Wireless ad hoc networks have been emerged to support applications, in which it is required/desired to have wireless ommunications among a variety of devices without relying on any infrastructure or central managements. In ad hoc networks, wireless devices, simply called nodes, have limited transmission range. Therefore, each node can directly communicate with only those within its transmission range and requires other nodes to act as routers in order to communicate with out-of-range estinations. One of the fundamental operations in ad hoc networks is broadcasting, where a node sends a message to all other nodes in the network. This can be achieved through flooding, in which every node transmits the first copy of the received message. However, flooding can impose a large number of redundant transmissions, which can result in significant waste of constrained resources such as bandwidth and battery power. One of the contributions of this work is to propose efficient broadcast algorithms which can significantly reduce the number of redundant transmissions. We also consider some of the security issues of ad hoc networks. In particular, we carefully analyze the effect of the wormhole attack, which is one of the most severe threats against ad hoc networks. We also propose a countermeasure, which is an improvement over the existing timing-based solutions against the wormhole attack. Finally, in the last chapter, we propose novel point compression techniques which can be used in Elliptic Curve Cryptography (ECC). ECC can provide the same level of security as other public key cryptosystems (such as RSA) with substantially smaller key sizes. Smaller keys can result in smaller system parameters, bandwidth savings, faster implementations and lower power consumption. These advantages make ECC interesting for ad hoc networks with restricted devices.