Authenticated key exchange protocol based on two hard problems

In this paper, we propose a new secured key exchange protocol which is based on two hard problems. The security proofs for the new protocol confirm their novelty and security.

AUTHENTICATED KEY EXCHANGE PROTOCOL

BASED ON TWO HARD PROBLEMS

Do Viet Binh*

Abstract: Arazi was the first author to propose the integration of a key exchange

protocol with a digital signature algorithm Other authors have subsequently proposed methods to increase the level of security and achieve the necessary properties of authenticated key exchange protocols However, these proposals exhibit several weaknesses and the majority of these protocols are based only on a single hard problem In this paper, we propose a new secured key exchange protocol which is based on two hard problems The security proofs for the new protocol confirm their novelty and security

Key words: Authentication, Hard problem, Key exchange

1 INTRODUCTION

The Diffie-Hellman key exchange protocol does not guarantee authentication between the two parties of the protocol [1] Based on this fact, it is possible to develop a new key exchange protocol by integrating the Diffie-Hellman key exchange protocol (DH) into a digital signature scheme (DSA) This inherits the advantages of DH and DSA when they are deployed in practice In paper [2], Arazi proposed improving the security of a key exchange protocol by integrating DH and DSA However, later research [3], [4], [8] has highlighted several drawbacks to this method Thus, other authors investigated ways to further improve the level of security and to achieve the required properties of authenticated key exchange (AKE) protocols [4-6], [9-11] Nevertheless, several limitations remain, and the majority of these proposals are based only on a hard problem [2-6], [8-11] This paper proposes a new secured authenticated key exchange protocol based on two hard problems The structure of the rest of the paper is as follows Section 2 presents an overview of related work in this area of study Section 3 briefly describes the digital signature scheme [7], which is the foundation for the new secure key exchange protocol based on two hard problems (DH-MM-KE) and provides security proofs for the proposed protocol The performance result of new protocol is reported in Section 4 Section 5 summarizes the paper

2 RELATED WORK

In 1993, Arazi designed a key exchange protocol with the idea of integrating the DH protocol into the DSA scheme [2] However, some other authors [3], [4], [8] have pointed out several weaknesses in Arazi’s scheme, such as small subgroup attacks, known key attacks, unknown key attacks, and key replay attacks Therefore, L.Harn [4] extended Arazi’s scheme to securely integrate the DH protocol into the DSA scheme Harn suggested three protocol alternatives for different types of application The key exchange protocols proposed by Harn hadthree important features: known-key security, unknown key-share security, and key replay security These three security properties are standard requirements for any authenticated key exchange protocol However, these protocols fail

to provide the other two security properties: forward secrecy and key freshness [9] In

2005, Phan [9] proposed a new protocol that had forward secrecy In this protocol, even if the long-term private key of one side is exposed, the previous session key cannot be determined In 2010, J Liu and J Li [6] suggested another protocol that overcomes the weaknesses of Phan’s key exchange protocol Liu and Li's protocol was more secure than Phan's protocol while still maintaining its advantages In 2014, D Sow et al [10], pointed

out weaknesses in the protocol suggested by Jeong et al [5] and presented their improvement However, all of these key exchange protocols are only based on one hard problem (the discrete logarithm problem – DLP)

3 DESIGN OF THE DH-MM-KE PROTOCOL 3.1 Signature scheme based on two hard problems

This section provides an overview of a digital signature scheme based on two hard problems [11] (called the MM scheme) This scheme uses a prime modulo p with the

values and are the private key and the public key, respectively, and are generated as in the RSA cryptosystem [26] is selected to be a small number (with a size between 16 and

1) Key generation:

The public key is ( , , ) The private key is ( , )

2) Signature generation:

The signature is the pair ( , )

3) Signature verification:

signature is rejected as invalid

3.2 DH-MM-KE protocol

This section proposes a new protocol, the Diffie Hellman–MM–Key Exchange protocol (DH-MM-KEP)

3.2.1 DH-MM-KEP design

several values of and check if it is a generator in both groups

We assume that user A wants to share the secret session key with user B Then:

1) A does the following:

2) B does the following:

3) A does the following:

4) B does the following:

A scenario for DH-MM-KEP is depicted in Figure 1

User A ( , , , , ) User B ( , , )

3 =

Fig 1 DH-MM-KE protocol

3.2.2 Security of the DH-MM-KE protocol

Property 1 DH-MM-KE has perfect forward secrecy

Proof The session key for the direction A to B is computed by A as

while it is computed by B as

Property 2 DH-MM-KE has key independency

Proof In DH-MM-KE, A and B compute = ( || ) and

Property 3 DH-MM-KE is secure against session state reveal (SSR) attacks

Proof If an attacker acquires the random numbers used by user A and user B, the

computed as follows:

