A scalar multiplication apparatus may include at least two encryptors, each adapted to receive an input point and a changed secret key to generate an encrypted output point; a first logic circuit adapted to receive the encrypted output points to perform a first logic operation; a second logic circuit adapted to receive a first logic operation result and a secret key to perform a second logic operation and generate the changed secret key; and a random number generator adapted to generate random number data. A scalar multiplication method may include receiving an input point and a changed secret key, generating first and second encrypted output points from the input point and changed secret key, performing a first logic operation on the first and second encrypted output points, and performing a second logic operation on a first logic operation result and a secret key and generating the changed secret key.