Given a set of elliptic points that satisfy an elliptic polynomial equation defined over a finite field, F, which requires N-bits to represent its elements, a new method of cryptographic encryption and decryption is presented which uses more than one quadratic variable that are termed y-coordinates to obtain an elliptic polynomial equation with multi y-coordinates instead of one y-coordinate. The additional y-coordinates are used to embed extra message data bits. A ny-fold increase in the number of embedded message data bits in a single elliptic point can be achieved with the improved method when using ny additional y-coordinates. The reason is that the number of points that satisfy an elliptic polynomial equation defined over F(p) and which can be used in the corresponding cryptosystem is increased by a factor of (#F).sup.ny, where # denotes the size of a field. The use of the additional y-coordinates can be used to reduce computational complexity. Alternatively, this can be used to increase security by making the bit positions where data bits are embedded known only to the sender and receiver. Also, it can be used as a countermeasure by randomizing the bit positions where data bits are embedded.