Resumen
Outsourcing computation has become increasingly popular due to its cost-effectiveness, enabling users with limited resources to conduct large-scale computations on potentially untrusted cloud platforms. In order to safeguard privacy, verifiable computing (VC) has emerged as a secure approach, ensuring that the cloud cannot discern users? input and output. Random permutation masking (RPM) is a widely adopted technique in VC protocols to provide robust privacy protection. This work presents a precise definition of the privacy-preserving property of RPM by employing indistinguishability experiments. Moreover, an innovative attack exploiting the greatest common divisor and the least common multiple of each row and column in the encrypted matrices is introduced against RPM. Unlike previous density-based attacks, this novel approach offers a significant advantage by allowing the reconstruction of matrix values from the ciphertext based on RPM. A comprehensive demonstration was provided to illustrate the failure of protocols based on RPM in maintaining the privacy-preserving property under this proposed attack. Furthermore, an extensive series of experiments is conducted to thoroughly validate the effectiveness and advantages of the attack against RPM. The findings of this research highlight vulnerabilities in RPM-based VC protocols and underline the pressing need for further enhancements and alternative privacy-preserving mechanisms in outsourcing computation.