A Wireless Body Area Network (WBAN) is formed by implanting tiny sensors on the human body in order to collect and communicate the human personal data. WBANs play an important role in mobile health monitoring such as monitoring the health of patients remotely. In order to take full advantage of WBANs in application scenarios such as healthcare, security and privacy must be ensured for inter-sensor communication in WBANs. The inter-sensor communication in WBAN is exposed to a variety of attacks, which pose major threats to its security. These threats can be overcome by using cryptographic techniques. Cryptographic schemes itself rely on good key agreement schemes. In WBANs, keys can be generated from biometrics i.e., Electrocardiogram (EKG), Electroencephalography (EEG), or finger prints. The advantage of using time variant biometrics i.e., EKG as a biometric for key agreement is that it possesses the properties of randomness and time variance. The keys produced from these biometric values also possess the same properties, and make it harder for an attacker to guess or regenerate the keys. The existing key agreement schemes are either computationally expensive or involve too much information exchange in order to complete the key agreement process. The increase in information exchange increases the communication complexity as well as the energy consumption. Similarly, some of the key agreement schemes are pre-loading based i.e., the keys are loaded into the memory of sensor nodes before deployment. Such schemes increase human involvement and also consume more memory and resources, which reduces the usability of the WBAN. This thesis aims to provide security and privacy solutions to WBANs, while keeping in mind the memory, energy, and processing constraints. The first contribution of this work is an electrocardiogram (EKG) based key agreement scheme using discrete wavelet transform (DWT) for the sake of generating common key in a WBAN. The scheme uses Keyed-Hashing Message Authentication Code (HMAC-MD5) to protect the personal information exchange process in a WBAN. A heterogeneous Wireless Sensor Network (WSN) is considered, which consists of a powerful High-end sensor (H-sensor) and several Low-end sensors (L-sensors) in order to form a cluster. The proposed scheme is evaluated in terms of entropy, randomness of keys, and key repetition. The scheme shows better entropy, and generates highly random keys with no repetitions. The second contribution of this work is an energy-efficient key agreement scheme for WBANs, which takes into account available resources of a node during the whole life cycle of key management. The proposed scheme is a cluster-based hybrid security framework that supports both intra-WBAN and inter-WBAN communications. The cluster formation process itself is secured by using Electrocardiogram (EKG) based key agreement scheme. The performance comparison of Low Energy Adaptive Clustering Hierarchy (LEACH) based key agreement scheme and the proposed key agreement scheme shows that the proposed scheme is more energy-efficient and provides better network lifetime. The third contribution of this work is a broadcast-based key agreement scheme using set reconciliation for secure communication in WBANs. The scheme allows the neighboring nodes to agree upon a common key with the personal server (PS), generated from feature set of the EKG signal of the host body. Minimal information is exchanged in a broadcast manner, and even if every node is missing a different subset, by reconciling these feature sets, the whole network will still agree upon a single common key. Due to lesser information exchange, if an attacker by any chance gets the information, will not be able to reproduce the key. The proposed scheme is evaluated in terms of security, energy consumption, communication overhead, and memory overhead. It is worth mentioning that the proposed scheme increases the lifetime of the network and decreases the energy consumption as well as the memory and communication overheads. The proposed set reconciliation based key agreement scheme mitigates the replay, selective forwarding, and denial of service attacks by a challenge response authentication mechanism.