This work succinctly presents historical and mathematical aspects of ancient and modern cryptography such as Caesar cipher, related ciphers, Vigenère cipher, Hill cipher and RSA cryptography. Guidance on the subject of cryptography and related activities in high school is sought at the BNCC and PCN-EM. The work develops mathematical requirements for an elementary understanding of the cryptographic systems studied. Among these requirements we have elementary concepts such as matrices, modular arithmetic and number theory, which are used in the presented cryptography theories. Some activities for the elementary school teacher to apply in their classes are suggested at the end.