CN107733655A - A kind of APUF safety certifying methods based on Polynomial Reconstructing - Google Patents

A kind of APUF safety certifying methods based on Polynomial Reconstructing Download PDF

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CN107733655A
CN107733655A CN201710953025.7A CN201710953025A CN107733655A CN 107733655 A CN107733655 A CN 107733655A CN 201710953025 A CN201710953025 A CN 201710953025A CN 107733655 A CN107733655 A CN 107733655A
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point
apuf
multinomial
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CN107733655B (en
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李冰
淡富奎
陈剑
陈帅
沈克强
董乾
张�林
王刚
赵霞
刘勇
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Southeast University
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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
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3271—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using challenge-response
    • H04L9/3278—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using challenge-response using physically unclonable functions [PUF]
    • 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
    • H04L9/0866—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving user or device identifiers, e.g. serial number, physical or biometrical information, DNA, hand-signature or measurable physical characteristics

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Storage Device Security (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention discloses a kind of APUF safety certifying methods based on Polynomial Reconstructing, this method includes registration and two stages of certification.In registration phase, server randomly generates a large amount of excitations and a random numberk, APUF, which produces to respond accordingly, is used as abscissa.After being encoded with CRCkTo find out corresponding true point in the multinomial of coefficient, and add substantial amounts of hash point and form point setV.Will excitation, point setVAnd after Hash multinomial coefficient hash (k) it is stored in server end.PUF circuits, which produce, in authentication phase, user's hand responds and is randomized, in point setVThe corresponding true point of middle inquiry is used to construct multinomial, obtains multinomial coefficient。hash() and hash (k) carry out contrast certification, identical then certification success.The addition of APUF response randomizations of the present invention and hash point, machine learning attack can be resisted to guarantee data security reliable.

