## 4 Cryptography and Wireless Security  
Cryptographic techniques form the first line of defense for securing wireless communications. Although this paper is not particularly focused on applied cryptography in wireless systems, we give a brief overview of the basic concepts. The three basic security requirements specified by the IEEE for wireless local area network (WLAN) environments are authentication, confidentiality, and integrity. _Authenticity_ is to ensure the identity of the sender of a message. _Confidentiality_ guarantees that amessage is kept secret and can only be read by the intended receiver. Finally, _integrity_ ensures that any tampering or distortion of a message by adversaries is identifiable. Many cryptographic protocols have been proposed to secure communications in wireless networks. There are two main cryptographic paradigms: symmetric and asymmetric. _Symmetric cryptographic systems_ (such as the Advanced Encryption Standard, AES [53]) use the same secret key for message encryption and decryption. They require the sender and receiver to agree on a shared key before communicating. Symmetric encryption is fast, relatively simple, and widely used for encrypting large data flows. _Asymmetric encryption schemes_ (such as the RSA public-key encryption scheme [54]) require the receiver to have a key pair--a public key known by others and a private key known only to the receiver. The sender encrypts a message with the public key of the receiver. The receiver, upon obtaining the ciphertext, decrypts it with her private key. In public-key signature scheme, a signer uses her private key to sign a message for message integrity purpose and produces a digital signature. A verifier, upon obtaining the signature and the message, uses the signer's public key to verify the digital signature and make sure that the message has not been tampered with. Asymmetric or public-key encryption schemes require the sender to know the correct public key of the receiver, similarly public-key signature scheme requires the verifier to know the public key of the signer. The authenticity of a public key is extremely important--using the wrong public key in decryption may result in the receiver erroneously accepting an adversary's message, possibly leading to attacks. Asymmetric cryptography is computationally more expensive than symmetric ones, making its usage in embedded or power constrained environments difficult. In an environment where there are central trust authorities, services can use digital certificates to bind a public key to an identity and verify that a public key belongs to an individual. For example, VeriSign is one of the Internet's major certificate authorities. The digital certificates used in SSL and HTTPS utilize _public key cryptographic schemes_. Specifically, they use a public key digital signature scheme for initial trust establishment. Once trust is established between the client and the server (e.g. a Web server and a client's browser in the HTTPS case), a shared key is negotiated and used for encrypting subsequent communications. In decentralized wireless networks (such as wireless ad-hoc networks) the infrastructure is fluidic--there is no pre-defined trust authority and the rate at which nodes join and leave the network may be high. The task of establishing trust between nodes is therefore difficult. For example, in Mobile Ad-Hoc Networks (MANETs) each node voluntarily forwards data to other nodes, but the determination of which nodes forward what data is made dynamically based on network connectivity. The mobile nature of MANETs leads to frequent network topology changes. Securing the communication in such a decentralized wireless system is challenging and may require advanced cryptographic tools such as threshold cryptography [55, 56]. In _threshold cryptosystems_, a secret (e.g. certificate or other valuable data) is split into shares, and any \(k\) nodes can combine their shares to recover the master secret, which may be used for signing certificates or other critical operations.