CN108173643B - Efficient secret key consensus transmission method - Google Patents

Efficient secret key consensus transmission method Download PDF

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CN108173643B
CN108173643B CN201611018455.1A CN201611018455A CN108173643B CN 108173643 B CN108173643 B CN 108173643B CN 201611018455 A CN201611018455 A CN 201611018455A CN 108173643 B CN108173643 B CN 108173643B
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equal
dimensional column
dimensional
secret
computing
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CN108173643A (en
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赵运磊
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Fudan University
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Shanghai Humin Blockchain Technology Co ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0819—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s)
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0838—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H04L9/0863—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving passwords or one-time passwords

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Compression, Expansion, Code Conversion, And Decoders (AREA)

Abstract

The invention provides an efficient secret key consensus transmission method, which comprises the following steps: sender
Figure DSB0000172847630000011
Determining secret information in advancek1∈{0，1}。
Figure DSB0000172847630000012
With a secret input four-dimensional column vector
Figure DSB0000172847630000013
Receiving party
Figure DSB0000172847630000014
With a secret input four-dimensional column vector
Figure DSB0000172847630000015
Wherein
Figure DSB0000172847630000016
And
Figure DSB0000172847630000017
the value distances of the corresponding dimensions are close;
Figure DSB0000172847630000018
coding and decoding
Figure DSB0000172847630000019
Transmitting a four-dimensional coded message
Figure DSB00001728476300000110
Figure DSB00001728476300000111
By
Figure DSB00001728476300000112
And
Figure DSB00001728476300000113
decoding to obtain k2＝k1。