Description

A kind of APUF safety certifying methods based on Polynomial Reconstructing
Technical field
The present invention relates to a kind of APUF safety certifying methods based on Polynomial Reconstructing, and in particular to a kind of anti-machine learning The APUF secure authentication technologies of attack, belong to field of information security technology.
Background technology
In recent years, developing rapidly with Internet of Things and REID, it is thing and thing, people and thing, interpersonal Conspiracy relation be established, so as on the basis of Sensor Network, internet and mobile radio communication formed a bigger complex web Network system.Most of electronic devices can all interact with network and communicate or be controlled by computer.Internet of Things produces substantial amounts of Information data, it is related to the links such as perception, storage, computing, transmission, its security is directly connected to the hair of Internet of Things industry Exhibition.The security of conventional electronics is based primarily upon the non volatile register such as EEPROM, Flash (Non-volatile Memory, NVM) carry out safety certification and key storage.However, the memory mechanism based on NVM is needed in IC manufacturing mistake Floating transistor technique is added in journey, increases manufacturing cost.Meanwhile NVM memory mechanisms are easily by a variety of physics such as intrusive mood attacks The threat of attack.This will cause substantial amounts of information leakage, and information security is on the hazard.In most cases conditional electronic simultaneously It is poor computing capability to be all present in device, it is resource-constrained the problem of, so, tradition is existed based on the authentication method of cryptography in application Very big obstacle.Inherent physique based on physical entity uniquely identifies the think of that single physical entity realizes effective certification Road, the concept of physics unclonable function (Physical Unclonable Function, PUF) are suggested.
PUF is a physical function.It will produce a correspondence when giving excitation, this function known to one and uniquely ring Should.The nanoscale structures of physical location where this response depends on PUF simultaneously.PUF essence is a kind of " chip finger print ", should " fingerprint " derives from unmanageable, unpredictable, unclonable chip manufacturing difference, and the physics that can be resisted for NVM is attacked Hit.Application most basic PUF is to realize certification using the unique mark of entity, with understanding of the people to PUF and application Deepen continuously, PUF is gradually applied to more fields such as system authentication, key generation again, and is increasingly becoming hardware security neck A hot issue in the research of domain.PUF is generally divided into " strong PUF " (Strong PUF) and " weak PUF " (Weak PUF) two Class：Strong PUF has exponential excitation response pair (Challenge Response Pairs, CRPs), is mainly used in recognizing safely Card；Weak PUF response the number of output is proportional with circuit scale, is mainly used in the storage of the key messages such as key, ID.
With the continuous development of machine learning techniques, research shows that some machine learning algorithms can be used for attacking strong PUF. Its attack effect is obvious.There is the method researched and proposed with reference to side channel analysis simultaneously, machine learning techniques can be broken through greatly The strong PUF structures that majority is suggested.For machine learning algorithm, researcher proposes different attack resistance methods, such as XOR The structure such as APUF, Controlled PUF and composite PUF.But all there is the problem of certain in these structures, with knot Structure complicate, PUF reliability decreases, at the same resource consumption increase, can not meet some it is resource-constrained in the case of PUF reliable reality It is existing.
The content of the invention
The technical problems to be solved by the invention are：A kind of APUF safety certifying methods based on Polynomial Reconstructing are provided, Using standard APUF, high reliability and attack resistance characteristic are reached based on Polynomial Reconstructing characteristic, while resource occupation amount is small.
The present invention uses following technical scheme to solve above-mentioned technical problem：
A kind of APUF safety certifying methods based on Polynomial Reconstructing, including two parts of registration phase and authentication phase, Wherein,
Registration phase comprises the following steps：
Step 1, the excitation using random number generator required for server end generates APUF；
Step 2, excitation is grouped, every group includes n excitation, and n is 16 positive integer times；
Step 3, each group excitation is input in APUF, according to APUF internal structures, exports corresponding response, and by every group Corresponding response is divided into n/16 groups；
Step 4, in the server, a random number k, k ∈ GF (2 are generated using random number generator16), compiled by CRC K is divided into deg (P) part after code, as multinomial P coefficient, structure deg (P) level multinomial P；
Step 5, response step 3 exported substitutes into step 4 multinomial independent variable, the value being calculated as ordinate, Response after being grouped by the use of step 3 obtains one containing the n/16 set Q truly put as abscissa；
Step 6, accelerated in set Q more than the random hash point of true point quantity, obtain new set V, at random Hash point is more than constant δ with truly the distance between point；
Step 7, the operation of step 4- steps 6 is carried out to every group of excitation, by the multinomial coefficient after every group of excitation, Hash with And new set V is stored in the database of server；
Authentication phase comprises the following steps：
Step 8, according to one group of given excitation, one of which of the group excitation from registration phase, it is right that APUF produces its The response answered, and n/16 groups are divided the response into, while carry out randomization；
Step 9, indexed the response after randomization as abscissa, true point is matched in new set V, this In the number l that truly puts be more than or equal to deg (P)+1, and be less than or equal to n/16；
Step 10, the true point matched to step 9 is combined, and is reconstructedIndividual multinomial, wherein meeting The multinomial of CRC-16 verifications is key multinomial, and key is obtained according to key multinomial；
Step 11, after certification is completed, by the multinomial after every group of excitation, Hash being stored in the database of server Coefficient and new set V are deleted.
As a preferred embodiment of the present invention, multinomial P form is as follows described in step 4：
Wherein, SkRepresentative polynomial P (x) coefficient, deg (P) representative polynomial P (x) series.
As a preferred embodiment of the present invention, set Q form is as follows described in step 5：
Q={ (ai,P(ai))|ai∈GF(216), i=1 ..., n/16 }
Wherein, aiRepresent i-th group of response after respond packet corresponding to one group of excitation, P (ai) represent aiSubstitute into multinomial The value being calculated in P, GF represent finite field, and n/16 is the number truly put.
As a preferred embodiment of the present invention, new set V-arrangement formula is as follows described in step 6：
