To overview relevant references from domestic and

foreign. The literatures on second-hand cars can be

roughly divided into several categories. We classify

information systems and platforms into one category [1]–

[6], policies and regulations into one category [7]–

[11], sales and marketing into one category [12]–[20],

technologies and artiﬁcial intelligence into one cate-

gory [4], [21]–[28], and services with strategies into

one category [29]–[31]. Research by Mbaye et al. [30]

shows that discrimination based on information rather

than taste is common in the French’s used car market.

Grodzinsky et al. [31] proposed an interesting topic

“Developing artiﬁcial agents worthy of trust–Would you

buy a used car from this artiﬁcial agent?”. Both buyers

and sellers will seek favorable prices for themselves, this

question is probably one of the most difﬁcult they have

to face; Marshall [29] points to the crux of the problem.

Gabbott [8] studies the second-hand car market in the

UK, noting that the consumer problem is very serious,

and also mentions the application of the compulsory

licensing system for second-hand car dealers introduced

in Scotland. In any second-hand market, there is a

buyer/seller information asymmetry, because the seller

may know the history of the product better than the

buyer. Nicks [7] presented an article “Speak no evil-

Known defects in the FTC’s used car rule”, described

the FTC’s (Federal Trade Commission) issued to a trade

regulation on used car sales that required dealers to

disclose to potential buyers known defect in 1981. Later,

the FTC removed this important consumer protection by

reissued rule version in 1985. Wang et al. [9] discuss

the second-hand car transaction model in China’s quality

certiﬁcation market, and there are two ways to make

the market successful: (1) eliminate the incompleteness

of information; (2) increase the cost of counterfeiting.

Certiﬁcation bodies are required to make actual quality

commitments, and to a certain extent assume relevant

responsibilities, in order to improve the effectiveness

of quality certiﬁcation, to further ensure the authority,

fairness and objectivity of certiﬁcation. In addition to

Gabbott’s mention of information asymmetry, Ahn [3]

proposed an article “Implementation for used trading

management system based blockchain (Case-used car)”;

he uses smart contracts to ensure the reliability of

Ethereum without third-party intervention. Furthermore,

the system alleviates information asymmetry between

buyers and sellers, and reduces with prevents brokerage

fees in the distribution process without a third party.

Yoo and Ahn [6] mentioned that in the second-hand car

trading market, all kinds of second-hand car trading dam-

ages are caused by the information asymmetry between

the buyer and the seller. Zhang and Ma [5] describe

an SVR (support vector machine regression) algorithm

Research on the Used Car System Based on Blockchain and

Cryptographic Technology

1CHI HUANG, 1CHENGLIAN LIU, 2SONIA C-I CHEN

1Department of Science and Engineering, Shiyuan College of Nanning Normal University,

Nanning 530226, CHINA

2School of Economics, Qingdao University, Qingdao 266061, CHINA

Abstract: Different countries have different issues with related to topic of used car in all of world, and used car

issues involve very wide range of fields, such as environmental protection, market economy, sales services,

information systems, regulations and policies, components, materials, and logistics so on. In this study the authors

would like to propose a scheme of used car transaction information system from perspective of mathematical

modelling. We introduce the concept of a third party appraiser as an arbitrator between buyers and sellers in this

solution. In order to avoid collusion between third parties and sellers, the blockchain and cryptography technology

be used to prevent collusion and ensure fair and just transactions.

Keywords: Third Party, Anonymous, Diffie-Hellman Protocol, Used Car Trading System

Received: April 21, 2021. Revised: June 23, 2022. Accepted: July 25, 2022. Published: September 14, 2022.

1. Introduction

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that can accurately estimate the price of used cars, and

the method can also be extended to other second hand

products. Sun et al. [4] presented an optimized BP

(back propagation) neural network algorithm to analyze

the price data of various vehicles, and then build the

second hand car price assessment model for an online

used car platform to get the best price for the car.

