CN106911461A - A kind of McEliece public key mask encryption methods of secure lightweight - Google Patents
A kind of McEliece public key mask encryption methods of secure lightweight Download PDFInfo
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- CN106911461A CN106911461A CN201710026047.9A CN201710026047A CN106911461A CN 106911461 A CN106911461 A CN 106911461A CN 201710026047 A CN201710026047 A CN 201710026047A CN 106911461 A CN106911461 A CN 106911461A
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- mceliece
- public key
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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
- H04L9/002—Countermeasures against attacks on cryptographic mechanisms
- H04L9/003—Countermeasures against attacks on cryptographic mechanisms for power analysis, e.g. differential power analysis [DPA] or simple power analysis [SPA]
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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)
- H04L9/0825—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) using asymmetric-key encryption or public key infrastructure [PKI], e.g. key signature or public key certificates
Abstract
The invention discloses a kind of McEliece public key mask encryption methods of secure lightweight, belong to field of information security technology.The design of the method is divided into two parts, that is, construct MDPC yards of McEliece cryptographic algorithm of Quasi Dyadic of key small volume and the mask protectiving scheme of the anti-power consumption analysis of design.MDPC yards of Quasi Dyadic of present invention construction are applied in McEliece cryptographic algorithms, can effectively reduce key volume.The present invention also designs protectiving scheme using mask technology, makes the anti-power consumption analysis of McEliece cryptographic algorithms.Meanwhile, the present invention also compensate for the core algorithm of ISW provable security frameworks, generate easy same time leakage two safety problems of share of a and b of power consumption that random counting method is produced.The McEliece type public key algorithms with high security and high efficiency of present invention design are more applicable for the embedded environment of resource-constrained.
Description
Technical field
McEliece asymmetric cryptographies the present invention relates to quantum computation attack can be resisted in field of information security technology
Technology.More particularly to a kind of consideration side channel safety based on the encryption of Quasi-Dyadic MDPC yards of McEliece public keys mask
Algorithm realizes technology, and power consumption analysis can be resisted using the method.
Background technology
The fast development of quantum computer, constitutes serious threat, especially to the cryptographic algorithm based on number theory problem
The proposition of Shor quantum algorithms, makes researcher more believe that the conventional cryptographic algorithm based on number theory difficult problem such as RSA, ECC will
It is no longer safe.
Cryptography scheme based on error correcting code can realize resisting quantum computation attack, however, initial based on Goppa yards
McEliece crypt algorithm keys volumes are larger, are not suitable in the embedded system of resource-constrained.Therefore, occur based on difference
The McEliece type public key algorithms of error correcting code, to reduce key volume.Researcher proposes to be based on LDPC, MDPC, QC- in succession
The McEliece algorithms of the error correcting codes such as MDPC, but there is the challenge of side-channel attack, particularly power consumption during cryptographic algorithm application
The threat of analysis.
Power consumption analysis are using the pass between data and energy ezpenditure handled in encryption device execution encryption and decryption operating process
Connection is attacked.As the research of side-channel attack technology deepens continuously, the research in terms of defence both at home and abroad is also never
It was interrupted, wherein the defence method of main flow includes mask technology and concealing technology, mask is protected due to its relative inexpensiveness, and
It is easily achieved, and is subject to the extensive concern of researcher.
2003, Ishai et al. proposed the mask scheme-Ishai-Sahai- of anti-high-order differential power analysis first
Wagner provable security frameworks.But there is safety problem and be difficult to be applied in actual environment in it, i.e. one of core algorithm
Generate two shares of power consumption information easy same time leakage sensitive data a and b that random counting method is produced.
The content of the invention
It is an object of the present invention to provide a kind of McEliece public key mask encryption methods of secure lightweight, to solve
McEliece algorithms have that key body is larger, can not resist power consumption analysis.
