Emulating OP_RAND

The discussion centers around an innovative approach to enhance privacy in cryptographic operations, specifically targeting the way addresses are handled. The proposal begins with the idea of incorporating a third point to obfuscate two points, labeled as addr_a and b, using an example equation $P_a + A_1 + T$. The technique under examination involves multiplying this sum by a scalar $t$, resulting in a new formulation: $t \cdot (P_a + A_1)$. This operation aims to generate two outputs, $X$ and $T$, where $T$ equals $t\cdot G$, and $X$ is the result of $t\cdot(P_a + A_1)$.

The essence of this approach lies in its potential to veil the original scalar $t$ through an adaptor signature, which would only later be revealed. This method suggests a sophisticated mechanism for maintaining confidentiality in transactions or data exchanges by adding layers of complexity to the direct visibility of involved points or addresses. The proposed scheme signifies a stride towards advanced privacy measures in cryptographic practices, leveraging mathematical operations to secure information further.