With the rapid development in network technology new network types based on wireless communication have emerged. A large family of wireless communication networks is the Mobile Ad hoc Networks (MANETs). While MANETs mobile devices should be able to connect with each other at any time and place, the vulnerabilities of MANET structure also introduce a wide range of attacks and present new challenges for the design of security mechanism ranging from developing and implementing lightweight cryptographic primitives to designing and analyzing secure protocols. Numerous security solutions and key management schemes such as symmetric and asymmetric cryptography have been used to support MANET environment. This paper conducted survey to gain a quick knowledge of security design demand and cryptography solutions to secure MANET. This survey focused on security schemas and case studies of cryptography techniques on Ad Hoc networks. Finally, conclusions are discussed.