Cryptographic Hash Functions from Expander Graphs

We propose constructing provable collision resistant hash functions from expander graphs in which finding cycles is hard. As examples, we investigate two specific families of optimal expander graphs for provable collision resistant hash function constructions: the families of Ramanujan graphs constructed by Lubotzky-Phillips-Sarnak and Pizer respectively. When the hash function is constructed from one of Pizer’s Ramanujan graphs, (the set of supersingular elliptic curves over with ℓ-isogenies, ℓ a prime different from p), then collision resistance follows from hardness of computing isogenies between supersingular elliptic curves. For the LPS graphs, the underlying hard problem is a representation problem in group theory. Constructing our hash functions from optimal expander graphs implies that the outputs closely approximate the uniform distribution. This property is useful for arguing that the output is indistinguishable from random sequences of bits. We estimate the cost per bit to compute these hash functions, and we implement our hash function for several members of the Pizer and LPS graph families and give actual timings.     

Using the Hill cipher to teach cryptographic principles

The Hill cipher is the simplest example of a block cipher, which takes a block of plaintext as input, and returns a block of ciphertext as output. Although it is insecure by modern standards, its simplicity means that it is well suited for the teaching of such concepts as encryption modes, and properties of cryptographic hash functions. Although these topics are central to modern cryptography, it is hard to find good simple examples of their use. The conceptual and computational simplicity of the Hill cipher means that students can experiment with these topics, see them in action, and obtain a better understanding that would be possible from a theoretical discussion alone. In this article, we define the Hill cipher and demonstrate its use with different modes of encryption, and also show how cryptographic hash functions can be both designed and broken. Finally, we look at some pedagogical considerations.     

一种具有灵活公钥的自生成证书公钥加密方案

Self-Generated-Certificate Public Key Cryptography (SGC-PKC), is the enhanced version of Certificateless Public Key Cryptography (CL-PKC). It preserves all advantages of CLPKC. Similar to CL-PKC, every user is given a partial private key by the KGC and generates his own private key and corresponding public key. In addition, it can defend against the Denialof- Decryption (DoD) Attack. In this paper, we propose a new approach to construction SGC-PKE scheme that derived from a new application of chameleon hash and give a concrete scheme. It is the first scheme which has flexible public key and reaches Girault's trusted level 3, the same level as is enjoyed in a traditional PKI.     

Efficient identity-based security schemes for ad hoc network routing protocols

Wireless ad hoc networks consist of nodes with no central administration and rely on the participating nodes to share network responsibilities. Such networks are more vulnerable to security attacks than conventional wireless networks. We propose two efficient security schemes for these networks that use pairwise symmetric keys computed non-interactively by the nodes which reduces communication overhead. We allow nodes to generate their broadcast keys for different groups and propose a collision-free method for computing such keys. We use identity-based keys that do not require certificates which simplifies key management. Our key escrow free scheme also uses identity-based keys but eliminates inherent key escrow in identity-based keys. Our system requires a minimum number of keys to be generated by the third party as compared to conventional pairwise schemes. We also propose an authenticated broadcast scheme based on symmetric keys and a corresponding signature scheme.     

基于小波变换的混沌图像置乱加密算法

给出一种在二维小波变换基础上进行混沌映射,将图像加密的方法。该方法应用二维小波分解算法分解图像信息,再对其实行正弦混沌映射,从而完成图像的加密。解密时,首先对系数进行正弦映射的逆映射,再进行二维小波重构,实现对原始图像的解密。仿真结果证明了该方法的有效性。     

GF（2^m）域高速椭圆曲线加密处理器设计

针对高速椭圆曲线加密应用的要求,设计了一种多项式基表示的有限域GF(2m)上的高速椭圆加密处理器.为提高运算速度,点加和倍点模块并行运算,且分别采用全并行结构实现;为减少资源,初始化和最后的坐标变换求逆模块通过优化分解成一系列乘和加运算,合并在一个模块中用串行结构实现.Xilinx公司的VirtexEXCV2600 FPGA硬件实现结果表明,完成有限域GF(2163)上任意椭圆曲线上的一次点乘的全部运算时间消耗约为31.6μs,适合高速椭圆曲线加密应用的要求.     

基于椭圆曲线密码组合公钥的ad hoc密钥管理方案

Ad Hoc网络是一种独具特色的网络,作为一种新型的无线,多跳、无中心分布式控制网络,它无需网络基础设施,具有很强的自组织性,鲁棒性.抗毁性和容易构建的特点,其安全问题一直是研究的热点和难点.文中提出了一种改进的基于椭圆曲线密码组合公嘲的ad hoc密钥管理方案.与原方案相比,除了保持快捷地计算出节点的公私钥对、扩展性好、无需证书等特性外,新方案进一步提高了ad hoc网络的安全性,避免了单点失败.     

Basis Translation Matrix between Two Isomorphic Extension Fields via Optimal Normal Basis

This paper proposes a method for generating a basis translation matrix between isomorphic extension fields. To generate a basis translation matrix, we need the equality correspondence of a basis between the isomorphic extension fields. Consider an extension field F_p^m where p is characteristic. As a brute force method, when p^m is small, we can check the equality correspondence by using the minimal polynomial of a basis element; however, when p^m is large, it becomes too difficult. The proposed methods are based on the fact that Type I and Type II optimal normal bases (ONBs) can be easily identified in each isomorphic extension field. The proposed methods efficiently use Type I and Type II ONBs and can generate a pair of basis translation matrices within 15 ms on Pentium 4 (3.6 GHz) when mlog₂ p = 160.     

A special attack on the multiparty quantum secret sharing of secure direct communication using single photons

The security of a multiparty quantum secret sharing protocol [L.F. Han, Y.M. Liu, J. Liu, Z.J. Zhang, Opt. Commun. 281 (2008) 2690] is reexamined. It is shown that any one dishonest participant can obtain all the transmitted secret bits by a special attack, where the controlled-(-iσ_y) gate is employed to invalidate the role of the random phase shift operation. Furthermore, a possible way to resist this attack is discussed.