That foundation is nothing other than the gospel.
In the first 12 verses, before Peter gives these elect exiles any instructions concerning how to live a midst persecution and suffering, he reminds them of the gospel and it's promises.
In verse 2 he reminds them that all 3 members of the Godhead played a part in their redemption: the father chose them as His own, the Spirit sanctified and regenerated them, and the Son justified them with His blood. In verses 3-12 Peter reminds them of the benefits of their salvation that were purchased and secured by God. You will notice that in each case Peter mentions that it is God who is doing and acting, not the believers. In verse 3 it is God who has caused them to be born again to a living hope and an inheritance that is imperishable. In verse 5 it is God's power that keeps them through faith as His own possession.
What Peter is doing is reminding them that because of God's great work in their salvation, they can look beyond this world to the one to come, where they will spend eternity with God. This reality is assured, not because of their will or their works, but because it is God Himself who is working in them to make it so. He has chosen them, He has sanctified them, He has justified them, and He is keeping them. Their salvation is assured because God is faithful. This assurance of what God has done, is doing, and will do is the rock on which they are to stand as they live their lives in a fallen world. Nothing else will do.
We must remember what God has done for us. We must learn to meditate on and rejoice in the gospel. We must learn to look beyond our circumstance to the reality of an eternal inheritance secured and kept for us by our God. Only as we do this will we be able to live a holy life in this world that will honor God and result in His praise and glory when He returns to judge the world and take us home.