Description

Efficient secret key consensus transmission method
Technical Field
The invention relates to the technical field of passwords and coding, in particular to a high-efficiency secret key consensus transmission method.
Background
With the rapid development of quantum computers, the development of quantum attack resistant cryptography and encoding algorithms is becoming more and more urgent. Lattice-based, especially based on the LWE and RLWE problems, new cryptosystems are the mainstream technology for post-quantum cryptography. The core modules of LWE and RLWE based cryptosystems (especially public key encryption, key agreement, etc.) achieve secret consensus and transfer from closely spaced, but unequal values. The existing secret consensus and transmission scheme has the defects of poor efficiency, high error rate, poor practicability and the like, and the development of a novel secret consensus and transmission method has great industrial and application values and is a core technology leading and occupying the highest point of the international information security industry.
Given two four-dimensional column vectors
Figure GDA0002911893850000011
And
Figure GDA0002911893850000012
definition of
Figure GDA0002911893850000013
Figure GDA0002911893850000014
Namely the relative amount
Figure GDA0002911893850000015
Wherein "is the rounding operator, defining the first order norm of the vector
Figure GDA0002911893850000016
Definition of
Figure GDA0002911893850000017
Is a square matrix of four orders. Set ZqIt can be expressed in two ways:
Figure GDA0002911893850000018
or
Figure GDA0002911893850000019
Figure GDA00029118938500000110
Wherein
Figure GDA00029118938500000111
Is the round-down operator. For an arbitrary integer x ∈ Z, | x! Z is definedqMin { x mod q, q-x mod q }; for arbitrary four-dimensional column vectors
Figure GDA00029118938500000112
Figure GDA00029118938500000113
Definition of
Figure GDA00029118938500000114
Disclosure of Invention
In order to solve the problems, the invention provides an efficient secret key consensus transmission method, which achieves the upper bound of the efficiency achieved by the secret key consensus transmission method and is the first secret consensus and transmission method achieving the upper bound of the efficiency internationally. In order to reduce the rate of difference, four-dimensional information is used to achieve one-bit secret consensus and transmission; the inventive method can be used to build the most efficient public key encryption system based on RLWE so far. The method comprises the following steps:
system parameters: params ═ q, m, g, d, where q, m, g, d are positive integers, satisfying: m is more than or equal to 2, q is more than or equal to g>2，0≤d<q (1-1/g) -2; generally, q is a prime number; order to
Figure GDA0002911893850000021
Figure GDA0002911893850000022
And
Figure GDA0002911893850000023
is a four-dimensional column vector; the system parameters may be determined by user negotiation decisions within the system, or by a process using the inventive method, or given by a trusted third party.
Given two four-dimensional column vectors
Figure GDA0002911893850000024
And
Figure GDA0002911893850000025
definition of
Figure GDA0002911893850000026
Figure GDA0002911893850000027
Namely the relative amount
Figure GDA0002911893850000028
Wherein "is the rounding operator, defining the first order norm of the vector
Figure GDA0002911893850000029
Definition of
Figure GDA00029118938500000210
Order to
Figure GDA00029118938500000211
Figure GDA00029118938500000212
A fourth-order square matrix is formed; for an arbitrary integer x ∈ Z, | x! Z is definedqMin { x mod q, q-x mod q }; for arbitrary four-dimensional column vectors
Figure GDA00029118938500000213
Wherein
Figure GDA00029118938500000214
Or
Figure GDA00029118938500000215
Figure GDA00029118938500000216
Is a rounded down operator, define
Figure GDA00029118938500000217
Two users (which may be devices, programs, etc.) in the system, the initializer who runs the inventive method is noted as
Figure GDA00029118938500000218
The responder of the running method is recorded as
Figure GDA00029118938500000219
Figure GDA00029118938500000220
With a secret input four-dimensional column vector
Figure GDA00029118938500000221
Figure GDA00029118938500000222
And secret information k1∈{0,1}；
Figure GDA00029118938500000223
With a secret input four-dimensional column vector
Figure GDA00029118938500000224
Figure GDA00029118938500000225
Satisfy the requirement of
Figure GDA00029118938500000226
The inventive method will make
Figure GDA00029118938500000227
And
Figure GDA00029118938500000228
achieving the same key agreement k1＝k2E {0,1}, where k2Will be composed of
Figure GDA00029118938500000229
And (4) calculating. For this purpose,
Figure GDA00029118938500000230
to the direction of
Figure GDA00029118938500000231
Transmitting a four-dimensional vector information
Figure GDA00029118938500000232
Specifically, the method comprises the following steps:
the sender encoding method comprises the following steps:
Figure GDA0002911893850000031
is calculated according to the following steps
Figure GDA0002911893850000032
And will be
Figure GDA0002911893850000033
To be transmitted to
Figure GDA0002911893850000034
Figure GDA0002911893850000035
The method comprises the following steps:
Figure GDA0002911893850000036
computing
Figure GDA0002911893850000037
Figure GDA0002911893850000038
Figure GDA0002911893850000039
Step two:
Figure GDA00029118938500000310
calculating and checking: if it is not
Figure GDA00029118938500000311
Making b equal to 0, otherwise making b equal to 1; note the book
Figure GDA00029118938500000312
Figure GDA00029118938500000313
Step three:
Figure GDA00029118938500000314
computing
Figure GDA00029118938500000315
Figure GDA00029118938500000316
Step four:
Figure GDA00029118938500000317
will be provided with
Figure GDA00029118938500000318
To be transmitted to
Figure GDA00029118938500000319
Receiver decoding method: receive from
Figure GDA00029118938500000320
After that time, the user can use the device,
Figure GDA00029118938500000321
k is calculated as follows2：
Figure GDA00029118938500000322
The method comprises the following steps: computing
Figure GDA00029118938500000323
Figure GDA00029118938500000324
Step two: computing
Figure GDA00029118938500000325
Figure GDA00029118938500000326
Step three: calculating and checking: if t is<1, then let k2If not, let k be2＝1。
For simplicity of description, the inventive method only describes how to agree on and transmit one bit of secret information from four-dimensional vectors that are relatively close in distance. In the practical application of the inventive method, each interactive party can have higher dimensional input; such as: the vectors in each party's input of the interaction are 1024-dimensional, in which case the 1024-dimensional vectors can be divided into 255 groups, each group being considered as a four-dimensional vector, and then the inventive method is run 256 times in parallel, so that 256 bits of information can be known and transmitted. The inventive method can also be extended to work where the input is a two-dimensional vector or an eight-dimensional vector.
Note k in the inventive method1Can be determined by the sender before running the inventive method, thus having excellent on-line and parallel computing capabilities, which is an important property of the inventive method. When the inventive method is used for key agreement, k1Is randomly selected from {0,1 }; when the inventive method is used for encryption, k1Any distribution over 0,1 can be obeyed. When applied to cryptosystem construction based on LWE or RLWE, the interactive parties running the method of the invention need to exchange LWE or RLWE data and derive vectors from these data, respectively
Figure GDA00029118938500000327
And
Figure GDA00029118938500000328
when applied to RLWE cryptosystems, q is typically a prime number;when applied to the LWE cryptosystem, q may be a prime number or a composite number.

