How do we know that Jesus' ransom is for the elect?

The doctrine of limited atonement asserts that Christ's sacrificial death was specifically intended for the elect. In John 17:2, Jesus mentions that He has authority to grant eternal life to 'as many as thou hast given him', indicating a specific group chosen by God. The apostle Paul echoes this in 1 Timothy 2:6, where it states that Jesus gave Himself as a ransom for all, understood as all the elect, those who were ordained to eternal life. This demonstrates God's sovereign plan of redemption is focused and particular rather than universal.