Since the end of the 1990s,cryptosystems implemented on smart cards have had to deal with two main categories of attacks:side-channel attacks and fault injection attacks.Countermeasures have been developed and validat...Since the end of the 1990s,cryptosystems implemented on smart cards have had to deal with two main categories of attacks:side-channel attacks and fault injection attacks.Countermeasures have been developed and validated against these two types of attacks,taking into account a well-defined attacker model.This work focuses on small vulnerabilities and countermeasures related to the Elliptic Curve Digital Signature Algorithm(ECDSA)algorithm.The work done in this paper focuses on protecting the ECDSA algorithm against fault-injection attacks.More precisely,we are interested in the countermeasures of scalar multiplication in the body of the elliptic curves to protect against attacks concerning only a few bits of secret may be sufficient to recover the private key.ECDSA can be implemented in different ways,in software or via dedicated hardware or a mix of both.Many different architectures are therefore possible to implement an ECDSA-based system.For this reason,this work focuses mainly on the hardware implementation of the digital signature ECDSA.In addition,the proposed ECDSA architecture with and without fault detection for the scalar multiplication have been implemented on Xilinxfield programmable gate arrays(FPGA)platform(Virtex-5).Our implementation results have been compared and discussed.Our area,frequency,area overhead and frequency degradation have been compared and it is shown that the proposed architecture of ECDSA with fault detection for the scalar multiplication allows a trade-off between the hardware overhead and the security of the ECDSA.展开更多
Based on the analysis of elliptic curve digital signature algorithm（ECDSA）,aiming at multilevel proxy signature in which the original signer delegates the digital signature authority to several proxies and its secur...Based on the analysis of elliptic curve digital signature algorithm（ECDSA）,aiming at multilevel proxy signature in which the original signer delegates the digital signature authority to several proxies and its security demands, a new multilevel proxy signature scheme based on elliptic curve discrete logarithm problem （ECDLP） is presented and its security are proved.展开更多
Proxy signature is a special digital signature which enables a proxy signer to sign messages on behalf of the original signer. This paper proposes a strongly secure proxy signature scheme and a secure multi-proxy sign...Proxy signature is a special digital signature which enables a proxy signer to sign messages on behalf of the original signer. This paper proposes a strongly secure proxy signature scheme and a secure multi-proxy signature scheme based on elliptic curve cryptosystem. Contrast with universal proxy signature schemes, they are secure against key substitute attack even if there is not a certificate authority in the system, and also secure against the original signer＇s forgery attack. Furtherlnore, based on the elliptic curve cryptosystem, they are more efficient and have smaller key size than other system. They can be used in electronics transaction and mobile agent environment.展开更多
The concept of multisignature, in which multiple signers can cooperate to sign the same message and any verifier can verify the validity of the multi-signature, was first introduced by Itakura and Nakamura. Several mu...The concept of multisignature, in which multiple signers can cooperate to sign the same message and any verifier can verify the validity of the multi-signature, was first introduced by Itakura and Nakamura. Several multisignature schemes have been proposed since. Chen et al. proposed a new digital multi-signature scheme based on the elliptic curve cryptosystem recently. In this paper, we show that their scheme is insecure, for it is vulnerable to the so-called active attacks, such as the substitution of a ＂false＂ public key to a ＂true＂ one in a key directory or during transmission. And then the attacker can sign a legal signature which other users have signed and forge a signature himself which can be accepted by the verifier.展开更多
The classical RSA is vulnerable to low private exponent attacks （LPEA） and has homomorphism. KMOV based on elliptic curve En（a,b） over Zn can resist LPEA but still has homomorphism. QV over En（a,b） not only can ...The classical RSA is vulnerable to low private exponent attacks （LPEA） and has homomorphism. KMOV based on elliptic curve En（a,b） over Zn can resist LPEA but still has homomorphism. QV over En（a,b） not only can resist LPEA but also has no homomorphism. However, QV over En（a,b） requires the existence of points whose order is Mn= 1cm{#Ep（a,b）, #Eq（a,b）}. This requirement is impractical for all general elliptic curves. Besides, the computation over En（a,b） is quite complicated. In this paper, we further study conic curve Cn（a,b） over Zn and its corresponding properties, and advance several key theorems and corollaries for designing digital signature schemes, and point out that Cn（a,b） always has some points whose order is Mn： 1cm{#Ep（a,b）,#Eq（a,b））. Thereby we present an improved QV signature over Cn（a,b）, which inherits the property of non-homomorphism and can resist the Wiener attack. Furthermore, under the same security requirements, the improved QV scheme is easier than that over En（a,b）, with respect plaintext embedding, inverse elements computation, points computation and points＇ order calculation. Especially, it is applicable to general conic curves, which is of great significance to the application of QV schemes.展开更多
基金The funding was provided by the Deanship of Scientific Research at King Khalid University through Research Group Project[grant number RGP.1/157/42].
