  Makaro is a logic puzzle with an objective to fill numbers into a rectangular
grid to satisfy certain conditions. In 2018, Bultel et al. developed a physical
zero-knowledge proof (ZKP) protocol for Makaro using a deck of cards, which
allows a prover to physically convince a verifier that he/she knows a solution
of the puzzle without revealing it. However, their protocol requires several
identical copies of some cards, making it impractical as a deck of playing
cards found in everyday life typically consists of all different cards. In this
paper, we propose a new ZKP protocol for Makaro that can be implemented using a
standard deck (a deck consisting of all different cards). Our protocol also
uses asymptotically less cards than the protocol of Bultel et al. Most
importantly, we develop a general method to encode a number with a sequence of
all different cards. This allows us to securely compute several numerical
functions using a standard deck, such as verifying that two given numbers are
different and verifying that a number is the largest one among the given
numbers.