Ogawa [1] and Kumar et al. [2] also contributed their

research results on used car trading platforms. In this

paper the authors would like to propose a scheme using

mathematical model and cryptology skill to used car

information system. Due to limited conditions, this study

lists parts of good contributions, but is a little different

then what is discussed in this article, please see Table 1.

TABLE 1

ENGLISH RELATED LITERATURES

System/PlatformPolicy/Rule Marketing Technology/AI Service/Strategy

Ogawa [1] Nicks [7] Huang & Liu [12] Sun et al. [4] Marshall [29]

Kumar et al. [2] Gabbott [8] Shibuya [13] Aksezer [21] Mbaye et al. [30]

Ahn [3] Wang et al. [9]Shibuya [14] Ozturan [22] Grodzinsky et al. [31]

Sun et al. [4] FTC [10] Shibuya [15] Yu et al. [23]

Zhang & Ma [5]Figlin [11] Shibuya [16] Sawicki & Scherer [24]

Yoo & Ahn [6] Wang & Wang [17] Sathiya et al. [25]

Haan & de Boer [18] Papagapiou et al. [26]

Kooreman & Hann [19] Guda & Tsurikov [27]

Rivas-S´anchez et al. [20]Pehlken et al. [28]

The COVID-19 epidemic has affected in the past two

years, the global economy slowed down, and China is no

exception. However, the large volume of China’s market

(such as a large population and relatively large supply

and demand) is accompanied by discussions on the

used car market. According to our survey, the Chinese

literature of used cars can also be roughly divided into

ﬁve categories: platform [32]–[34], block chain [35],

education [36]–[39], occupation (certiﬁcated) [40], [41],

and others [42], [43]. The information system-related

content is classiﬁed in the platform, based on blockchain

or virtual currency of used car topic is classiﬁed in

blockchain. In China’s education system, there is a type

of vocational education; i.e. in the curriculum design of

automobile engineering or mechanical engineering, one

course name is “used car identiﬁcation and evaluation”,

this is classiﬁed in education. In recent years, China has

also attached importance to the development of profes-

sional license (or certiﬁcated) system. There are many

emerging categories, including used car brokers, third-

party appraisers and so on. This category of occupation

refers to these. On September 24, 2021, the People’s

Bank of China issued a notice on further preventing and

dealing with the risk of speculation in virtual currency

transactions. The notice pointed out that virtual currency

does not have the same legal status as legal currency. Bit-

coin, Ethereum, Tether and other virtual currencies have

the main characteristics of being issued by non-monetary

authorities, using encryption technology and distributed

accounts or similar technologies, and existing in digital

form. They are not legal compensation and should not

and cannot be used as currency in the market [44], [45].

Even so, it does not affect the application of blockchain

and cryptology to the used car transaction system. Wu

and Liu [46] described an anonymous delivery system

using blind signature scheme. Later, Wu et al. [47] also

presented a conception which used anonymity purchas-

ing to mobile payment. Zhang et al. [48] connected

RSA [49] with ElGamal [50] two algorithms in their idea

on mobile purchasing without bank card. Lv et al. [51]

applied to library complaint information system. Based

on mathematical reasoning and model inference, we get

inspiration there. Some Chinese related literatures lists

in Table 2.

TABLE 2

CHINESE RELATED LITERATURES

Platform Blockchain Education Occupation Others

Lu & Yu [32] Zhu [35] Wang & Wang [36] Gao [40] Cheng & Song [42]

Liu et al. [33] Yin & Peng [37] Qiao [41] Zhang [43]

Li [34] Yin & Lin [38]

Liu et al. [39]

The well-known algorithms ElGamal [50] and Difﬁe-

Hellman [52] schemes have similar properties in public

key cryptosystems, our study adopts the spirit of these

two algorithms to propose a framework and concept

of used car trading system. The role of the seller, the

buyer and the third party are independent of each others.

Eliminate collusion between any two sides (such as

collusion between the buyer and the seller, or collusion

between the seller and the third party), and strengthen

the role and ability of the third party appraiser under

this framework. There are totally eight phases in this

framework, and we conceptually introduce the main six

phases here. Namely, inquiring, forwarding, checking,

paying, conﬁrming, and delivering phases. We would

describe as following sections.