文摘Since the end of the 1990s,cryptosystems implemented on smart cards have had to deal with two main categories of attacks:side-channel attacks and fault injection attacks.Countermeasures have been developed and validated against these two types of attacks,taking into account a well-defined attacker model.This work focuses on small vulnerabilities and countermeasures related to the Elliptic Curve Digital Signature Algorithm(ECDSA)algorithm.The work done in this paper focuses on protecting the ECDSA algorithm against fault-injection attacks.More precisely,we are interested in the countermeasures of scalar multiplication in the body of the elliptic curves to protect against attacks concerning only a few bits of secret may be sufficient to recover the private key.ECDSA can be implemented in different ways,in software or via dedicated hardware or a mix of both.Many different architectures are therefore possible to implement an ECDSA-based system.For this reason,this work focuses mainly on the hardware implementation of the digital signature ECDSA.In addition,the proposed ECDSA architecture with and without fault detection for the scalar multiplication have been implemented on Xilinxfield programmable gate arrays(FPGA)platform(Virtex-5).Our implementation results have been compared and discussed.Our area,frequency,area overhead and frequency degradation have been compared and it is shown that the proposed architecture of ECDSA with fault detection for the scalar multiplication allows a trade-off between the hardware overhead and the security of the ECDSA.
基金Supported by the National Natural Science Foun-dation of China (70471031)
文摘Based on the analysis of elliptic curve digital signature algorithm（ECDSA）,aiming at multilevel proxy signature in which the original signer delegates the digital signature authority to several proxies and its security demands, a new multilevel proxy signature scheme based on elliptic curve discrete logarithm problem （ECDLP） is presented and its security are proved.
文摘Proxy signature is a special digital signature which enables a proxy signer to sign messages on behalf of the original signer. This paper proposes a strongly secure proxy signature scheme and a secure multi-proxy signature scheme based on elliptic curve cryptosystem. Contrast with universal proxy signature schemes, they are secure against key substitute attack even if there is not a certificate authority in the system, and also secure against the original signer＇s forgery attack. Furtherlnore, based on the elliptic curve cryptosystem, they are more efficient and have smaller key size than other system. They can be used in electronics transaction and mobile agent environment.
基金This work is supported by the National Natural Science Foundation of China under Grant No. 90304014 and the National Grand Fundamental Research 973 Program of China under Grant No. 2003CB314805.
文摘The concept of multisignature, in which multiple signers can cooperate to sign the same message and any verifier can verify the validity of the multi-signature, was first introduced by Itakura and Nakamura. Several multisignature schemes have been proposed since. Chen et al. proposed a new digital multi-signature scheme based on the elliptic curve cryptosystem recently. In this paper, we show that their scheme is insecure, for it is vulnerable to the so-called active attacks, such as the substitution of a ＂false＂ public key to a ＂true＂ one in a key directory or during transmission. And then the attacker can sign a legal signature which other users have signed and forge a signature himself which can be accepted by the verifier.
基金Supported by the National Natural Science Foundation of China (Grant No. 10128103)
文摘The classical RSA is vulnerable to low private exponent attacks （LPEA） and has homomorphism. KMOV based on elliptic curve En（a,b） over Zn can resist LPEA but still has homomorphism. QV over En（a,b） not only can resist LPEA but also has no homomorphism. However, QV over En（a,b） requires the existence of points whose order is Mn= 1cm{#Ep（a,b）, #Eq（a,b）}. This requirement is impractical for all general elliptic curves. Besides, the computation over En（a,b） is quite complicated. In this paper, we further study conic curve Cn（a,b） over Zn and its corresponding properties, and advance several key theorems and corollaries for designing digital signature schemes, and point out that Cn（a,b） always has some points whose order is Mn： 1cm{#Ep（a,b）,#Eq（a,b））. Thereby we present an improved QV signature over Cn（a,b）, which inherits the property of non-homomorphism and can resist the Wiener attack. Furthermore, under the same security requirements, the improved QV scheme is easier than that over En（a,b）, with respect plaintext embedding, inverse elements computation, points computation and points＇ order calculation. Especially, it is applicable to general conic curves, which is of great significance to the application of QV schemes.
