Paper 2020/644

ALBATROSS: publicly AttestabLe BATched Randomness based On Secret Sharing

Ignacio Cascudo and Bernardo David


In this paper we present ALBATROSS, a family of multiparty randomness generation protocols with guaranteed output delivery and public verification that allows to trade off corruption tolerance for a much improved amortized computational complexity. Our basic stand alone protocol is based on publicly verifiable secret sharing (PVSS) and is secure under in the random oracle model under the decisional Diffie-Hellman (DDH) hardness assumption. We also address the important issue of constructing Universally Composable randomness beacons, showing two UC versions of Albatross: one based on simple UC NIZKs and another one based on novel efficient ``designated verifier'' homomorphic commitments. Interestingly this latter version can be instantiated from a global random oracle under the weaker Computational Diffie-Hellman (CDH) assumption. An execution of ALBATROSS with $n$ parties, out of which up to $t=(1/2-\epsilon)\cdot n$ are corrupt for a constant $\epsilon>0$, generates $\Theta(n^2)$ uniformly random values, requiring in the worst case an amortized cost per party of $\Theta(\log n)$ exponentiations per random value. We significantly improve on the SCRAPE protocol (Cascudo and David, ACNS 17), which required $\Theta(n^2)$ exponentiations per party to generate one uniformly random value. This is mainly achieved via two techniques: first, the use of packed Shamir secret sharing for the PVSS; second, the use of linear $t$-resilient functions (computed via a Fast Fourier Transform-based algorithm) to improve the randomness extraction.

Available format(s)
Cryptographic protocols
Publication info
A minor revision of an IACR publication in ASIACRYPT 2020
Randomness generationmultiparty computationpublic verificationsecret sharing
Contact author(s)
ignacio cascudo @ imdea org
bernardo @ bmdavid com
2020-10-23: revised
2020-06-03: received
See all versions
Short URL
Creative Commons Attribution


      author = {Ignacio Cascudo and Bernardo David},
      title = {ALBATROSS: publicly AttestabLe BATched Randomness based On Secret Sharing},
      howpublished = {Cryptology ePrint Archive, Paper 2020/644},
      year = {2020},
      note = {\url{}},
      url = {}
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