In our authentication protocol, user needs to transmit several sensitive information wrapped with an elliptic curve points. In reality, wireless sensor does not carry rich resource such as network bandwidth at a premium. Thus, it is desirable to represent those points in a possible minimum form, which is usually referred as point compression.
In a full representation of point compression, an affin point(xa,ya) requires 2n bits, where n = ⌈log2(p)⌉, assuming the prime field is 𝔽p. The compressed data is trivially reduced to n+1 bits by given the x-coordinate of a point plus an additional bit that is used to distinguish two different solutions (±y) of recovering the correct y coordinate. Precisely, we need to check for the least significant bit of the least significant coefficient of y coordinate.
In our proposed implementation, we adapted SECG secp160r1[14] recommended parameters to define our elliptic curve. In that standard, each element in the elliptic curve consumes 160 bits.