Sensor networks are frequently deployed in physically insecure environments and capture sensitive data, making security a paramount challenge. Cryptographic techniques, such as encryption and hashing, are useful in addressing these concerns. However, the use of these schemes greatly increases the energy consumption of sensor nodes and thus shortens their lifetime. To address this challenge, we propose encompression (encryption + compression) as a strategy to achieve low-energy secure data transmission in sensor networks. Our proposal combines, for the first time, compressive sensing (CS), a powerful and general approach for exploiting sparsity of sensor data, with encryption and integrity checking of the compressively sensed data. While encompression can be realized using any compression technique, CS is particularly well suited since it can be realized with a very low computational and energy footprint that is compatible with the constraints of sensor nodes. We present an evaluation of a hardware implementation of encompression, wherein the CS, encryption, and integrity checking algorithms are realized using a 65-nm CMOS technology. We also present a system-level evaluation of encompression by realizing it in software on a commercial embedded sensor platform and measuring the energy consumption. The evaluation of encompression in hardware shows that, with the use of a reasonable compression ratio of 6-10×, encompression results in an energy reduction of 55-65% over a hardware implementation of encryption and integrity checking alone. The system-level evaluation demonstrates that the energy of an application that captures, encompresses, and transmits data is reduced by upto 78% using encompression vs. traditional encryption and integrity checking. Our results also demonstrate that the total sensor node energy consumption with encompression may even be less than the case where neither cryptography nor compression is employed (for a compression ratio of 10×, this "energy bonus" can be upto 14%). These results suggest that the use of CS may be a gamechanger in enabling state-of-the-art cryptography to be employed in highly energy-constrained sensor networks.