Contributes to oxidative stress resistance by reducing cysteine-sulfinic acid formed under exposure to oxidants in the peroxiredoxins PRDX1, PRDX2, PRDX3 and PRDX4 (PubMed:15448164, PubMed:15590625). Does not act on PRDX5 or PRDX6 (PubMed:15448164, PubMed:15590625). May catalyze the reduction in a multi-step process by acting both as a specific phosphotransferase and a thioltransferase (PubMed:15448164, PubMed:15590625). {ECO:0000269|PubMed:15448164, ECO:0000269|PubMed:15590625}. This is the function of SRXN1 (sulfiredoxin 1, ENSG00000271303).