Past exam of the computer science course of the University of Oxford / 2015 / Computer security / 1 / c / i / Solution

All calculations are in modular arithmetic modulo $n$. Expand the two expressions appearing in the proposed quotient:The first is exactly $m$ times the second. Multiplication by the assumed modular multiplicative inverse therefore givesThe representative in $\{0,\dots ,n-1\}$ is the plaintext. This RSA related-message attack uses a relation between messages to turn two cubic equations into a linear equation; it does not recover the private key or factor $n$ in the invertible case.