SHRINCS: 324-byte stateful post-quantum signatures with static backups

In the discussion on cryptographic security, particularly focusing on the Winternitz One-Time Signature Scheme (WOTS) and its variant WOTS+, a significant point of interest is the role of checksums in preventing certain types of attacks. The emphasis here is on a specific attack vector where an alternative message, denoted as (m'), attempts to impersonate or replace the original message (m) during the verification process. This attempt hinges on crafting (m') such that each of its digits is greater than or equal to the corresponding digit in (m). The design of the checksum mechanism in both WOTS and WOTS+ plays a pivotal role in thwarting this attack strategy.

The checksum's utility lies in its calculation method, which inherently ensures that any modified message (m') with the stated property will result in a checksum value smaller than that of the original message (m). This discrepancy in checksum values between the original and modified messages serves as a robust countermeasure against the described attack, effectively invalidating the falsified message (m') during the verification phase. In the case of WOTS, the process of creating a valid signature for the altered message would necessitate the exposure of a preimage within one of the checksum chains, thereby compromising the integrity of the attack.

This mechanism underscores the cryptographic strength and thoughtfulness embedded in the design of WOTS and WOTS+, highlighting their resilience against a nuanced attack vector that seeks to exploit the numerical relationship between the original and altered messages. Through the implementation of a checksum that critically evaluates the sum of the message's components, these systems maintain their security posture by ensuring that any unauthorized manipulation of the message content is detectably flagged, preserving the authenticity and reliability of the communication.