Abstract: There is described a method of performing a cryptographic operation which includes performing a masked inversion of a ring element f?Rq. where Rq is a commutative ring and the ring element f is represented by a plurality of shares .

Abstract: Lattice-based threshold signature schemes and threshold decryption schemes are described. The threshold signature schemes are described in two or three rounds and are secure under Module Learning with Errors and Module Short integer Solution assumptions. In each of the signature and threshold decryption schemes, blinders may be introduced to shield information about the secret key that may otherwise be leaked by honest participants in the scheme.