基于FCSR的流密码设计与分析
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摘要
带进位的反馈移位寄存器(FCSR,Feedback with Carry Shift Registers)与线性反馈移位寄存器(LFSR,Linear Feedback Shift Registers)具有相似的结构,但是其使用带进位加法使得生成序列天生具有极高的线性复杂度。由于当前使用非线性序列源设计流密码已经成为主流,FCSR作为一类非常重要的非线性序列源,利用其设计流密码自然成为了热点。
本文主要研究如何利用FCSR设计性质优秀的密钥流生成器,在研究FCSR的性质与基于FCSR的密钥流生成器F-FCSR-Hv2的基础之上,先对F-FCSR-Hv2等基于滤波的密钥流生成器进行改进,提出了改进方案一“联合的F-FCSR密钥流生成器”与“全动态滤波密钥流生成器DF-FCSR-8";然后用FCSR替代LFSR进行钟控设计,得到具有良好性质的钟控密钥流生成器；再综合利用前面设计的密钥流生成器得到了钟控全动态滤波密钥流生成器；最后研究了用于RFID(Radio Frequency Identification)射频识别技术的轻量级认证算法SQUASH,在此基础上设计出基于FCSR的用于RFID的轻量级认证算法SQUASH+和与加密结合的算法SQUASH+DF-FCSR。
主要的结果如下：
1.研究了基于FCSR滤波的密钥流生成器F-FCSR-Hv2,分析了Hell-Johansson攻击对FCSR滤波方案攻击的思想,在此基础上提出了一个基于FCSR滤波的改进方案一联合的F-FCSR密钥流生成器,以增加寄存器为代价,在保证吞吐率和密钥流良好统计特性的基础上,还可以抵抗Hell-Johansson攻击和其他攻击。
2.提出了一个全动态滤波密钥流生成器DF-FCSR-8,该生成器改变了原来滤波密钥流生成器在产生滤波输出时使用静态滤波的设计思路,引入了全动态滤波器,使得攻击者不能获取滤波器的滤波向量,无法列出足够的线性方程组,从而可以抵抗Hell-Johansson攻击,其他分析表明DF-FCSR-8可以抵抗相关攻击和代数攻击等攻击；测试表明密钥流具有良好统计特性。
3.提出基于FCSR的钟控密钥流生成器,设计了基于FCSR的停走钟控密钥流生成器和基于FCSR的交替钟控密钥流生成器,给出了两个生成器的参数以及生成序列的周期、线性复杂度下界,并分析了抵抗Hell-Johansson等攻击和其他攻击的能力等等,结果表明基于FCSR的停走钟控密钥流生成器具有大周期高线性复杂度下界,但是统计特性不够好,而基于FCSR的交替钟控密钥流生成器具有大周期、高线性复杂度下界、统计特性良好、且能抵抗Hell-Johansson攻击和其他攻击。
4.综合了基于FCSR的全动态密钥流生成器和钟控密钥流生成器的特点,提出两个基于FCSR的全动态钟控密钥流生成器一基于FCSR的全动态停走钟控密钥流生成器SGDF-FCSR-8和基于FCSR的全动态交替钟控密钥流生成器ASDF-FCSR-8。给出了设计参数、生成序列的周期以及线性复杂度下界,测试了统计特性,并给出了ASDF-FCSR-8抵抗Hell-Johansson攻击以及其他攻击的能力,结果表明,虽然SGDF-FCSR-8统计特性比基于FCSR的停走钟控密钥流生成器的统计特性好,但仍未能通过全部的伪随机性测试；而ASDF-FCSR-8在具有交替钟控密钥流生成器大周期、高线性复杂度、良好统计特性的基础之上,提高了吞吐率。
5.研究了应用于RFID环境下的轻量级认证算法SQUASH,在标准SQUASH基础上利用FCSR对其进行改进,提出了SQUASH+算法,该算法可以在保证安全性的基础上更高效的完成应答的计算。综合SQUASH+和基于FCSR的流密码的特点,提出了一个将认证与全动态滤波密钥流生成器相结合的轻量级混合算法-SQUASH+DF-FCSR,该算法利用FCSR作为计算数据发生器,在认证完成的同时也将流密码初始化过程完成,进而进行加密,使得FCSR寄存器同时供认证和加密使用,节约了空间,提高了效率,是一个在RFID环境下实用的轻量级认证加密混合算法。
本文设计的密钥流生成器可用一些资源受限的环境中,如于传感器网络、Ad-Hoc无线通信网络以及RFID环境中。
The Feedback with Carry Shift Registers (FCSR for short) has the similar structure with Linear Feedback Shift Registers (LFSR for short), but its generated sequence has high linear complexity by using addition with carry. Now it is very popular to design the stream cipher by means of nonlinear components. So, as an important nonlinear component, the FCSR is playing a key role in stream cipher design.
