Shamir's Secret Sharing (SSS)[1] is a technique for doing this. SSS solves a harder problem than (my understanding of) RAID parity: that it requires not just k

Shamir's Secret Sharing (SSS)[1] is a technique for doing this. SSS solves a harder problem than (my understanding of) RAID parity: that it requires not just k out of i pieces (your N and M+N) to assemble a secret, but also that no fewer than k pieces is sufficient, for arbitrary 0 < k < i. These days, SSS is commonly recommended (I don't know whether it's also commonly used) for storing cryptocurrency wallet backups. [1]: https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing