“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.
43:31.
Maria Lectrix 
The lapsed is an interesting reading. Cyprian’s teaching on wealth are very radical:
“What deceived many was a blind attachment to their patrimony, and if they were not free and ready to take themselves away, it was because their property held them in chains . . . chains which shackled their courage and choked their faith and hampered their judgment and throttled their souls… And our Lord, the teacher of the good, looking to the future warning us against this, saying: ‘If you want to be perfect, go, sell your possessions and give to the poor, and you will have treasure in heaven. Then come, follow me.’ If the rich would do this, riches would not be their ruin; if they stored up their treasure in heaven, they would not have an enemy and a thief within their own household; their heart and thought and care would be in heaven, if their treasure lay in heaven: no man could be overcome by the world if he had nothing in the world to overcome him. He would follow our Lord untrammeled and free as the apostles and many others did at that time, and some have often done since, leaving their parents and possessions behind to bind themselves inseparably to Christ.
But how can those who are tethered to their inheritance be following Christ? And can those who are weighed down by earthly desires be seeking heaven and aspiring to the heights above? They think of themselves as owners, whereas it is they rather who are owned: enslaved as they are to their own property, they are not the masters of their money but its slaves. The apostle was pointing to our times and to these very men he said: ‘Those who want to be rich fall into temptation and a trap and into many foolish and harmful desires that plunge men into ruin and destruction. For the love of money is a root of all kinds of evil. Some people, eager for money, have wandered from the faith and pierced themselves with many griefs.’ On the other hand, what rewards does not our Lord hold out as He invites us to scorn the property we have! For the small, insignificant losses of this world, what rich compensation He makes!” – Cyprian, 200-258 AD, (The Lapsed 11-12)