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Montgomery modular multiplication based Tate pairing algorithm and hardware structure therefor

An algorithm and modular multiplication technology, applied in the field of cryptographic algorithm implementation, can solve the problem of negligible conversion operation overhead and achieve the effect of reducing hardware overhead and power consumption overhead

Active Publication Date: 2015-11-18
TSINGHUA UNIV
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

However, if a data conversion can correspond to n times of modular multiplication operations, when n is large, the overhead of conversion operations becomes negligible

Method used

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  • Montgomery modular multiplication based Tate pairing algorithm and hardware structure therefor
  • Montgomery modular multiplication based Tate pairing algorithm and hardware structure therefor
  • Montgomery modular multiplication based Tate pairing algorithm and hardware structure therefor

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Embodiment Construction

[0043] The embodiments will be described in detail below in conjunction with the accompanying drawings.

[0044] The arithmetic operations included in the calculation process of the MDL algorithm are GF(3 m Addition, subtraction, cube and multiplication on ), GF(3 6m ) on cube and multiplication. First the GF(3 6m ) on the multiplication, cubic operation with GF (3 m ) to achieve each operation. details as follows:

[0045] GF(3 6m ) can be seen as GF(3 3m ), the irreducible polynomial in between is g(z)=z 2 +1; while GF(3 2m ) can be seen as 2 times GF(3 m ), the irreducible polynomial is h + (y)=y 3 -y-1. The specific mapping is expressed as follows:

[0046] GF(3 6m )≌GF(3 3m )[z] / g(z)

[0047] GF(3 3m )≌GF(3 m )[y] / h + (y)

[0048] Consider GF(3 6m) on the multiplication c=ab, where a i ,b j ∈GF(3 m ), using the above equivalent mapping relationship, a∈GF(3 6m ) can be determined by GF(3 3m ) The two elements of ) are expressed as:

[0049] ...

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Abstract

The invention belongs to the technical field of realization of cryptographic algorithms of embedded systems and particularly relates to a ternary finite field Montgomery modular multiplication based Tate pairing algorithm and a hardware structure for realizing the algorithm. The algorithm comprises: converting X coordinates and Y coordinates of two input points P and R on an elliptic curve to a Montgomery domain from a defined GF(3m) domain; according to an MDL (minimum description length) algorithm procedure taking multiplication, addition / subtraction and cubic operation on GF(3m) as basic operations, performing operation in the Montgomery domain; and converting a calculation result to the GF(3m) domain from the Montgomery domain, and performing 33m-1-power modular exponentiation on the calculation result. The hardware structure comprises a top-level processor, a controller, a ternary accumulator, a ternary multiplier, a register file and an SRAM (static random access memory), wherein the controller is used for controlling input of the ternary accumulator and the ternary multiplier and read-write operation of the SRAM and the register file so as to control data transmission of the whole circuit.

Description

technical field [0001] The invention belongs to the technical field of cryptographic algorithm realization of embedded systems, and in particular relates to a Tate pair algorithm based on ternary finite field Montgomery (Montgomery) modular multiplication and a hardware structure for realizing the algorithm. Background technique [0002] A bilinear pairing is a map with special properties, denoted as Suppose G 1 is the additive group, G 2 are multiplicative groups, and their orders are all prime numbers. The bilinear pairing operation is the process of mapping two additive groups into a multiplicative group, namely G 1 ×G 1 →G 2 , then for all P, Q∈G 1 And all a, b∈Z, a≠0, b≠0 satisfy [0003] e ^ ( a P , b Q ) = e ^ ( P , ...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F7/523
Inventor 李翔宇马江莎
Owner TSINGHUA UNIV
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