Claims (1)

1. An efficient method for key consensus transmission, the method comprising:
system parameters: params ═ q, m, g, d, where q, m, g, d are positive integers, satisfying: m is more than or equal to 2, q is more than or equal to g, and d is more than or equal to 0 and less than q (1-1/g) -2;
order to
Figure FDA0002891743030000011
And
Figure FDA0002891743030000012
is a four-dimensional column vector; given two four-dimensional column vectors
Figure FDA0002891743030000013
And
Figure FDA0002891743030000014
definition of
Figure FDA0002891743030000015
Figure FDA0002891743030000016
Namely the relative amount
Figure FDA0002891743030000017
Wherein "is the rounding operator, defining the first order norm of the vector
Figure FDA0002891743030000018
Definition of
Figure FDA0002891743030000019
Figure FDA00028917430300000110
Order to
Figure FDA00028917430300000111
A fourth-order square matrix is formed; for an arbitrary integer x ∈ Z, | x! Z is definedqMin { x mod q, q-x mod q }; for arbitrary four-dimensional column vectors
Figure FDA00028917430300000112
Wherein
Figure FDA00028917430300000113
Or
Figure FDA00028917430300000114
Figure FDA00028917430300000115
Figure FDA00028917430300000144
Is a rounded down operator, define
Figure FDA00028917430300000116
Figure FDA00028917430300000117
The system comprises a sender and a receiver, wherein the sender records the sender
Figure FDA00028917430300000118
The receiver records as
Figure FDA00028917430300000119
Figure FDA00028917430300000120
With a secret input four-dimensional column vector
Figure FDA00028917430300000121
And secret information k1∈{0,1}；
Figure FDA00028917430300000122
With a secret input four-dimensional column vector
Figure FDA00028917430300000123
Satisfy the requirement of
Figure FDA00028917430300000124
Figure FDA00028917430300000125
To the direction of
Figure FDA00028917430300000126
Transmitting a four-dimensional vector information
Figure FDA00028917430300000127
The method specifically comprises the following steps:
Figure FDA00028917430300000128
computing
Figure FDA00028917430300000129
Figure FDA00028917430300000130
If it is not
Figure FDA00028917430300000131
Making b equal to 0, otherwise making b equal to 1; note the book
Figure FDA00028917430300000132
Computing
Figure FDA00028917430300000133
Figure FDA00028917430300000134
Will be provided with
Figure FDA00028917430300000135
To be transmitted to
Figure FDA00028917430300000136
Figure FDA00028917430300000137
Receive from
Figure FDA00028917430300000138
After that time, the user can use the device,
Figure FDA00028917430300000139
computing
Figure FDA00028917430300000140
Computing
Figure FDA00028917430300000141
||1(ii) a If t is<1, then let k2If not, let k be21 is ═ 1; by the method
Figure FDA00028917430300000142
And
Figure FDA00028917430300000143
achieving the same key agreement k1＝＝k2∈{0,1}。
CN201611018455.1A 2016-11-18 2016-11-18 Efficient secret key consensus transmission method Active CN108173643B (en)

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