Step 1. The buyer consults the second-hand car dealer

for car purchase information.

Step 2. Used car dealers provide information to third-

party appraisers.

Step 3. The third party provides professional informa-

tion to the buyer.

Step 4. The buyer shall make a decision and pay ac-

cording to the suggestions of the third-party

2. Literatures Review 3. Our Scheme and Methodology

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appraiser, and entrust the third party to buy the

second-hand car.

Step 5. The third-party appraiser exercises the agency

right to buy a car from a third party.

Step 6. The used car dealer shall deliver the car to the

buyer according to the agreement.

More detailed information ﬂow, please see Figure 1.

Purchaser

Third

Second

3. Check

4. Pay

1. Inquire

2. Forward

5. Conﬁrm

6. Deliver Hand

(Merchant)

Party

Inspector

Fig. 1. The Diagram of Our Scheme.

We usually assume pis a large prime which its over

1024 bits length, and gis a primitive root of Z∗

p, others

symbols and meanings are shown as follows.

Notation and Signiﬁcant:

p: prime number.

g: primitive root of Z∗

xi: secret key in ElGamal-like algorithm.

yi: public in ElGamal-like algorithm.

h(): one-way hash function.

Mi: digitized message.

Purchaser: express buyer or consumer.

Third party: express the third party inspector (or ap-

praiser).

Second hand: express the second hand car (or used car)

dealer or merchant or seller.

The purchaser randomly selects a secret key xawhere

gcd(xa, p −1) = 1, and ﬁnds the public key

ya≡gxa(mod p).(1)

The merchant also randomly selects a secret key xband

ﬁnds its public key

yb≡gxb(mod p).(2)

The third party randomly selects a secret key xc, and

ﬁnds its public key

yc≡gxc(mod p).(3)

They did not publish their secret key but published their

own public key, see Figure 2.

Puchaser Third Party Second Hand

yb≡gkbmod p

yc≡gkcmod p

ya≡gxamod p

ra≡gkamod prc≡gkcmodprb≡gkbmod p

Fig. 2. Initializing Phase.

Purchaser computes Sawhere

Sa≡ya·rc(mod p),(4)

and

mi≡h(Mi) (mod p),(5)

before he sends Saand mito second hand car dealer or

merchant, see Equation (4) to (5) and Figure 3.

1. {Sa,mi}

Puchaser Third Party

Sa≡ya·rcmod p

mi≡Mimod p

Second Hand

Fig. 3. Inquiring Phase.

When merchant receives Saand miby purchaser, he

uses his secret key xbto generate T1before forward to

third party, see Equation (6) and Figure 4.

T1≡Sxb

a·mi·r−xb

c(mod p).(6)

Puchaser Third Party

Second Hand

T1≡Sxb

a·mi·r−xb

cmod p2. {T1}

Fig. 4. Forwarding Phase.

Third party inspector uses his secret key xcto sign

the parameter T1before transmit T2to purchaser, see

Equation (7) and Figure 5.

T2≡(T1)xc·m−xc

i(mod p).(7)

Puchaser Third Party

Second Hand

3. {T2}T2≡(T1)xc·m−xc

imod p

Fig. 5. Check Phase.

3.1. System Initializing Phase

3.3. Forwarding Phase

,QTXLULQJ3KDVH

3.4. Checking Phase

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Purchaser receives parameter T2by third party inspec-

tor; purchaser pays for inspector after the information of

inspection has conﬁrmed. Purchaser generates T3and

then returns to inspector, see Equation (8) and Figure 6.

T3≡(T2)·(rb)ka(mod p).(8)

4. {T3}

Puchaser Third Party

T3≡(T2)·(rb)kamod p

Second Hand

Fig. 6. Paying Phase.

Purchaser authorized inspector to buy the second hand

car, namely inspector delegates purchaser to buy the car.

Inspector calculates T4and transmits to merchant, see

Equation (9) and Figure 7.