This thesis focuses on the usage of FCSR as keystream generator in stream cipher. Firstly based on the properties of FCSR, we study a keystream generator-F-FCSR-Hv2and improve it in two ways, and then propose two generators—Combined F-FCSR keystream generator and Dynamic filter keystream generator DF-FCSR-8. Next, we use FCSR in clock control instead of LFSR, which show better property than those based on LFSR. Combining the dynamic filter generator and clock controlled generator, we build a new type of keystream generator. Finally, aiming the Radio Frequency Identification (RFID for short) technology and the light weight certification scheme-SQUASH, we present a new certification scheme based on FCSR called SQUASH+, and a scheme called SQUASH+DF-FCSR for both certification and encryption, which is combination of the SQUASH+and the light weighted DF-FCSR.
The main result of this thesis is as follows:
1. Based on the properties of F-FCSR-Hv2generator and analysis of the Hell-Johansson attack which is an effective attack for F-FCSR-Hv2, an improved generator for filtered FCSR generator called Combined F-FCSR generator is presented. This generator maintains high output rate and good property at the cost of increasing more registers, and is resistant to Hell-Johansson attack and other attacks as well.
2. A new generator named dynamic filtered generator DF-FCSR-8is proposed. This generator uses dynamic filter as the filter of an FCSR's main register instead of the original static one. Because the filter is changed each time, the attacker cannot acquire enough linear functions so that this generator can resist Hell-Johansson attack. Other analyses indicate that DF-FCSR-8can withstand the correlation attack, algebraic attack and other attacks. While the test shows that DF-FCSR-8has good statistic characteristics.
3. Using FCSR to construct clock controlled generator instead of LFSR, two genera-tors:Stop and Go generator based on FCSR and Alternating Step generator based on FCSR, are proposed. This thesis gives the parameters of those generators, the period of generated sequence, lower bound of linear complexity, the ability against Hell-Johansson attack and other attacks, and statistic properties. Those results show that Stop and Go generator has a large period and high lower bound of linear complexity, but less good statistic property, while Alternating Step Generator has large period, high lower bound of linear complexity, good statistic properties, and ability to against Hell-Johansson attack and other attacks.
4. With the combination of dynamic filtered generator and clock controlled generator, two generators:SGDF-FCSR-8and ASDF-FCSR-8, are developed. The former is a combi-nation of Stop and Go generator and dynamic filtered generator; the later is a combination of Alternating Step generator and dynamic filtered generator. This thesis gives the parameters, the period of generated sequence, lower bound of linear complexity, and the ability against Hell-Johansson attack and other attacks, and also tests statistic properties of both generators. Although SGDF-FCSR-8has better statistic property than Stop and Go generator, it does not pass all the tests. WhereasASDF-FCSR-8improves the output rate based on a large period of Alternating Step Generator, and also has high lower bound on linear complexity and good statistic properties.
5. Through the investigation of a lightweight certification scheme, SQUASH, which is used in RFID environment, an improved version SQUASH+is given based on FCSR and standard SQUASH in this thesis. This scheme can complete the computation much more effi-ciently while ensuring the security. After that, considering the SQUASH+and the properties of stream-cipher based on FCSR, this thesis give a lightweight scheme named SQUASH+DF-FCSR which uses the FCSR as the data generator. The calculation process for certification is also initializing the keystream generator, and then encrypts the data. The FCSR is employed for both the certification and encryption, which makes the scheme more effective and use less memory. This scheme is a good practical lightweight scheme combined with certification and encryption in RFID environment.