V=Q ∪ Q '=Q ∪ { (bj,cj)|bj,cj∈GF(216), j=1 ..., m, m ＞ ＞ n/16 }
Wherein, Q represents the set truly put, the set of the random hash point of Q ' expressions, and m is the number of random hash point, n/ 16 number truly to put, GF represent finite field, (bj,cj) represent random hash point.
As a preferred embodiment of the present invention, random hash point described in step 6 is more than normal with truly the distance between point It is as follows to measure δ forms：
Wherein, d represents random hash point and truly the distance between point, (ai,P(ai)) represent true point, (bj,cj) table Show random hash point, m is the number of random hash point, and n/16 is the number truly put.
The present invention compared with prior art, has following technique effect using above technical scheme：
1st, a kind of APUF safety certifying methods based on Polynomial Reconstructing of the present invention, have higher reliability and safety Property.It make use of the APUF structures of standard to produce response in whole system, do not increase resource consumption, ensure that whole system can By property.Using interpolation point in Polynomial Reconstructing randomness so as to APUF export response carry out randomization, by APUF's Excitation is converted into true point and stored, and has upset the corresponding relation between APUF excitations and response, has been reasonably resistant to machine Learning attack, drastically increase security.
2nd, it is long-range to add quantity in server end data storage using fuzzy safety box principle in truly point by the present invention In the hash point truly put, it is ensured that distance is more than a certain particular value between any two point in fuzzy safety box, the particular value by Designer voluntarily chooses so that attacker can only take brute force attack method to crack, and greatly improve the safety of key storage Property.
Brief description of the drawings
Fig. 1 is a kind of schematic diagram of the APUF safety certifying methods based on Polynomial Reconstructing of the present invention.
Fig. 2 is the specific schematic diagram of registration phase provided by the invention.
Fig. 3 is the specific schematic diagram of authentication phase provided by the invention.
Embodiment
Embodiments of the present invention are described below in detail, the example of the embodiment is shown in the drawings.Below by The embodiment being described with reference to the drawings is exemplary, is only used for explaining the present invention, and is not construed as limiting the claims.
As shown in figure 1, a kind of APUF safety certifying methods based on Polynomial Reconstructing are realized by APUF security certification systems, Whole system generallys include APUF modules and multinomial structure module.Server randomly generates a large amount of excitations, while produces one Random number.Excitation is used for the corresponding excitation of APUF modules generation and is used as abscissa.Random number is after CRC-16 verifications For multinomial coefficient.Make abscissa using excitation, find out all true points in the polynomial, add a large amount of hash points and form point Collection.By excitation, the multinomial after Hash and point set storage in the server.In verification process, swashing in user's hand The excitation encouraged with storage in the server is identical.By in the excitation input APUF in user's hand, response is produced, response is upset defeated Go out, find true point in a concentration, by the true point found out, utilize Lagrange's interpolation to reconstruct multinomial, extract multinomial Coefficient carries out Hash with the Hash coefficient stored in server compared with, and identical then certification is successfully, on the contrary then fail.The present invention carries The authentication method structured flowchart gone out is as shown in Figures 2 and 3.
As shown in Fig. 2 be registration phase, including：
The first step：Excitation required for generating APUF at certificate server end using random number generator.
Second step：Because standard APUF output responses only have 1bit, rung so carrying out packet transaction to excitation and forming more bit Should, every group includes 320 excitations.Such as formula (1)：
G={ c1,c2,…,c320} (1)
3rd step：The excitation for being grouped completion is input in APUF, according to PUF internal structures ai=APUFs (ci), it will Responded corresponding to output.Response is divided into 16bit*20 groups simultaneously：
R={ a1,a2,…,a20} (2)
4th step：In the server, random number generator generates a random number k (k ∈ GF (216)).Encoded by CRC K is divided into 7 (multinomial series deg (P)) parts, the coefficient such as formula (3) as multinomial P afterwards.Deg (P) is built according to (4) Level multinomial P.
K={ s1,s2,…,sdeg(P)} (3)
5th step：Using the response in step 3, often 16bit mono- indexes as polynomial abscissa, shares 20 horizontal seats Scale value.One can be obtained containing 20 set truly put Q.
Q={ (ai,P(ai))|ai∈GF(216), i=1 ..., 20 } (5)
6th step：Because caused true point preserves nonvolatile memory (non-in the server in step 5 Volatile memory, NVM) in, therefore it is highly susceptible to physical attacks.In order to ensure the security of data, it is necessary to gather Accelerated in Q and be much larger than the true random hash point for putting quantity to encrypt true point.All hash points have to pass through sieve Choosing.Hash point have to be larger than a constant δ with truly the distance between point.The collection that hash point is formed is combined into Q '.Finally give Point set is V=Q ∪ Q '.(m ＞ ＞ 20)
Q '={ (bj,cj)|bj,cj∈GF(216), j=1 ..., m } (6)
7th step：Excitation group g, hash (k) and point set V are stored in database by server after completing above-mentioned steps In.Handled by all stage, APUF response can be stored securely in NVM by hash (k) and V encryption.
As shown in figure 3, be authentication phase, including：
The first step：Corresponding response r' is produced according to given one group of excitation g, APUF.This response is being transferred to clothes Pass through randomization before business device, meet certain randomness, so as to upset the corresponding relation between exciter response, reach To the effect of resistance machine learning attack.
R'={ a1',a2',…,a20'} (8)
rd={ ad1,ad2,…,ad20}={ a10',a20',…,a7'} (9)
Second step：The response upset in step 1 indexes as abscissa, can be matched in point set V corresponding True point.(8≤l≤20)
QD={ (adh,V(adh)) | h=1 ..., l } (10)
3rd step：, may be mixed with some hash points in the true point matched due to influence of noise.7 grades of multinomials are constructed, At least need 8 points.Find out combination a littleReconstructIndividual multinomial, find out and wherein meet CRC-16 verification inspections The multinomial looked into, as key multinomial, certification success.For attacker, under the response condition that there is no APUF, It is extremely difficult to obtain key from the set V containing hash point.
4th step：After completing certification, g, the hash (k) and point set V being stored in server NVM are deleted.
The technological thought of above example only to illustrate the invention, it is impossible to protection scope of the present invention is limited with this, it is every According to technological thought proposed by the present invention, any change done on the basis of technical scheme, the scope of the present invention is each fallen within Within.

