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Practical resilient efficient Quantum Key Distribution Abstract. In 1984, Bennett and Brassard came up with the revolutionary idea of quantum key distribution that we now know as the BB84 protocol. Rigorous proofs of correctness and tolerable error rates were given 12 years later by Shor and Preskill. Many other QKD protocols have since been proposed; and some of them also come with correctness proofs of varying rigour. However, most of these protocols are designed for ideal single photon sources and detectors. Real devices are far from the ideal. So already it is unclear whether QKD implementations on real devices are secure enough. Another issue that is often overlooked is the efficiency of the classical postprocessing in a QKD protocol. One postprocessing step called information reconciliation has never been rigorously proved to be both correct and optimal for a malicious unbounded eavesdropper, as well as efficient. In this work we mathematically model real devices and come up with new QKD protocols, all variants of BB84 but for real devices. Our protocols are practical in that they are designed to correctly work with the limitations of existing devices. They are resilient in that they can tolerate some amounts photon erasures and loss of purity of single photon sources. They are computationally efficient. On the way, we achieve optimal and efficient information reconciliation for QKD for the first time. We obtain new elementary proofs of security which allows to obtain three new variants of BB84: 1. A strictly one way variant where all communication is from Alice to Bob 2. An almost one way variant with only constant amount of back communication from Bob to Alice. 3. A two way variant where the basis sifting step sends only \sqrt{n}polylog(n) bits of basis information instead of n bits used in the original BB84. About. https://www.tcs.tifr.res.in/~pgdsen/ Host. IIIT Hyderabad