T4≡(T3)kc·(T2)−kc(mod p).(9)

5. {T4}

Puchaser Third Party

T4≡(T3)kc·(T2)−kcmod p

Second Hand

Fig. 7. Conﬁrming Phase.

Merchant passed inspector’s conﬁrmation, he then

delivers T5to purchaser before uses semi key k−1

bto

sign T4, see Equation (10) and Figure 8.

T5≡(T4)k−1

b(mod p).(10)

6. {T5}

Puchaser Third Party

T5≡(T4)k−1

b(mod p)

Second Hand

Fig. 8. Conﬁrming Phase.

If the merchant does not collude with a third party, the

merchant can fetch rkc

aafter recovered T4by inspector,

the proof see Equation (11) and (12).

≡rka

c(mod p).(11)

Proof.

≡(T4)k−1

b(modp)

≡[(rka

b)kc]k−1

b(mod p)

≡rkc

a(mod p)

≡rka

c(mod p).(12)

By Equation (12), the proof is ﬁnished.

Purchaser

Third

Second

3. T2

4. T3

1. {Sa, mi}

2. {T1, mi}

5. T4

6. T5Hand

(Merchant)

Party

Inspector

Fig. 9. A Concept of Used Car Scheme Based on Cryptographic

Protocol.

In this section, we discuss two types of security: theo-

retical security and practical security. And then describes

three deﬁnitions, three lemmas, and three scenarios of

attack model.

Deﬁnition 1. Discrete Logarithm Problem (DLP)

As known parameters {p, g, yi}where the formula

yi≡gxi(mod p), it is very hard to ﬁnd the pri-

vate key xiwhile prime approaching inﬁnite. Based

on this assumption of computation and condition, it is

called solving the discrete logarithm problem (Solving

Discrete Logarithm Problem) [53]. The current public

key cryptosystem based on discrete logarithm has value

parameters that are greater than 1024 bit length or 2048

bit length.

Deﬁnition 2. Computation Difﬁe-Hellman Problem

(CDHP)

The Computation Difﬁe-Hellman Problem [54]is derived

on the Difﬁe-Hellman key exchange principle (Difﬁe

Hellman Key Exchange) [55]. The main ideas are de-

scribed as follows: Given {g, gx, gy}to ﬁnd gxy.

Here, gis known parameter, the xand yare unknown

parameters.

Deﬁnition 3. Decisional Difﬁe-Hellman Problem

(DDHP)

The Decisional Difﬁe-Hellman Problem [56] is a

variant of the Difﬁe-Hellman computation problem.

3.5. Paying Phase

3.6. Confirming Phase

3.7. Delivering Phase

3.8. Purchaser Verifying Phase

4. Security Analysis

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Given {g, gx, gy, gz}, to ﬁnd the Zpis satisﬁed

z=xy. Given {g, gx, gy}, to ﬁnd gxy . Here the

parameter gis known, and the parameters {x, y, z}

are all unknown.

We suppose adversary is holding unlimited computing

resources and time, he then can offenses any target in-

formation system what he wants. If the system is secure

against this attack, this is to say theoretical security, also

called unconditional security.

Lemma 1. If purchaser is honest, the

Equations (4), (5), (8) and (12) would be correct.

Proof. As known from Equation (4) since Sa≡ya·rc

(mod p). The merchant can verify Equation (13) since

ya·rc

≡Sa(mod p).(13)

If purchaser cheated, it does not hold to the Equa-

tion (13). This stage is for the merchant to verify the

purchaser. Another veriﬁcation method, the merchant

produced T1, he can check

≡yxb

a·mi(mod p).(14)

If it does not hold, it means the purchaser is a liar.

Lemma 2. If merchant is honest, the Equations (5), (6)

and (10) would be correct.

Proof. In forwarding phase, the merchant uses his secret

key xbto produce T1; then in checking phase, the third

party also uses his secret key xchonestly, the T2is

the starting point of the agreement signed by the three

sides such as purchaser, merchant and the third party

inspector. In T3phase, the purchaser has signed mark

“r−ka

b” where it express both sides i.e. purchaser and

merchant. In T4phase, the third party inspector uses his

semi-key kcand −kcfor his agency right. Turn around

to T5phase, it became (ra)kc. It showed the merchant

honestly; otherwise, it is a contradiction.