To achieve these goals, the present invention uses following technical solution：A kind of McEliece of secure lightweight
Public key mask encryption method, including key small volume the Quasi-Dyadic MDPC yards of construction of McEliece cryptographic algorithms and
The design two large divisions of the mask protectiving scheme of anti-power consumption analysis：
First, the construction process of Quasi-Dyadic MDPC yards of McEliece cryptographic algorithm of the key small volume includes
Following steps：
Step 1, constructs MDPC yards of Quasi-Dyadic：In finite fieldOn, design the form of Midst density check matrix：
Wherein HnIt is dyadic matrix, ifN=0,1 ..., n0- 1, dyadic matrix HnExpression
Form：
Memory only needs to storage dyadic matrix HnFirst trip, i.e. seed random vector hn.
Step 2, the check matrix H generated using step 1 generates public/private keys pair：Key is generated by the side for communicating,
Quasi-Dyadic MDPC error correcting codes parameter [n, k, t], n represent code word size, and k represents every group information group of linear block codes
Length, is dimension, and t represents the digit of code energy error correction, and the method that public key is designed into the dyadic matrix that is defined is as follows：
1) the random quasi- dyadic matrix of n ranks is generatedCalculate n row k column matrixSo that XHP=
T, H represent check matrix, and P represents the permutation matrix of random generation；
2) the K ranks of random generation X can invertible sub-matrix S；
3) public key G '=SHP is calculated, G ' is the quasi- dyad submatrix of T, only need to stores G ' first trip elements, mainly in conjunction with
The generation method of expression formula (2) dyadic matrix, obtains a complete public key matrix G '.
The public key matrix of design only needs to store the first trip of all dyadic matrixs, i.e. seed random vector when actually used
hn.
Private key is defined as：N rank permutation matrix P, k rank invertible matrix S, r row n row check matrix Hs.
Step 3, design encryption, decryption portion：The opposing party of communication will send messages to other side, if m be k bits in plain text,
Random generation meets the Hamming weight of n-bit error correction vector e, w (*) the expression * of w (e)≤t, calculates ciphertext c=mG '+e, will be close
Literary c is sent to other side.
After other side receives ciphertext c, it is decrypted, is multiplied by private key transposed matrix P on the right of ciphertext c firstT, i.e. c '=
cPT, using c ' as the input of Fast Decoding Algorithim, m*S is then obtained by Quasi-Dyadic MDPC yards of Fast Decoding Algorithim
Result, most rear right is multiplied by the inverse matrix S of private key S-1Recover in plain text.
2nd, the design process of the mask protectiving scheme of the anti-power consumption analysis comprises the following steps：
McEliece type public key algorithms are divided into linear operation and nonlinear operation.When XOR linear operation hardware is realized
Consumed energy is than more uniform, but domain multiplying nonlinear arithmetic hardware realizes that energy ezpenditure, than larger, easily produces side channel letter
The leakage of breath.The present invention improve Ishai-Sahai-Wagner provable security frameworks, solve one of its core algorithm generation with
The formula of machine number：Easily the same time leaks two peaces of share of a and b to the power consumption information of generation
Full problem, the mask scheme of further design domain multiplying nonlinear computing.Comprise the following steps：
Step 1, the mask scheme initialization of domain multiplying nonlinear computing：
(1) assume that a and b is two sensitive datas, make a=g (k), b=h (k), g (*) and h (*) are domain F2Linear pass
System, k is domainRandom number；
(2)ai=g (ki),bi=h (ki), i ∈ [0:D], wherein ai, biAnd kiIt is respectively the random d+ for splitting into of a, b and k
1 share.For example：
Step 2, according to 1 and definition 2 is defined, introduces random number variable k and v 'i,j, derive formula (3)：
Define 1(f maps：), x, y represent sensitive
Data a, b.
Define 2
vi,jRepresent random number.
Step 3, obtains mask scheme generating random number expression formula of the present invention, i.e., by defining 3 and defining 4 derivation formulas (3)
(4)：
(w maps to define 3w (x)=h (x) g (x):)
Define 4
Step 4, the d+1 random number generated with the principle shown in table 1 protects a and b d+1 share of two sensitive datas
Domain multiplication operation.
The mask scheme Implementation of pseudocode of table 1
Principle shown in table 1 is specially：I and j, v are designated as under random array vi,j(i<J) it is to be produced by random number generator
It is raw, vi,j(i>J) it is to be produced by the generation random number formula that designs；Using d+1 random number vi,jXOR guarantor is carried out respectively
Shield a is multiplied with the d+1 share domain of b；The random number that the present invention is used all is separate.
