
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