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A circuit to realize the tate pair algorithm based on Montgomery modular multiplication

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: 2018-02-16
TSINGHUA UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

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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  • A circuit to realize the tate pair algorithm based on Montgomery modular multiplication
  • A circuit to realize the tate pair algorithm based on Montgomery modular multiplication
  • A circuit to realize the tate pair algorithm based on Montgomery modular multiplication

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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]

[0047]

[0048] Consider GF(3 6m ) on the multiplication c=ab, where a i ,b j ∈GF(3m ), 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]

[0050] Then GF(3 6m )superior and The multiplication ...

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Abstract

The invention belongs to the technical field of cryptographic algorithm implementation of embedded systems, and in particular relates to a Tate pair algorithm based on ternary finite field Montgomery modular multiplication and a hardware structure for realizing the algorithm, comprising: combining two input points on an elliptic curve The X and Y coordinates of P and R are respectively transformed from the defined GF(3m) domain to the Montgomery domain; according to the MDL algorithm flow that uses the multiplication, addition / subtraction and cubic operations on GF(3m) as the basic operations, in Montgomery Perform operations separately on the field; then convert the calculation result from the Montgomery field back to the GF(36m) field, and then calculate the 33m‑1 modular exponentiation of the result. The hardware structure includes: top-level processor, controller, ternary accumulator, ternary multiplier, register file, SRAM; the controller controls the input of the ternary accumulator and ternary multiplier and the input of SRAM and register file. Read and write operations, thereby controlling the data transmission of the entire 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 circuit for realizing Tate pair algorithm based on ternary finite field Montgomery (Montgomery) modular multiplication. 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 Then for all P, Q∈G 1 And all a, b∈Z, a≠0, b≠0 satisfy [0003] [0004] Bilinear pairing is widely used in a variety of public key cryptography schemes, such as IBE (Identity Based Encryption, identity-based encryption) encryption, the public key used in the encryption process is not from the PKI (Public KeyInfrastructure, public key infrastructure ) from the certificate issued by th...

Claims

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Application Information

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