“On the Lapsed” concludes with some scary stories about receiving the Eucharist unworthily, more praise of the martyrs, and a moving call to repentance for the whole community.
I should probably explain a couple things, though. The “peace” from the martyrs was a custom where people asked those about to get martyred to forgive them their sins against them. This was fine, but it grew into asking the martyrs to forgive all their sins, and then to martyrs signing “Get Out of Sins Free, Do Not Pass the Priest, Do Not Do Penance” cards that said the martyr had forgiven X his sins, so X should be admitted to communion in all Christian communities. And then, there were the martyrs who forgave and then got spared martyrdom. (Oops.) So Bishop Cyprian is reining this in, and telling people to go confess to their priests instead, as is normal. (Even if they’ll also have to do the normal huge amount of penance for a huge sin.)
The certificates Cyprian refer to were some kind of signed affidavit that the bearer had made a sacrifice to the Emperor and wasn’t a Christian. Apparently, Cyprian wasn’t enamored of the fake ID method of avoiding persecution.
(Read the Catholic Encyclopedia for the details on both kinds of papers.)
Btw, Cyprian wasn’t martyred in this persecution, because he “withdrew” from Carthage, as he advocates to others. But he was martyred in a later one, and the people of North Africa were very proud of him.