Microsoft patents lighter encryption for low-power devices

1. A method for encrypting a message by a sender to a recipient, the method comprising: using one or more hardware processors: encrypting an encryption key k with a first encryption function to create an encrypted key, the first encryption function being a commutative function; transmitting the encrypted key to the recipient over a packet-based network; receiving a response message from the recipient over the packet-based network; decrypting the response message using a reverse function of the first encryption function to produce a first key message, the first key message comprising the encryption key k encrypted by a commutative encryption function of the recipient; transmitting the first key message to the recipient over the packet-based network, the first key message being decryptable by the recipient using a reverse function of the commutative encryption function of the recipient to produce the encryption key k; breaking the message into a plurality of message portions; converting the encryption key k into a signed-digit representation T using an odd base; identifying a plurality of non-commutative functions, each non-commutative function corresponding to a particular digit position of T; for each particular one of the plurality of message portions, creating a corresponding one of a plurality of transformed message portions by: selectively applying each of the plurality of non-commutative functions to the particular one of the plurality of message portions in a defined order, wherein selectively applying comprises, for each particular digit position in T: applying the non-commutative function corresponding to the particular digit position in T, an inverse of the non-commutative function corresponding to the particular digit position in T, or no function, based upon a value of T at the particular digit position; and transmitting, over the packet-based network, the plurality of transformed message portions to the recipient.