Thus, DH-MM-KE is secure against session state reveal attacks

Property 4 DH-MM-KE is secure against key-compromise impersonation attacks

Proof This protocol uses the mutual authentication between two entities A and B

Thus, authentication fails if the attacker is active and does not simultaneously know

to compute the session key directly, assuming that he knows the long-term private key of

impersonation attacks

Property 5 DH-MM-KE is secure against unknown key-share attacks

Proof Key confirmation can prevent unknown key-share attacks User B confirms the

( , )

( , , , , ) Because this shared secret key is a one-way hash function of

message is not replay and knows that it is indeed from user B B could also do something

Property 6 DH-MM-KE is secure based on two hard problems

Proof In DH-MM-KE, A and B compute = ( || ) and

Therefore, DH-MM-KE is secure which based on two hard problems

4 EXPERIMENT

The time consumption of the proposed protocol is strongly depends on length of choosen Therefore, we operate proposed protocol with several length of

The PC that we use to test running jdk1.8 and having two cores of Intel CPU with processing speed of 1.6 GHz and primary memory capacity of 8GB operating with Windows 10

Table 1 Experiment result

5 CONCLUSION

We have proposed a authenticated key exchange protocol based on two hard problems Therefore, they have a higher level of security than existing protocols

The security of these protocols have been verified, and the existence of all the necessary properties required for a general security protocol has been proven This protocol can also be applied in practice

REFERENCES

[1] Diffie W, Hellman M (1976), “New Directions in Cryptography.IEEE Transactions

on Information Theory”; 22: 644-654

[2] Arazi B (1993), “Integrating a key distribution procedure into the digital signature

standard” Electronics Letters; 29: 966-967

[3] Brown D, Menezes A (2001), “A Small Subgroup Attack on Arazi's Key Agreement

Protocol” Bulletin of the ICA;37: 45-50

[4] Harn L, Mehta M, Hsin WJ (2004), “Integrating Diffie-Hellman key exchange into

the digital signature algorithm (DSA)” IEEE Communications Letters; 8: 198-200

[5] Jeong IR, Kwon JO, Lee DH (2007), “Strong Diffie-Hellman DSA Key Exchange”

IEEE Communications Letters; 11: 432-433

[6] Liu J, Li J (2010), “A Better Improvement on the Integrated Diffie-Hellman - DSA

Key Agreement Protocol” IEEE Communications Letters; 11: 114-117

[7] Minh NH, Binh DV, Giang NT, Moldovyan NA (2012), “Blind signature protocol

based on difficulty of simultaneous solving two difficult problems” Applied

Mathematical Sciences; 6: 6903 – 6910

[8] Nyberg K, Rueppel R (1994), “Weaknesses in some recent key agreement

protocols” Electronics Letters; 30: 26-27

[9] Phan RCW (2005), “Fixing the integrated Diffie-Hellman DSA key exchange

protocol” IEEE Communications Letters; 9: 570-572

[10] Sow D, Camara1 MG, Sow D (2014), “Attack on “Strong Diffie-Hellman-DSA

KE” and Improvement” Journal of Mathematics Research; 6: 70-75

[11] Viet HV, Minh NH, Truyen BT, Nga NT (2013), “Improving on the integrated

Diffie-Hellman-DSA key agreement protocol” In: 2013 Third World Congress on

Information and Communication Technologies (WICT 2013); 15-18 December 2013; Hanoi, Vietnam: pp 106-110

TÓM TẮT

PHÁT TRIỂN GIAO THỨC TRAO ĐỔI KHÓA CÓ XÁC THỰC

DỰA TRÊN HAI BÀI TOÁN KHÓ

Arazi là người đầu tiên đề xuất tích hợp chữ ký số và giao thức trao đổi khóa Các tác giả khác cũng đề xuất các giao thức nhằm nâng cao tính bảo mật và đạt được các tính chất an toàn cần thiết của giao thức trao đổi khóa có xác thực Tuy nhiên, các giao thức này tồn tại nhiều điểm yếu và đa phần chỉ dựa trên một bài toán khó Trong bài báo này, xin được đề xuất một giao thức trao đổi khóa an toàn dựa trên hai bài toán khó và chứng minh tính bảo mật của giao thức mới này

Từ khóa: Xác thực, Bài toán khó, Trao đổi khóa

Nhận bài ngày 28 tháng 6 năm 2017 Hoàn thiện ngày 28 tháng 7 năm 2017 Chấp nhận đăng ngày 18 tháng 8 năm 2017

Địa chỉ: Military Information Technology Institute, Hanoi, Vietnam;

*

Email: binhdv@gmail.com