Cryptographic wallets are an essential tool to securely store and maintain users’ secret keys and consequently their funds in Blockchain networks. A compelling approach to construct such wallets is to share the user’s secret key among several devices, such that an adversary must corrupt multiple machines to extract the entire secret key. Indeed, many leading cryptocurrency companies such as Coinbase, Binance, or ZenGo have started offering such distributed wallets to their customers. An important feature of a cryptographic wallet is its compatibility with the so-called BIP32 specification, the most widely adopted standard for cryptographic wallets. Essentially, BIP32 specifies the notion of a hierarchical deterministic wallet, which allows to create a key hierarchy in a deterministic fashion. Unfortunately, despite significant interest, no practically efficiently solution for a fully distributed wallet scheme, that also follows the BIP32 standard, exists. In this work, we show the first concretely efficient construction of a fully distributed wallet that is compliant with the BIP32 standard. To this end, we first provide a game-based notion of threshold signatures with rerandomizable keys and show an instantiation via the Gennaro and Goldfeder threshold ECDSA scheme (CCS’18). We then observe that one of BIP32’s key derivation mechanisms, the so-called hardened derivation, cannot efficiently be translated to the threshold setting. Instead, we devise a novel and efficient hardened derivation mechanism for the threshold setting that satisfies the same properties as the original mechanism as specified by BIP32. As a final contribution, we evaluate our solution with respect to its running time and communication cost.

The problem of finding the kth Ranked Element (KRE) is of particular interest in collaborative studies for financial and medical agencies alike. Many of the applications of KRE deal with sensitive information that needs to be protected. The protocol by Chandran et al. (SECRYPT'22) considers a model where multiple parties hold datasets with many elements and wish to compute the kth element of their joint dataset. In their model, all participating parties interact with a central party in a star network topology. However, they leak some intermediate information to the central party.