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The problem of transaction reordering in blockchains, also known as the blockchain anomaly [Christopher Natoli and Vincent Gramoli, 2016], can lead to fairness limitations [Kelkar et al., 2020] and front-running activities [Philip Daian et al., 2020] in cryptocurrency. To cope with this problem despite f < n/3 byzantine processes, Zhang et al. [Zhang et al., 2020] have introduced the ordering linearizability property ensuring that if two transactions or commands are perceived by all correct processes in the same order, then they are executed in this order. They proposed a generic distributed protocol that first orders commands and then runs a leader-based consensus protocol to agree on these orders, hence requiring at least 11 message delays. In this paper, we parallelize the ordering with the execution of the consensus to require only 6 message delays. For the ordering, we introduce the ordered reliable broadcast primitive suitable for broadcast-based cryptocurrencies (e.g., [Daniel Collins et al., 2020]). For the agreement, we build upon the DBFT leaderless consensus protocol [Tyler Crain et al., 2018] that was recently formally verified [Bertrand et al., 2021]. The combination is thus suitable to ensure ordering linearizability in consensus-based cryptocurrencies (e.g., [Tyler Crain et al., 2021]).