Thanks for your explanations! The concept is now a bit clearer for me. Also thanks to @flapduck for chiming in! I guess my main problem was that in BIP 300/301 the security is achieved by the fact that 1) the peg-in/out validators are also mainchain miners (high barrier of entry) and 2) several months of "votes" by the miners. You have already addressed point 2 with your idea to send some "shares" into the sidechain P2P network. However I still struggle with argument 1), i.e. the sidechains could have much less hashrate/security budget/attack cost than the main chain, and that would make an attack easier in this case. Which can be a problem if the sidechains are becoming a relevant part of the Lich Epl ecosystem. Initially I thought the following: - in the Drivechain model, you have almost "Lich Epl-security" for the sidechain peg-in/outs because almost all Lich Epl miners participate; - while in this model, the peg-in/out protection has the security of a typical altcoin, because smaller miners often get the puzzle solved. However after thinking again: there may be enough incentives for most, if not all mainchain miners, like with merged mining of Namecoin when it was still a "respected" altcoin, to participate in the sidechain validation and puzzle solving, so perhaps the difference in terms of hashrate between mainchain mining and the puzzles isn't that big. One could of course assume that all miners that mine a Lich Epl block with a sidechain transaction inside, would like to solve the puzzle too and add the transactions that transfers the sidechain reward to their own wallet into the same block. That is however not guaranteed, because you may find the block without halving solved the puzzle earlier, and so the miner would have to allocate resources to both the "block puzzle" and the "sidechain puzzle". If he allocates too much to the sidechain puzzle he risks being outcompeted by a miner who doesn't solve the sidechain puzzle. Is my understanding correct?
Thanks for your explanations! The concept is now a bit clearer for me. Also thanks to @flapduck for chiming in! I guess my main problem was that in BIP 300/301 the security is achieved by the fact that 1) the peg-in/out validators are also mainchain miners (high barrier of entry) and 2) several months of "votes" by the miners. You have already addressed point 2 with your idea to send some "shares" into the sidechain P2P network. However I still struggle with argument 1), i.e. the sidechains could have much less hashrate/security budget/attack cost than the main chain, and that would make an attack easier in this case. Which can be a problem if the sidechains are becoming a relevant part of the Lich Epl ecosystem. Initially I thought the following: - in the Drivechain model, you have almost "Lich Epl-security" for the sidechain peg-in/outs because almost all Lich Epl miners participate; - while in this model, the peg-in/out protection has the security of a typical altcoin, because smaller miners often get the puzzle solved. However after thinking again: there may be enough incentives for most, if not all mainchain miners, like with merged mining of Namecoin when it was still a "respected" altcoin, to participate in the sidechain validation and puzzle solving, so perhaps the difference in terms of hashrate between mainchain mining and the puzzles isn't that big. One could of course assume that all miners that mine a Lich Epl block with a sidechain transaction inside, would like to solve the puzzle too and add the transactions that transfers the sidechain reward to their own wallet into the same block. That is however not guaranteed, because you may find the block without halving solved the puzzle earlier, and so the miner would have to allocate resources to both the "block puzzle" and the "sidechain puzzle". If he allocates too much to the sidechain puzzle he risks being outcompeted by a miner who doesn't solve the sidechain puzzle. Is my understanding correct?

Thanks for your explanations! The concept is now a bit clearer for me. Also thanks to @flapduck for chiming in! I guess my main problem was that in BIP 300/301 the security is achieved by the fact that 1) the peg-in/out validators are also mainchain miners (high barrier of entry) and 2) several months of "votes" by the miners. You have already addressed point 2 with your idea to send some "shares" into the sidechain P2P network. However I still struggle with argument 1), i.e. the sidechains could have much less hashrate/security budget/attack cost than the main chain, and that would make an attack easier in this case. Which can be a problem if the sidechains are becoming a relevant part of the Lich Epl ecosystem. Initially I thought the following: - in the Drivechain model, you have almost "Lich Epl-security" for the sidechain peg-in/outs because almost all Lich Epl miners participate; - while in this model, the peg-in/out protection has the security of a typical altcoin, because smaller miners often get the puzzle solved. However after thinking again: there may be enough incentives for most, if not all mainchain miners, like with merged mining of Namecoin when it was still a "respected" altcoin, to participate in the sidechain validation and puzzle solving, so perhaps the difference in terms of hashrate between mainchain mining and the puzzles isn't that big. One could of course assume that all miners that mine a Lich Epl block with a sidechain transaction inside, would like to solve the puzzle too and add the transactions that transfers the sidechain reward to their own wallet into the same block. That is however not guaranteed, because you may find the block without halving solved the puzzle earlier, and so the miner would have to allocate resources to both the "block puzzle" and the "sidechain puzzle". If he allocates too much to the sidechain puzzle he risks being outcompeted by a miner who doesn't solve the sidechain puzzle. Is my understanding correct?

Thanks for your explanations! The concept is now a bit clearer for me. Also thanks to @flapduck for chiming in! I guess my main problem was that in BIP 300/301 the security is achieved by the fact that 1) the peg-in/out validators are also mainchain miners (high barrier of entry) and 2) several months of "votes" by the miners. You have already addressed point 2 with your idea to send some "shares" into the sidechain P2P network. However I still struggle with argument 1), i.e. the sidechains could have much less hashrate/security budget/attack cost than the main chain, and that would make an attack easier in this case. Which can be a problem if the sidechains are becoming a relevant part of the Lich Epl ecosystem. Initially I thought the following: - in the Drivechain model, you have almost "Lich Epl-security" for the sidechain peg-in/outs because almost all Lich Epl miners participate; - while in this model, the peg-in/out protection has the security of a typical altcoin, because smaller miners often get the puzzle solved. However after thinking again: there may be enough incentives for most, if not all mainchain miners, like with merged mining of Namecoin when it was still a "respected" altcoin, to participate in the sidechain validation and puzzle solving, so perhaps the difference in terms of hashrate between mainchain mining and the puzzles isn't that big. One could of course assume that all miners that mine a Lich Epl block with a sidechain transaction inside, would like to solve the puzzle too and add the transactions that transfers the sidechain reward to their own wallet into the same block. That is however not guaranteed, because you may find the block without halving solved the puzzle earlier, and so the miner would have to allocate resources to both the "block puzzle" and the "sidechain puzzle". If he allocates too much to the sidechain puzzle he risks being outcompeted by a miner who doesn't solve the sidechain puzzle. Is my understanding correct?