In this paper, we present two explicit invalid-curve attacks on the genus 2 hyperelliptic curve over a finite field. First, we propose two explicit attack models by injecting a one-bit fault in a given divisor. Then, ...In this paper, we present two explicit invalid-curve attacks on the genus 2 hyperelliptic curve over a finite field. First, we propose two explicit attack models by injecting a one-bit fault in a given divisor. Then, we discuss the construction of an invalid curve based on the faulted divisor. Our attacks are based on the fact that the Hyperelliptic Curve Scalar Multiplication (HECSM) algorithm does not utilize the curve parameters and We consider three hyperelliptic curves as the attack targets. For curve with security level 186 (in bits), our attack method can get the weakest invalid curve with security level 42 (in bits); there are 93 invalid curves with security level less than 50. We also estimate the theoretical probability of getting a weak hyperelliptic curve whose cardinality is a smooth integer. Finally, we show that the complexity of the fault attack is subexponential if the attacker can freely inject a fault in the input divisor. Cryptosystems based on the genus 2 hyperelliptic curves cannot work against our attack algorithm in practice.展开更多
To achieve privacy and authentication sinmltaneously in mobile applications, various Three-party Password-authenticated key exchange （3PAKE） protocols have been proposed. However, some of these protocols are vulnera...To achieve privacy and authentication sinmltaneously in mobile applications, various Three-party Password-authenticated key exchange （3PAKE） protocols have been proposed. However, some of these protocols are vulnerable to conventional attacks or have low efficiency so that they cannot be applied to mobile applications. In this paper, we proposed a password-authenticated multiple key exchange protocol for mobile applications using elliptic curve cryptosystem. The proposed protocol can achieve efficiency, reliability, flexibility and scalability at the same time. Compared with related works, the proposed protocol is more suitable and practical for mobile applications.展开更多
Wireless Sensor Networks (WSNs) are being deployed for a wide variety of applications and the security problems of them have received considerable attention. Considering the limitations of power, computation capabilit...Wireless Sensor Networks (WSNs) are being deployed for a wide variety of applications and the security problems of them have received considerable attention. Considering the limitations of power, computation capability and storage resources, this paper proposed an efficient defense against collusion scheme based on elliptic curve cryptography for wireless sensor networks in order to solve the problems that sensor node-key leaking and adversaries make compromised nodes as their collusions to launch new attack. In the proposed scheme, the group-key distribution strategy is employed to compute the private key of each sensor node, and the encryption and decryption algorithms are constructed based on Elliptic Curve Cryptography (ECC). The command center (node) only needs to broadcast a controlling header with three group elements, and the authorized sensor node can correctly recover the session key and use it to decrypt the broadcasting message. Analysis and proof of the proposed scheme's efficiency and security show that the proposed scheme can resist the k-collusion attack efficiently.展开更多
基金supported by the National Basic Research Program （973 Program）under Grant No.2013CB834205 the National Natural Science Foundation of China under Grant No.61272035 the Independent Innovation Foundation of Shandong University under Grant No.2012JC020
文摘In this paper, we present two explicit invalid-curve attacks on the genus 2 hyperelliptic curve over a finite field. First, we propose two explicit attack models by injecting a one-bit fault in a given divisor. Then, we discuss the construction of an invalid curve based on the faulted divisor. Our attacks are based on the fact that the Hyperelliptic Curve Scalar Multiplication (HECSM) algorithm does not utilize the curve parameters and We consider three hyperelliptic curves as the attack targets. For curve with security level 186 (in bits), our attack method can get the weakest invalid curve with security level 42 (in bits); there are 93 invalid curves with security level less than 50. We also estimate the theoretical probability of getting a weak hyperelliptic curve whose cardinality is a smooth integer. Finally, we show that the complexity of the fault attack is subexponential if the attacker can freely inject a fault in the input divisor. Cryptosystems based on the genus 2 hyperelliptic curves cannot work against our attack algorithm in practice.
基金Acknowledgements This work was supported by the National Natural ScienceFoundation of China under Grants No. 60873191, No. 60903152, No. 60821001, and the Beijing Natural Science Foundation under Grant No. 4072020.
文摘To achieve privacy and authentication sinmltaneously in mobile applications, various Three-party Password-authenticated key exchange （3PAKE） protocols have been proposed. However, some of these protocols are vulnerable to conventional attacks or have low efficiency so that they cannot be applied to mobile applications. In this paper, we proposed a password-authenticated multiple key exchange protocol for mobile applications using elliptic curve cryptosystem. The proposed protocol can achieve efficiency, reliability, flexibility and scalability at the same time. Compared with related works, the proposed protocol is more suitable and practical for mobile applications.
基金Supported by the Six Great Talent Peak Plan of Jiangsu Province (No.06-E-044)the "Qinlan Project" Plan of Jiangsu Province 2006
文摘Wireless Sensor Networks (WSNs) are being deployed for a wide variety of applications and the security problems of them have received considerable attention. Considering the limitations of power, computation capability and storage resources, this paper proposed an efficient defense against collusion scheme based on elliptic curve cryptography for wireless sensor networks in order to solve the problems that sensor node-key leaking and adversaries make compromised nodes as their collusions to launch new attack. In the proposed scheme, the group-key distribution strategy is employed to compute the private key of each sensor node, and the encryption and decryption algorithms are constructed based on Elliptic Curve Cryptography (ECC). The command center (node) only needs to broadcast a controlling header with three group elements, and the authorized sensor node can correctly recover the session key and use it to decrypt the broadcasting message. Analysis and proof of the proposed scheme's efficiency and security show that the proposed scheme can resist the k-collusion attack efficiently.