The proposed keystream generator in this thesis can be used in some environment with limited resources, such as sensor network, Ad-Hoc wireless communication net work and RFID environment..
本文主要研究如何利用FCSR设计性质优秀的密钥流生成器,在研究FCSR的性质与基于FCSR的密钥流生成器F-FCSR-Hv2的基础之上,先对F-FCSR-Hv2等基于滤波的密钥流生成器进行改进,提出了改进方案一“联合的F-FCSR密钥流生成器”与“全动态滤波密钥流生成器DF-FCSR-8";然后用FCSR替代LFSR进行钟控设计,得到具有良好性质的钟控密钥流生成器；再综合利用前面设计的密钥流生成器得到了钟控全动态滤波密钥流生成器；最后研究了用于RFID(Radio Frequency Identification)射频识别技术的轻量级认证算法SQUASH,在此基础上设计出基于FCSR的用于RFID的轻量级认证算法SQUASH+和与加密结合的算法SQUASH+DF-FCSR。
主要的结果如下：
1.研究了基于FCSR滤波的密钥流生成器F-FCSR-Hv2,分析了Hell-Johansson攻击对FCSR滤波方案攻击的思想,在此基础上提出了一个基于FCSR滤波的改进方案一联合的F-FCSR密钥流生成器,以增加寄存器为代价,在保证吞吐率和密钥流良好统计特性的基础上,还可以抵抗Hell-Johansson攻击和其他攻击。
2.提出了一个全动态滤波密钥流生成器DF-FCSR-8,该生成器改变了原来滤波密钥流生成器在产生滤波输出时使用静态滤波的设计思路,引入了全动态滤波器,使得攻击者不能获取滤波器的滤波向量,无法列出足够的线性方程组,从而可以抵抗Hell-Johansson攻击,其他分析表明DF-FCSR-8可以抵抗相关攻击和代数攻击等攻击；测试表明密钥流具有良好统计特性。
3.提出基于FCSR的钟控密钥流生成器,设计了基于FCSR的停走钟控密钥流生成器和基于FCSR的交替钟控密钥流生成器,给出了两个生成器的参数以及生成序列的周期、线性复杂度下界,并分析了抵抗Hell-Johansson等攻击和其他攻击的能力等等,结果表明基于FCSR的停走钟控密钥流生成器具有大周期高线性复杂度下界,但是统计特性不够好,而基于FCSR的交替钟控密钥流生成器具有大周期、高线性复杂度下界、统计特性良好、且能抵抗Hell-Johansson攻击和其他攻击。
4.综合了基于FCSR的全动态密钥流生成器和钟控密钥流生成器的特点,提出两个基于FCSR的全动态钟控密钥流生成器一基于FCSR的全动态停走钟控密钥流生成器SGDF-FCSR-8和基于FCSR的全动态交替钟控密钥流生成器ASDF-FCSR-8。给出了设计参数、生成序列的周期以及线性复杂度下界,测试了统计特性,并给出了ASDF-FCSR-8抵抗Hell-Johansson攻击以及其他攻击的能力,结果表明,虽然SGDF-FCSR-8统计特性比基于FCSR的停走钟控密钥流生成器的统计特性好,但仍未能通过全部的伪随机性测试；而ASDF-FCSR-8在具有交替钟控密钥流生成器大周期、高线性复杂度、良好统计特性的基础之上,提高了吞吐率。
5.研究了应用于RFID环境下的轻量级认证算法SQUASH,在标准SQUASH基础上利用FCSR对其进行改进,提出了SQUASH+算法,该算法可以在保证安全性的基础上更高效的完成应答的计算。综合SQUASH+和基于FCSR的流密码的特点,提出了一个将认证与全动态滤波密钥流生成器相结合的轻量级混合算法-SQUASH+DF-FCSR,该算法利用FCSR作为计算数据发生器,在认证完成的同时也将流密码初始化过程完成,进而进行加密,使得FCSR寄存器同时供认证和加密使用,节约了空间,提高了效率,是一个在RFID环境下实用的轻量级认证加密混合算法。
本文设计的密钥流生成器可用一些资源受限的环境中,如于传感器网络、Ad-Hoc无线通信网络以及RFID环境中。
The Feedback with Carry Shift Registers (FCSR for short) has the similar structure with Linear Feedback Shift Registers (LFSR for short), but its generated sequence has high linear complexity by using addition with carry. Now it is very popular to design the stream cipher by means of nonlinear components. So, as an important nonlinear component, the FCSR is playing a key role in stream cipher design.
