Fast and simple constant-time hashing to the BLS12-381 elliptic curve

Pairing-friendly elliptic curves in the Barreto-Lynn-Scott family are seeing a resurgence in popularity because of the recent result of Kim and Barbulescu that improves attacks against other pairing-friendly curve families. One particular Barreto-Lynn-Scott curve, called BLS12-381, is the locus of significant development and deployment effort, especially in blockchain applications. This effort has sparked interest in using the BLS12-381 curve for BLS signatures, which requires hashing to one of the groups of the bilinear pairing defined by BLS12-381.While there is a substantial body of literature on the problem of hashing to elliptic curves, much of this work does not apply to Barreto-Lynn-Scott curves. Moreover, the work that does apply has the unfortunate property that fast implementations are complex, while simple implementations are slow.In this work, we address these issues. First, we show a straightforward way of adapting the “simplified SWU” map of Brier et al. to BLS12-381. Second, we describe optimizations to this map that both simplify its implementation and improve its performance; these optimizations may be of interest in other contexts. Third, we implement and evaluate. We find that our work yields constant-time hash functions that are simple to implement, yet perform within 9% of the fastest, non–constant-time alternatives, which require much more complex implementations.

The Rise and Fall of the Branchhead Boys

Louisiana had the Longs, Virginia had the Byrds, Georgia had the Talmadges, and North Carolina had the Scotts. In this history of North Carolina’s most influential political family, Rob Christensen tells the story of the Scotts and how they dominated Tar Heel politics. Three generations of Scotts – W. Kerr Scott, Robert Scott, and Meg Scott Phipps – held statewide office. Despite stereotypes about rural white southerners, the Scotts led a populist and progressive movement strongly supported by rural North Carolinians – the so-called Branchhead Boys, the rural grassroots voters who lived at the heads of tributaries throughout the heat of North Carolina. Though the Scotts held power in various government positions in North Carolina for generations, they were instrumental in their own downfall. From Kerr Scott’s regression into reactionary race politics to Meg Scott Phipps’s corruption trial and subsequent prison sentence, the Scott family lost favor in their home state, their influence dimmed and their legacy in question. Weaving together interviews from dozens of political luminaries and deep archival research, Christensen offers an engaging and definitive historical account of not only the Scott family’s legacy but also how race and populism informed North Carolina politics during the twentieth century.

Making Kindness Common

Unlike Rich Maiore, my girls Amanda and Lucy had the good fortune of learning about Alex Scott when they were very young. Like many schools in the neighborhood—just a few miles from the Scott family home—our local preschool held an Alex's Lemonade Stand each summer. In preparation, Amanda and Lucy and all their classmates made signs, checked their supplies, and urged parents, grandparents, and anyone who'd listen to stop by. On the big day, my husband Jason and I took time off from work and stood in line and bought glasses of lemonade. We bought yellow bracelets that said “One Cup at a Time.” And we listened as these children, including our own, retold the story of a little girl just about their age who had a terrible disease and a big heart. We watched, and they watched, a whole neighborhood of families stop what they were doing and, for a moment, let themselves be inspired by a single act of kindness that grew larger than anyone could have ever dreamed. What happens when we see other people act generously?

Scott Family Enterprises: Building the Path to Effective Governance

As founders of First Interstate BancSystem, which held $8.6 billion in assets and had recently become a public company, and Padlock Ranch, which had over 11,000 head of cattle, the Scott family had to think carefully about business and family governance. Now entering its fifth generation, the family had over 80 shareholders across the US. In early 2016, the nine-member Scott Family Council (FC) and other family and business leaders considered the effectiveness of the Family Governance Leadership Development Initiative launched two years earlier. The initiative's aim was to ensure a pipeline of capable family leaders for the business boards, two foundation boards, and FC. Seven family members had self-nominated for governance roles in mid-2015. As part of the development initiative, each was undergoing a leadership development process that included rigorous assessment and creation of a comprehensive development plan. As the nominees made their way through the process and other family members considered nominating themselves for future development, questions remained around several interrelated areas, including how to foster family engagement with governance roles while guarding against damaging competition among members; how to manage possible conflicts of interest around dual employee and governance roles; and how to extend the development process to governance for the foundations and FC. The FC considered how best to answer these and other questions, and whether the answers indicated the need to modify the fledgling initiative. This case illustrates the challenges multigenerational family-owned enterprises face in developing governance leaders within the family. It serves as a good example of governance for a large group of cousins within a multienterprise portfolio. Students can learn and apply insights from this valuable illustration of family values, vision, and mission statement.