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Instead of sending the ring as @Marius describes, Jane sends one of her unlocked locks to Mike using that method instead. Mike then uses Jane's lock to lock the lock-box containing the ring and sends it to Jane. Example:

Jane sends a box containing lock1 secured by lock2 to Mike.

Mike sends the box back now secured by lock2 and lock3 to Jane.

Jane removes lock2 and sends it to Mike.

Mike removes lock3 and uses lock1 to secure the ring in a lock-box and sends it to Jane.

This would prevent the ring from being stolen. Obviously this could lead to an infinite loop of the thief stealing Jane's locks, but the ring is never stolen. Maybe after a few locks are stolen, the thief gives up since he is only getting locks. Or maybe Jane puts a venomous snake in the box, knowing Mike is a trained snake handler ;-)

Instead of sending the ring as @Marius describes, Jane sends one of her unlocked locks to Mike using that method instead. Mike then uses Jane's lock to lock the lock-box containing the ring and sends it to Jane. Example:

Jane sends a box containing lock1 secured by lock2 to Mike.

Mike sends the box back now secured by lock2 and lock3 to Jane.

Jane removes lock2 and sends it to Mike.

Mike removes lock3 and uses lock1 to secure the ring in a lock-box and sends it to Jane.

This would prevent the ring from being stolen. Obviously this could lead to an infinite loop of the thief stealing Jane's locks, but the ring is never stolen. Maybe after a few locks are stolen, the thief gives up since he is only getting locks. Or maybe Jane puts a venomous snake in the box, knowing Mike is a trained snake handler ;-)

Instead of sending the ring as @Marius describes, Jane sends one of her unlocked locks to Mike using that method instead. Mike then uses Jane's lock to lock the lock-box containing the ring and sends it to Jane. Example:

Jane sends a box containing lock1 secured by lock2 to Mike.

Mike sends the box back now secured by lock2 and lock3 to Jane.

Jane removes lock2 and sends it to Mike.

Mike removes lock3 and uses lock1 to secure the ring in a lock-box and sends it to Jane.

This would prevent the ring from being stolen. Obviously this could lead to an infinite loop of the thief stealing Jane's locks, but the ring is never stolen. Maybe after a few locks are stolen, the thief gives up since he is only getting locks. Or maybe Jane puts a venomous snake in the box, knowing Mike is a trained snake handler ;-)

Instead of sending the ring as @Marius describes, Jane sends one of her unlocked locks to Mike using that method instead. Mike then uses Jane's lock to lock the lock-box containing the ring and sends it to Jane. Example:

Jane sends a box containing lock1 secured by lock2 to Mike.

Mike sends the box back now secured by lock2 and lock3 to Jane.

Jane removes lock2 and sends it to Mike.

Mike removes lock3 and uses lock1 to secure the ring in a lock-box and sends it to Jane.

This would prevent the ring from being stolen. Obviously this could lead to an infinite loop of the thief stealing Jane's locks, but the ring is never stolen. Maybe after a few locks are stolen, the thief gives up since he is only getting locks. Or maybe Jane puts a venomous snake in the box, knowing Mike is a trained snake handler ;-)

Instead of sending the ring as @Marius describes, Jane sends one of her unlocked locks to Mike using that method instead. Mike then uses Jane's lock to lock the lockbox containing the ring and sends it to Jane. Example:

Jane sends a box containing lock1 secured by lock2 to Mike.

Mike sends the box back now secured by lock2 and lock3 to Jane.

Jane removed lock2 and sends it to Mike.

Mike removes lock3 and uses lock1 to secure the ring in a lockbox and sends it to Jane.

This would prevent the ring from being stolen. Obviously this could lead to an infinite loop of the thief stealing Jane's locks, but the ring is never stolen. Maybe after a few locks are stolen, Jane puts a venomous snake in the box instead, knowing Mike is a trained snake handler ;-)

Instead of sending the ring as @Marius describes, Jane sends one of her unlocked locks to Mike using that method instead. Mike then uses Jane's lock to lock the lock-box containing the ring and sends it to Jane. Example:

Jane sends a box containing lock1 secured by lock2 to Mike.

Mike sends the box back now secured by lock2 and lock3 to Jane.

Jane removes lock2 and sends it to Mike.

Mike removes lock3 and uses lock1 to secure the ring in a lock-box and sends it to Jane.

This would prevent the ring from being stolen. Obviously this could lead to an infinite loop of the thief stealing Jane's locks, but the ring is never stolen. Maybe after a few locks are stolen, the thief gives up since he is only getting locks. Or maybe Jane puts a venomous snake in the box, knowing Mike is a trained snake handler ;-)