Claims (5)

1. a kind of APUF safety certifying methods based on Polynomial Reconstructing, it is characterised in that including registration phase and authentication phase Two parts, wherein,
Registration phase comprises the following steps：
Step 1, the excitation using random number generator required for server end generates APUF；
Step 2, excitation is grouped, every group includes n excitation, and n is 16 positive integer times；
Step 3, each group excitation is input in APUF, according to APUF internal structures, exports corresponding response, and it is corresponding by every group Response be divided into n/16 groups；
Step 4, in the server, a random number k, k ∈ GF (2 are generated using random number generator16), after CRC is encoded K is divided into deg (P) part, as multinomial P coefficient, structure deg (P) level multinomial P；
Step 5, response step 3 exported substitutes into step 4 multinomial independent variable, and the value being calculated is as ordinate, with step Response after rapid 3 packet obtains one containing the n/16 set Q truly put as abscissa；
Step 6, accelerated in set Q more than the random hash point of true point quantity, obtain new set V, random hash Point is more than constant δ with truly the distance between point；
Step 7, the operation of step 4- steps 6 is carried out to every group of excitation, by the multinomial coefficient after every group of excitation, Hash and newly Set V be stored in the database of server；
Authentication phase comprises the following steps：
Step 8, produced according to one group of given excitation, one of which of the group excitation from registration phase, APUF corresponding to it Response, and n/16 groups are divided the response into, while carry out randomization；
Step 9, indexed the response after randomization as abscissa, true point is matched in new set V, here very The number l of real point is more than or equal to deg (P)+1, and is less than or equal to n/16；
Step 10, the true point matched to step 9 is combined, and is reconstructedIndividual multinomial, wherein meeting CRC-16 schools The multinomial tested is key multinomial, and key is obtained according to key multinomial；
Step 11, after certification is completed, by the multinomial coefficient after every group of excitation, Hash being stored in the database of server And new set V is deleted.
2. the APUF safety certifying methods based on Polynomial Reconstructing according to claim 1, it is characterised in that described in step 4 Multinomial P form is as follows：
<mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>deg</mi> <mrow> <mo>(</mo> <mi>P</mi> <mo>)</mo> </mrow> </mrow> </msubsup> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>&amp;CenterDot;</mo> <msup> <mi>x</mi> <mrow> <mi>deg</mi> <mrow> <mo>(</mo> <mi>P</mi> <mo>)</mo> </mrow> </mrow> </msup> </mrow>
Wherein, SkRepresentative polynomial P (x) coefficient, deg (P) representative polynomial P (x) series.
3. the APUF safety certifying methods based on Polynomial Reconstructing according to claim 1, it is characterised in that described in step 5 Set Q form is as follows：
Q={ (ai,P(ai))|ai∈GF(216), i=1 ..., n/16 }
Wherein, aiRepresent i-th group of response after respond packet corresponding to one group of excitation, P (ai) represent aiSubstitute into multinomial P The value being calculated, GF represent finite field, and n/16 is the number truly put.
4. the APUF safety certifying methods based on Polynomial Reconstructing according to claim 1, it is characterised in that described in step 6 New set V-arrangement formula is as follows：
V=Q ∪ Q '=Q ∪ { (bj,cj)|bj,cj∈GF(216), j=1 ..., m, m ＞ ＞ n/16 }
Wherein, Q represents the set truly put, and the set of the random hash point of Q ' expressions, m is the number of random hash point, and n/16 is The number truly put, GF represent finite field, (bj,cj) represent random hash point.
5. the APUF safety certifying methods based on Polynomial Reconstructing according to claim 1, it is characterised in that described in step 6 Random hash point and the distance between true point are as follows more than constant δ forms：
<mrow> <mi>d</mi> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>P</mi> <mo>(</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>-</mo> <msub> <mi>c</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>&gt;</mo> <mi>&amp;delta;</mi> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> <mo>/</mo> <mn>16</mn> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>m</mi> </mrow>
Wherein, d represents random hash point and truly the distance between point, (ai,P(ai)) represent true point, (bj,cj) represent random Hash point, m are the number of random hash point, and n/16 is the number truly put.
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