Recently, many platforms have outsourced tasks to numerous smartphone devices known as Mobile Crowd-sourcing System (MCS). The data is collected and transferred to the platform for further analysis and processing. These data needs to maintain confidentiality while moving from smartphones to the platform. Moreover, the limitations of computation resources in smartphones need to be addressed to balance the confidentiality of the data and the capabilities of the devices. For this reason, elliptic curve cryptography (ECC) is accepted, widespread, and suitable for use in limited resources environments such as smartphone devices. ECC reduces energy consumption and maximizes devices' efficiency by using small crypto keys with the same strength of the required cryptography of other cryptosystems. Thus, ECC is the preferred approach for many environments, including the MCS, Internet of Things (IoT) and wireless sensor networks (WSNs). Many implementations of ECC increase the process of encryption and/or increase the space overhead by, for instance, incorrectly mapping points to EC with extra padding bits. Moreover, the wrong mapping method used in ECC results in increasing the computation efforts. This study provides comprehensive details about the mapping techniques used in the ECC mapping phase, and presents performance results about widely used elliptic curves. In addition, it suggests an optimal enhanced mapping method and size of padding bit to secure communications that guarantee the successful mapping of points to EC and reduce the size of padding bits.
Keywords: concatenation method; elliptic curve cryptography; encoding phase; mapping phase; mobile crowed-sourcing systems; probability method.