Beneficial effects of the present invention：
1st, secure lightweight of the present invention based on Quasi-Dyadic MDPC yards of McEliece type Public Key Crypto Scheme,
Quantum computation attack can be resisted, quasi- dyad code is designed to reduce key volume by by public key, it is adaptable to resource-constrained
Embedded device.
2nd, secure lightweight of the present invention based on Quasi-Dyadic MDPC yards of McEliece type Public Key Crypto Scheme,
Unshielded McEliece algorithms are improved by designing mask scheme, applying it can resist power consumption point in embedded device
Analysis.
Brief description of the drawings
Fig. 1 is the McEliece algorithm for encryption handling process schematic diagrames that the inventive method is implemented.
Specific embodiment
The following is specific embodiment of the invention, and further clear, complete is made to technical scheme with reference to accompanying drawing
Site preparation is described.The code length n=128 of quasi- dyad error correcting code C, dimension k=64, codimension r=64, the error correcting capability t=49 of code.
A kind of secure lightweight is based on Quasi-Dyadic MDPC yards of McEliece type public key cryptography methods, including key
The construction of Quasi-Dyadic MDPC yards of McEliece cryptographic algorithm of small volume and the mask protection side of anti-power analysis
The design two large divisions of method：
First, the construction process of Quasi-Dyadic MDPC yards of McEliece cryptographic algorithm of the key small volume includes
Following steps：
Step 1, constructs MDPC yards of Quasi-Dyadic：In finite fieldOn, the form of Midst density check matrix is designed,
N in the present embodiment0=2：
H=[H0|H1] (1)
Wherein H0And H1It is dyadic matrix, if
Dyadic matrix H0And H1Expression-form：
H0And H1Element be h0And h1Element, according to dyadic matrix described in the content of the invention construction rule computing.
Step 2, the check matrix H generated using step 1 generates public/private keys pair：By communicate a side generation key,
Quasi-Dyadic MDPC error correcting codes parameter [n, k, t]=[128,64,49], n represents code word size, and k represents linear block codes
Every group information group length, be dimension, t represents the digit of code energy error correction, by public key design be defined dyadic matrix method such as
Under：
1) the quasi- dyadic matrix of random n=128 ranks is generatedCalculate the matrix of the row of 128 row 64So that XHP=T, H represent check matrix, P represents the permutation matrix of random generation；
2) 64 ranks of random generation X can invertible sub-matrix S；
3) G '=SHP is calculated, G ' is the quasi- dyad submatrix of T, only G ' first trip elements need to be stored, with reference to expression formula (2)
The generation method of dyadic matrix, obtains a complete public key matrix G '.
The public key matrix of design only needs to store the first trip of all dyadic matrixs, i.e. seed random vector when actually used
h0And h1.
Table 1 is based on the McEliece type Public Key Crypto Scheme key volumetric analyses of quasi- dyad code
Drawn by table 1, the present invention designed by QD-MDPC yards and existing QC-LDPC yards and QC-GRS code-phase ratio, enter one
Step reduces public key volume.
Private key is defined as：N=128 rank permutation matrix P, k=64 rank invertible matrix S, the row check matrix H of 64 row 128.
Step 3, design encryption, decryption portion：The opposing party of communication will send messages to other side, if m is k=64 bits
In plain text, random generation meets the Hamming weight of n=128 bit error correction vectors e, w (*) the expressions * of w (e)≤49, calculates c=mG '
+ e, other side is sent to by ciphertext c.
After other side receives ciphertext c, it is decrypted, is multiplied by private key transposed matrix P on the right of ciphertext c firstT, i.e. c '=
cPT, using c ' as the input of Fast Decoding Algorithim, m*S is then obtained by Quasi-Dyadic MDPC yards of Fast Decoding Algorithim
Result, most rear right is multiplied by the inverse matrix S of private key S-1Recover in plain text.
