Threshold signatures and blind signatures are fundamental cryptographic primitives that havebeen studied widely. Threshold signatures first introduced by Yvo Desmedt in 1994 distributes thesigning responsili bility among many signers in such a way that a valid signature on any messagecannot be generated unless a sufficient number of signers collaborate. This helps in mitigating therisk associated with a single signer’s key being compromised. For example, threshold signaturesare used in cryptocurrency wallets. Blind signatures were first introduced by David Chaum in1982 and has applications in areas like eCash, eVoting etc. Here the signer and message holder aretwo different entities. The user having the message want to receive signer’s signature on his/hermessage with the constraint that the signer must not be able to link message-signature pair. Atthe same time the user must also not be able to generate even one more than the requested numberof signatures.Focus of this talk is the construction of lattice based threshold and blind signatures. Latticebased construction of cryptographic primitives are interesting because they are believed to be postquantum secure. In this talk we will present the lattice based construction by Boneh et al givenin 2018 and our solution to improve its efficiency in terms of the size of the signature. The size ofthe signature in Boneh et al’s construction is of the order ̃Ω(λ3) which we manage to bring downto ̃Ω(λ). Security of threshold signatures requires that any adversary should not be able to forgea valid signature on any new message even after seeing many message-signature pairs. This mustbe true even if a set of signers (less than the threshold number) collude. The notion of corruptedsigners is captured by allowing the adversary to corrupt some of the signers which means that theadversary gets the secret keys of the corrupted parties. Boneh et al.’s construction provides onlyselective security in which the set of corrupted parties is revealed before any signing query. Wedefine a notion for adaptive unforgeability in which the adversary can corrupt the parties at anytime during the sec urity experiment. We will present our solution to achieve adaptive unforgeabilityin ROM and pre-processing model.In case of blind signatures many lattice based constructions have been proposed but have flawedproofs. Hauck et al gave a three round construction of blind signatures in ROM with completesecurity proofs. The signature size is of the order ̃Ω(λ3+Qλ), whereQis the upper bound on thenumber of signatures produced. We give a two round construction in ROM which is much simplerand more efficient than Hauck et al construction. The signature size in our construction is of theorder ̃Ω(λ). In the talk we will also briefly present our construction of blind signature scheme.