Lemma 3. If third party inspector honest, the Equa-

tions (7), (9) and (11) would be correct.

Proof. The third party inspector uses his key xc,kcto

all, then the Equations (15), (16) and (17) do not hold.

T2≡yxbxc

a(mod p),(15)

since

T4≡rkakc

b(mod p),(16)

and

T5≡rkc

a(modp).(17)

Obviously, those are contradicts to Lemma 1 and

Lemma 2. Thus, the third party inspector is honest to

all.

The practical security is also called conditional se-

curity. If a system depends on the computational cost to

defense any cryptanalysis, we say computational security

or conditional security.

Scenario 1: Outside attack

If attacker tries to ﬁnd the private key xaby ya, modulus

pand an element primitive generator gof Z∗

p. The at-

tacker would challenge the DLP which describes through

Deﬁnition 1.

Scenario 2: Insider attack

We suppose the attacker came from merchant side,

namely one of employee instead of his manager to use

a fake secret key x′

bby pass forwarding phase.

T′

1≡(Sa)x′

b·mi·(rc)−x′

b(mod p).(18)

And then cheated third party inspector to calculate

T′

2≡(T′

1)xc·m−xc

i≡(ya)x′

b·xc(mod p).(19)

Consequently, purchaser replies T′

3to third party inspec-

tor as following:

T′

3≡T′

2·rka

b≡(ya)x′

b·xc·rka

b(mod p).(20)

Third party received T′

3and calculated T′

4, prompt

T′

4≡(T′

3)kc·(T′

2)−kc(mod p).(21)

Although the insider deceived third party inspector and

successfully passed T′

1to T′

4phases. However, the insider

can not pass T′

5since he did not own the original semi-

key kb, therefore he would fail and stop on delivering

phase since he faked semi-key k′

−1to ﬁnd

T56≡ T′

5≡(T′

4)k′−1

b(mod p).(22)

Thus, the insider can not cheat purchaser successfully

on the ﬁnal stage. The concept of description is shown

in Figure 10.

Scenario 3: Message leakage issue

As known from Equation (5), the original message

had digitized and hashed, if insider wants to recover

Mi, it is very hard since insider challenges one-way

hash functions [57] such as two properties: re-image

resistance and collision resistance.

4.1. Theoretical Security

4.2. Practical Security

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Purchaser

Third

Second

3. T′

4. T′

1. {Sa, mi}

2. {T′

1, mi}

5. T′

6. T′

5Hand

(Merchant)

Party

Inspector

Fig. 10. Simulating insider attack model.

In this paper the authors propose a used car trading

system based on blockchain and cryptography technol-

ogy. Our scheme is different from other literatures in the

following points: (1) The method we proposed is very

speciﬁc, not just a concept. According to this algorithm,

we can realize the code and transform it into an infor-

mation system. (2) We use blockchain and cryptography

technology to protect consumers’ individual privacy. (3)

This is an anonymity scheme. (4) We give three deﬁni-

tions, three lemmas, three simulated attack scenarios, and

twenty-two mathematical formulas, which perfectly pro-

vide strong theoretical support for our scheme; especially

in the provably secure. There is another key point, we

prevent third-party inspector colluded with seller to cheat

buyer; or third-party inspector colluded with buyer to

cheat seller. These are not mentioned in other literatures,

It is the highlight and contribution of this paper.

The authors would like to thank the reviewers for

their comments that help improve the manuscript. This

work is partially supported by the project number

X2021110650493 from College Students Innovation and

Entrepreneurship Training Program of China by Qingdao

University.

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5. Conclusion

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WSEAS TRANSACTIONS on COMPUTER RESEARCH

DOI: 10.37394/232018.2022.10.14

Chi Huang, Chenglian Liu, Sonia C-I Chen

E-ISSN: 2415-1521

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Volume 10, 2022