2nd, the design process of the mask protectiving scheme of the anti-power consumption analysis comprises the following steps：
McEliece types public key algorithm can be divided into linear operation and nonlinear operation.XOR linear operation hardware reality
Current consumed energy is than more uniform, but domain multiplying nonlinear arithmetic hardware realizes that energy ezpenditure, than larger, easily produces side letter
The leakage of road information.The present invention improves Ishai-Sahai-Wagner provable security frameworks, solves its core algorithm all one's life
Into the formula of random number：Easily the same time leaks two shares of a and b to the power consumption information of generation
Safety problem, the mask scheme of further design domain multiplying nonlinear computing.Comprise the following steps：
Step 1, the mask scheme initialization of domain multiplying nonlinear computing：
(1) assume that a=87 and b=13 is two sensitive datas, k=21 makes 87=g (21), 13=h (21), g (*) and h
(*) is domain F2Linear relationship, k is domainRandom number.
(2)ai=g (ki),bi=h (ki), i ∈ [0:2], wherein ai, biAnd kiIt is respectively that a, b and k split into 3 at random
Share.For example：
Step 2, according to 1 and definition 2 is defined, introduces random number variable k and v 'i,j, derive formula (3)：
Define 1(f maps：), x, y represent sensitive
Data a, b.
Define 2
vi,jRepresent random number.
Step 3, obtains mask scheme generating random number expression formula of the present invention, i.e., by defining 3 and defining 4 derivation formulas (3)
(4)：
(w maps to define 3w (x)=h (x) g (x):)
Define 4
Step 4,3 random numbers generated with the principle shown in table 2 protect a and the sensitive datas 3 of b two domain of share
Multiplication operation.
The mask scheme Implementation of pseudocode of table 2
Principle shown in table 2 is specially：I and j, v are designated as under random array vi,j(i<J) it is to be produced by random number generator
It is raw, vi,j(i>J) it is to be produced by the generation random number formula that designs；Using d+1 random number vi,jXOR guarantor is carried out respectively
Shield a is multiplied with the d+1 share domain of b；The random number that the present invention is used all is separate.The McEliece of present invention design is covered
The ciphering process of code encryption scheme is as shown in Figure 1.
Embodiment described above is only that embodiments of the present invention are described, not to it is of the invention design and
Scope is defined, and on the premise of design concept of the present invention is not departed from, ordinary skill technical staff is to the present invention in this area
The all variations and modifications made of technical scheme, protection scope of the present invention all should be fallen into.
Claims (7)
1. McEliece public key mask encryption methods of a kind of secure lightweight, it is characterised in that including construction key small volume
Quasi-Dyadic MDPC yards of McEliece cryptographic algorithms, the mask protectiving scheme of the anti-power consumption analysis of design；
The Quasi-Dyadic MDPC yards of process of McEliece cryptographic algorithms of the construction key small volume includes following step
Suddenly：
Step 1, constructs MDPC yards of Quasi-Dyadic：In finite fieldOn, design Midst density check matrix H；
Step 2, the Midst density check matrix H generated using step 1 generates public/private keys pair：It is close by the side generation for communicating
Key, Quasi-Dyadic MDPC error correcting codes parameter [n, k, t], n represents code word size, and k represents every group information of linear block codes
Group length, is both dimension, and t represents the digit of code energy error correction, and public key is designed into the dyadic matrix that is defined；
Private key is defined as：N rank permutation matrix P, k rank invertible matrix S, r row n row check matrix Hs；
Step 3, design encryption, decryption portion：The opposing party of communication will send messages to other side, if m be k bits in plain text, at random
Generation meets the Hamming weight of n-bit error correction vector e, w (*) the expression * of w (e)≤t, ciphertext c=mG '+e is calculated, by ciphertext c
Other side is sent to, the quasi- dyad submatrix of the quasi- dyadic matrix T of the n ranks that G ' is randomly generated；
After other side receives ciphertext c, it is decrypted, is multiplied by private key transposed matrix P on the right of ciphertext c firstT, i.e. c '=cPT, so
The result of m*S is obtained by Quasi-Dyadic MDPC yards of Fast Decoding Algorithim afterwards, most rear right is multiplied by the inverse matrix S of private key S-1
Recover in plain text；
The mask protectiving scheme of the anti-power consumption analysis of design comprises the following steps：
Step 4, the mask method initialization of domain multiplying nonlinear computing：
(1) assume that a and b is two sensitive datas, make a=g (k), b=h (k), g (*) and h (*) are domain F2Linear relationship, k is
DomainRandom number；
(2)ai=g (ki),bi=h (ki), i ∈ [0:D], wherein ai, biAnd kiIt is respectively the random d+1 part for splitting into of a, b and k
Volume；
Step 5, according to 1 and definition 2 is defined, introduces random number variable k and vi′,j, derive formula
Wherein：vi,jRepresent random number；
Defining 1 is(f maps：), x, y represent sensitive number
According to a, b；
Defining 2 is
Step 6, by defining 3 and defining the expression formula in 4 derivation steps 5
Obtain mask of the present invention
Scheme generating random number expression formula
Wherein：
It is that (w maps w (x)=h (x) g (x) to define 3:)；
Defining 4 is
Step 7, generates d+1 random number, protects the d+1 share domain multiplication operation of two sensitive datas of a and b.
