Formalized verification method of finite field GF(2 ^ n) based on Coq

A formal verification, finite field technology, applied in the formal verification supporting encryption algorithm and modular multiplication operation, the security software reliability verification field based on the theorem prover Coq, can solve the problem of mathematical derivation and mathematical algorithm reliability verification and other problems to avoid mistakes

Inactive Publication Date: 2020-02-14
NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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Problems solved by technology

Although the model-based method improves software productivity and reduces software defects, it cannot solve the problem of mathematical derivation and reliability verification of mathematical algorithms

Method used

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  • Formalized verification method of finite field GF(2 ^ n) based on Coq
  • Formalized verification method of finite field GF(2 ^ n) based on Coq
  • Formalized verification method of finite field GF(2 ^ n) based on Coq

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Embodiment example

[0098] The invention can be used to generate finite-field multiplicative masks against side-channel attacks.

[0099] According to the paper "On Masked Galois-Field Multiplication for Authenticated Encryption Resistant to Side Channel Analysis" published by Hirokazu Oshida et al., finite field multiplication can be used to generate masks against side channel attacks, and the present invention provides a formal definition that can Method for multiplication over finite fields GF (2^n) of arbitrary length and size.

[0100] The invention can be used to verify the column confusion part in the AES algorithm. In the column confusion process of the AES algorithm, the operation on the finite field GF (2^8) is used to realize the confusion operation. The addition and multiplication operations defined in the invention Can be used for column obfuscation operation, set to (a 0 a 1 a 2 a 3 ) performs a column obfuscation operation, and the result is (b 0 b 1 b 2 b 3 ),

[0101...

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Abstract

The invention discloses a finite field GF (2 ^ n) element based on a theorem prover Coq, a formal description method of operation on the finite field GF (2^n) element, and a method for carrying out formal verification on defined operation key properties. According to the invention, the strictness and reliability of the theorem prover Coq are utilized to solve the disadvantage that the previous method cannot ensure the availability of a specific operation result or a corresponding operation rule. The method mainly comprises the following steps: (1) formally defining any finite field GF(2^n) element and an operation on the GF(2^n) element in Coq, wherein the method comprises operations of addition, multiplication and multiplication inverse element solving; (2) defining an equivalence relation for judging the element equivalence of the finite field GF(2^n); (3) completing formal verification of additive properties suitable for any finite field GF(2^n) in Coq; and (4) performing formalizedverification of related properties suitable for multiplication of any finite field GF(2^n) in Coq.

Description

technical field [0001] The invention discloses a formalized verification method of a Coq-based finite field GF(2^n), which is mainly used to support the formalized verification of encryption algorithms and modular multiplication operations. The invention belongs to the field of formal verification, and is a safety software reliability verification method based on a theorem prover Coq. Background technique [0002] The scale of modern embedded software is getting larger and larger, and traditional software testing techniques are difficult to guarantee the correctness of system functions. On the other hand, the loopholes of the system provide opportunities for hackers to intrude, seriously affecting the security of the system. This situation makes the information industry rethink traditional software development methods, so various formal methods and model-based methods are introduced into the software development process. A typical example is the formal verification of block...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F11/36G06F7/72
CPCG06F7/724G06F11/3608
Inventor 陈钢范永乾崔敏
Owner NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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