On Universal Classes of Extremely Random Constant-Time Hash Functions

2004 ◽  
Vol 33 (3) ◽  
pp. 505-543 ◽  
Author(s):  
Alan Siegel
1979 ◽  
Vol 18 (2) ◽  
pp. 143-154 ◽  
Author(s):  
J.Lawrence Carter ◽  
Mark N. Wegman

2002 ◽  
Vol 9 (27) ◽  
Author(s):  
Anna Östlin ◽  
Rasmus Pagh

Many algorithms and data structures employing hashing have been analyzed under the <em>uniform hashing</em> assumption, i.e., the assumption that hash functions behave like truly random functions. In this paper it is shown how to implement hash functions that can be evaluated on a RAM in constant time, and behave like truly random functions on any set of n inputs, with high probability. The space needed to represent a function is O(n) words, which is the best possible (and a polynomial improvement compared to previous fast hash functions). As a consequence, a broad class of hashing schemes can be implemented to meet, with high probability, the performance guarantees of their uniform hashing analysis.


Author(s):  
Riad S. Wahby ◽  
Dan Boneh

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.


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