2. a kind of McEliece public key mask encryption methods of secure lightweight according to claim 1, it is characterised in that institute
The expression formula for stating Midst density check matrix is：
Wherein, HnIt is dyadic matrix, ifN=0,1 ..., n0- 1, dyadic matrix HnExpression-form：
。
3. McEliece public key mask encryption methods of a kind of secure lightweight according to claim 2, it is characterised in that will
Public key designs the dyadic matrix that is defined, and specific method is as follows：
1) the random quasi- dyadic matrix of n ranks is generatedCalculate n row k column matrixSo that XHP=T, H table
Show check matrix, P represents the permutation matrix of random generation；
2) the K ranks of random generation X can invertible sub-matrix S；
3) public key G '=SHP is calculated, G ' is the quasi- dyad submatrix of T, only G ' first trip elements need to be stored, with reference in check matrix
The generation method of dyadic matrix, obtains a complete public key matrix G '.
4. a kind of McEliece public key mask encryption methods of the secure lightweight according to claim 2 and 3, its feature exists
In designed public key matrix only needs to store the first trip of all dyadic matrixs, i.e. seed random vector h when actually usedn
.
5. a kind of McEliece public key mask encryption methods of secure lightweight according to claim 1, it is characterised in that institute
The mask solution principle for stating step 7 is specially：I and j, v are designated as under random array vi,j(i<J) it is to be produced by random number generator
It is raw, vi,j(i>J) it is to be produced by the generation random number formula that designs；Using d+1 random number vi,jXOR guarantor is carried out respectively
Shield a is multiplied with the d+1 share domain of b；The random number that the present invention is used all is separate.
6. a kind of McEliece public key mask encryption methods of secure lightweight according to claim 2, it is characterised in that institute
State n0Value is 2, now sets H0And H1Value be：
。
7. a kind of McEliece public key mask encryption methods of secure lightweight according to claim 3, it is characterised in that institute
State X and be set to the column matrix of 128 row 64, S is set to 64 rank matrixes.
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| CN107070633A (en) * | 2017-03-20 | 2017-08-18 | 江苏大学 | A kind of AES mask encryption methods of anti-high-order power consumption analysis |
| CN108712256A (en) * | 2018-07-02 | 2018-10-26 | 复旦大学 | A kind of encryption-decryption algorithm based on elliptic curve subfield cable |
| CN111756727A (en) * | 2020-06-23 | 2020-10-09 | 电子科技大学 | McElience system encryption and decryption method based on QC-LDPC code |
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| CN108712256A (en) * | 2018-07-02 | 2018-10-26 | 复旦大学 | A kind of encryption-decryption algorithm based on elliptic curve subfield cable |
| CN108712256B (en) * | 2018-07-02 | 2021-10-26 | 复旦大学 | Encryption and decryption algorithm based on elliptic curve subdomain subcodes |
| CN111756727A (en) * | 2020-06-23 | 2020-10-09 | 电子科技大学 | McElience system encryption and decryption method based on QC-LDPC code |
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