cryptography:

H(x) is 512 bit blake2b digest of x
HS(x) is 256 bit blake2b digest of x
MD(x, k) is 512 bit blake2b hmac of x with secret value k
MDS(x, k) is 256 bit blake2b hmac of x with secret value k
SE(k, n, x) is chacha20 encrypt data x using symettric key k and nounce n
SD(k, n, x) is chacha20 dectypt data x using symettric key k and nounce n
S(k, x) is sign x with ed25519 using secret key k
EDKG() is generate ec keypair (p, s) public key p (32 bytes), secret key s (64 bytes)
V(k, x, sig) is verify x data using signature sig using public key k
EDDH(a, b) is curve25519 scalar multiplication of a and b
HKE(a, b, x) is hashed key exchange between a and b using a secret key x HS(a + b + EDDH(x, b))
TKE(a, b, x, n) is a transport shared secret kdf using MDS(n, HKE(a, b, x))

when A is client and B is server where n is a 32 bytes shared random

client computes TKE(A.pk, B.pk, A.sk, n)
server computes TKE(A.pk, B.pk, B.sk, n)

PDH(a, b, x) is path shared secret generation HS(a + b + EDDH(x, b))

PKE(a, b, x, n) is a path shared secret kdf using MDS(n, PDH(a, b, x))

given A is the path creator and B is a hop in the path and n is 32 bytes shared random

A computes PKE(A.pk, B.pk, A.sk, n) as S_a
B computes PKE(A.pk, B.pk, B.sk, n) as S_b

S_a is equal to S_b

RAND(n) is n random bytes

PQKG() is generate a sntrup4591761 key pair (sk, pk)
PQKE_A(pk) is alice generating (x, k) where x is sntrup4591761 ciphertext block and k is the session key
PQKE_B(x, sk) is bob calculating k where x is sntrup4591761 ciphertext block, sk is bob's sntrup4591761 secretkey and k is the session key