Multisig will be an important factor in merchant adoption, particularly in areas with lower amounts of trust. In particular, integration of Monero into something like Open Bazaar would require multisig. Although multisig is already on the road map, I think raising a reward would help move it along (and funding for specific proposals is a good way to show community support for projects).

In particular, who ever claims this bounty must implement ring multi-signatures roughly as described by Shen Noether in shnoe.wordpress.com/2016/03/22/ring-multisignature in monero-wallet-cli (and preferably the GUI as well), and get their code merged into the official monero-project repo (in the unlikely circumstance that political conflicts arise preventing this merge (such as unforeseen corruption in the monero-project), the controller of the FFS will reward the developer at their discretion). It would be coded with respect to RingCT transactions, since normal transactions will be phased out soon.

In particular, there would be 3 milestones.

35% of the Reward: n-of-n multisig

The reason this is a milestone is because n-of-n multisig is substantially easier than full k-of-n multisig. It only requires some tweaks to the offline signing code. Yet, it lays the ground work for full k-of-n multisig. Also, it is good for cold storage.

Also, although it requires more work on the part of users, it will allow for open bazzar style escrow accounts. Namely, the escrow generates two keys, escrow-buyer and escrow-seller, and gives them to the buyer and seller, respectively. Then the seller creates a buyer-seller spend key, and sends it to the seller (but not the escrow). The public keys corresponding to these private keys are published. Then the buyer sends moneroj into a 3-of-3 multisig of the buyer-seller, escrow-buyer, and escrow-seller keys. Then any 2 of the buyer, seller, and escrow will control all three keys, but no one of them will, satisfying a open bazaar style escrow. These milestone does not qualify for more of the reward, do the complexity it would require for the user for escrow, and since it is the easiest of the milestones.

Additionally, it would allow for unidirectional payment channels (by using 2-of-2 multisig).

55% of the Reward: 2-of-3 multisig

This will require the most coding out of the milestones. It will be the most beneficial for merchants.

10% of the Reward: k-of-n multisig

This will only be some tweaks to 2-of-3 multisig. It is useful in certain cold storage scenarios, controlling the funds of a business or project, etc... If the claimer of this bounty implements k-of-n first, they automatically qualify for the other two milestones, since n-of-n and 2-of-3 are special cases of k-of-n.

It is still to be determined what the total reward should be. I am not sure how long it will take, as I am not a developer. Before this is requested to be added to "open tasks", this should be determined.