Square Always Exponentiation

Embedded exponentiation techniques have become a key concern for security and efficiency in hardware devices using public key cryptography. An exponentiation is basically a sequence of multiplications and squarings, but this sequence may reveal exponent bits to an attacker on an unprotected implementation. Although this subject has been covered for years, we present in this paper new exponentiation algorithms based on trading multiplications for squarings. Our method circumvents attacks aimed at distinguishing squarings from multiplications at a lower cost than previous techniques. Last but not least, we present new algorithms using two parallel squaring blocks which provide the fastest exponentiation to our knowledge.