This thesis focuses on the usage of FCSR as keystream generator in stream cipher. Firstly based on the properties of FCSR, we study a keystream generator-F-FCSR-Hv2and improve it in two ways, and then propose two generators—Combined F-FCSR keystream generator and Dynamic filter keystream generator DF-FCSR-8. Next, we use FCSR in clock control instead of LFSR, which show better property than those based on LFSR. Combining the dynamic filter generator and clock controlled generator, we build a new type of keystream generator. Finally, aiming the Radio Frequency Identification (RFID for short) technology and the light weight certification scheme-SQUASH, we present a new certification scheme based on FCSR called SQUASH+, and a scheme called SQUASH+DF-FCSR for both certification and encryption, which is combination of the SQUASH+and the light weighted DF-FCSR.
The main result of this thesis is as follows:
1. Based on the properties of F-FCSR-Hv2generator and analysis of the Hell-Johansson attack which is an effective attack for F-FCSR-Hv2, an improved generator for filtered FCSR generator called Combined F-FCSR generator is presented. This generator maintains high output rate and good property at the cost of increasing more registers, and is resistant to Hell-Johansson attack and other attacks as well.
2. A new generator named dynamic filtered generator DF-FCSR-8is proposed. This generator uses dynamic filter as the filter of an FCSR's main register instead of the original static one. Because the filter is changed each time, the attacker cannot acquire enough linear functions so that this generator can resist Hell-Johansson attack. Other analyses indicate that DF-FCSR-8can withstand the correlation attack, algebraic attack and other attacks. While the test shows that DF-FCSR-8has good statistic characteristics.
3. Using FCSR to construct clock controlled generator instead of LFSR, two genera-tors:Stop and Go generator based on FCSR and Alternating Step generator based on FCSR, are proposed. This thesis gives the parameters of those generators, the period of generated sequence, lower bound of linear complexity, the ability against Hell-Johansson attack and other attacks, and statistic properties. Those results show that Stop and Go generator has a large period and high lower bound of linear complexity, but less good statistic property, while Alternating Step Generator has large period, high lower bound of linear complexity, good statistic properties, and ability to against Hell-Johansson attack and other attacks.
4. With the combination of dynamic filtered generator and clock controlled generator, two generators:SGDF-FCSR-8and ASDF-FCSR-8, are developed. The former is a combi-nation of Stop and Go generator and dynamic filtered generator; the later is a combination of Alternating Step generator and dynamic filtered generator. This thesis gives the parameters, the period of generated sequence, lower bound of linear complexity, and the ability against Hell-Johansson attack and other attacks, and also tests statistic properties of both generators. Although SGDF-FCSR-8has better statistic property than Stop and Go generator, it does not pass all the tests. WhereasASDF-FCSR-8improves the output rate based on a large period of Alternating Step Generator, and also has high lower bound on linear complexity and good statistic properties.
5. Through the investigation of a lightweight certification scheme, SQUASH, which is used in RFID environment, an improved version SQUASH+is given based on FCSR and standard SQUASH in this thesis. This scheme can complete the computation much more effi-ciently while ensuring the security. After that, considering the SQUASH+and the properties of stream-cipher based on FCSR, this thesis give a lightweight scheme named SQUASH+DF-FCSR which uses the FCSR as the data generator. The calculation process for certification is also initializing the keystream generator, and then encrypts the data. The FCSR is employed for both the certification and encryption, which makes the scheme more effective and use less memory. This scheme is a good practical lightweight scheme combined with certification and encryption in RFID environment.
The proposed keystream generator in this thesis can be used in some environment with limited resources, such as sensor network, Ad-Hoc wireless communication net work and RFID environment..
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