how to convert a coordinate (x,y) to a unique value

Question

how to convert a elliptic point to a unique value?

ie using ECC for curve y2=x3+x+1 and p=23 i generated elliptic points and for a message, I mapped the characters of the message to elliptic points so computed.

Now i want to pass the set of points to another cryptographic algorithm say goldwasser inorder to perform encryption.

Is there any algorithm to convert the point to a integral value?

Answer 1

Look for Elliptic Curve Point Compression.

In OpenSSL(which follows X9.62 standard), there are functions for this purpose:

• BIGNUM *EC_POINT_point2bn() - convert EC point to bignum
• char *EC_POINT_point2hex() - convert EC point to hex string

And ofcourse, functions to convert it back:

• EC_POINT *EC_POINT_bn2point()
• EC_POINT *EC_POINT_hex2point()

For JAVA, check out the answer of this post.