SPHINCS+ Algorithm

SPHINCS+ is a digital signature algorithm designed to remain secure even against an attacker with a large quantum computer, built entirely from cryptographic hash functions rather than from number-theoretic problems such as factoring or discrete logarithms that quantum computers are expected to break. It signs a message using a one-time signature scheme called WOTS+ together with a technique called FORS that signs a randomly selected small subset of possible values, and it organizes an effectively unlimited number of these one-time keys into a layered hypertree structure built from many Merkle trees stacked on top of each other, so that verifying a signature means checking a chain of inclusion proofs up through that hypertree until reaching a single public root value; this hash-based design also directly fixes weaknesses in an earlier scheme called SPHINCS, including its vulnerability to certain multi-target attacks. A large team of cryptographers, including Daniel J. Bernstein and Andreas Hulsing among many others, first released SPHINCS+ in November 2017, and the United States National Institute of Standards and Technology standardized it in August 2024 as part of FIPS 205, one of the first two post-quantum digital signature algorithms it approved.