I'm curious about their decision to eschew "complicated secret primitives": > Red October is based on combinatorial techniques and trusted cryptographic primit

I'm curious about their decision to eschew "complicated secret primitives": > Red October is based on combinatorial techniques and trusted cryptographic primitives. We investigated using complicated secret primitives like Shamir's sharing scheme, but we found that a simpler combinatorial approach based on primitives from Go's standard library was preferable to implementing a mathematical algorithm from scratch. Red October uses 128-bit AES, 2048-bit RSA and scrypt as its cryptographic primitives. While it's usually preferable to rely on well-tested cryptographic code, I wonder if this scheme is weaker because of the matroyshka doll approach taken with encryption. My personal concerns are mitigated by the fact that the secret-managing server could be made physically secure, but I'm concerned that their approach allows incremental progress to be made in decrypting secrets. For example, if users A_1,A_2...A_N all provide passwords, of which any 3 can decrypt a package, then there will be N * N-1 * N-2 / 6 copies of the secret on the server. (In general: N choose K, where N is the number of parties to the secret and K is the number required to decrypt.) For the previous example, 20 users and 3 needed to decrypt, 1140 ciphertexts will be generated. The worst case scenario is when K approaches N/2, 20 users with any 10 able to decrypt would produce close to 184,756 ciphertexts. My problems, from a naive non-cryptographer's view, are: 1. That's a lot of data, and cryptographers tend to loathe giving attacks more data. 2. I'm wondering if there's any approaches to cracking these secrets that can take advantage of the fact that the same plaintext secret is going to be available as a very large number of ciphertexts. It seems that a meet-in-the-middle attack might substantially reduce the security guarantees here. Could any cryptographers chime in? Is Red October a good model for securing secrets?