In "The Playdough Protocols" I described how ancient Sumerians used tamper evidence both in the form of physical seals and in the form of tamper evident numbers, in particular checksums. These are forerunners both of modern plastic sealing (used for evidence bags, in banking to store and transport cash and other valuables, to protect food from tampering, and so on) and modern cryptographic hash functions, whereby one can detect whether digital content has been altered.
Daniel Nagy has uncovered a more particular connection between ancient auditing techniques and modern cryptography. He writes how Chinese merchants, at least as far back as the 3rd century A.D., used remainders of division by prime numbers instead of checksums to ensure that nothing had been stolen from storage or cargo. The security of the Chinese system was based on what we still call the Chinese Remainder Theorem. The theorem is also used in some modern cryptographic systems based on the difficulty of factoring, and in particular the RSA scheme for decryption and digital signatures.