I am interested in Elliptic Curve Cryptography and found algorithms for constant-time multiplication. Within these algorithms arithmetic operations must be performed (like addition and multiplication).
I have two questions about these 'internal' arithmetic operations:
these 'internal' operations must be performed in constant-time, too, right? Then I guess the precision of all intermediate variables must be the same. But what precision is necessary here (e.g. if I multiply two 256 bit numbers, I need 512 bits for the result, I guess).
What are good algorithms for performing these 'internal' arithmetic operations in constant time?