| CPC H04L 9/085 (2013.01) [G06F 7/725 (2013.01); G06F 17/17 (2013.01); H04L 9/14 (2013.01); H04L 9/3066 (2013.01); H04L 9/3093 (2013.01); H04L 9/3218 (2013.01); H04L 9/0841 (2013.01); H04L 9/3236 (2013.01); H04L 9/50 (2022.05)] | 17 Claims |

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1. A computer-implemented method comprising:
determining, at a plurality of participants, a function usable to map finite field elements;
generating, by each participant of the plurality of participants and based on the function, polynomials evaluated in a set of points;
distributing the polynomials, by each participant to each other participant of the plurality of participants, to determine a sum of the polynomials distributed to the plurality of participants;
determining, at each of a first participant and a second participant of said plurality of participants:
a master polynomial from the sum of the polynomials distributed to the plurality of participants, wherein the master polynomial corresponds to a power of a secret; and
based at least in part on the power of the secret, a common reference string; and
generating a smart contract comprising a first transaction input provided by said first participant and a second transaction input provided said second participant.
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