Scheme | Merkle tree | XMSS | XMSS in RFC 8391 | LMS | GMSS | XMSSMT | HSS | SPHINCS | SPHINCS +  |
---|---|---|---|---|---|---|---|---|---|
Required security of underlying function in hash tree and pseudorandom key selection | CR | SPR | PRF of G(n); multi-function multi-target SPR of H | SPR | CR | SPR | SPR | PRF of F; Subset-resilience of Hdgt; SPR of H | PQ-MM-SPR of H and tweakable hash; PQ-PRF of F; PQ-target subset resilience of Hdgt |
Model | Standard | Standard | RO | RO | Standard | Standard | RO | Standard | RO |