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import Baseimport ./curve25519/x25519.bend as Ximport ./ed25519/ed25519.bend as E# Signatures: Ed25519 (RFC 8032). Keys and signatures are byte lists (U32# values below 256) of the RFC lengths; malformed ones are rejected as# values.##   generate_keypair(seed)   secret = the 32-byte seed, public = [s]B#   generate_keypair_os()    the same from 32 bytes of IO.random_u32#   sign(sk, msg)            the 64-byte signature, None for a bad key#   verify(pk, msg, sig)     True iff sig is valid (cofactorless check,#                            non-canonical S >= L rejected)## Correctness against RFC 8032 is proved (spec/crypto/sign.bend,# proofs/crypto/ed25519). Scalar multiplication and scalar arithmetic are# branch-free on secrets; Bend has no timing model, so constant time is by# construction, not proved.type Keypair is Data:  Keypair{secret: List<&2, U32>, public: List<&2, U32>}def keypair_if(+seed: List<&2, U32>, ok: Bool) -> Maybe<&2, Keypair>:  match ok:    case True{}:      Some{Keypair{seed, E.public_key(seed)}}    case False{}:      None{}def generate_keypair(+seed: List<&2, U32>) -> Maybe<&2, Keypair>:  keypair_if(seed, X.valid_bytes(32n, seed))def word_bytes(+w: U32, rest: List<&2, U32>) -> List<&2, U32>:  Con{U32.and(w, 255), Con{U32.and(U32.shrn(w, 8n), 255), Con{U32.and(U32.shrn(w, 16n), 255), Con{U32.shrn(w, 24n), rest}}}}def random_bytes(n: Nat, acc: List<&2, U32>) -> IO(List<&2, U32>):  match n:    case 0n:      IO.pure(List<&2, U32>, acc)    case 1n+m:      do IO<List<&2, U32>>:        w : U32 <- IO.try(U32, IO.random_u32())        rest : List<&2, U32> <- random_bytes(m, acc)        return word_bytes(w, rest)def generate_keypair_os() -> IO(Maybe<&2, Keypair>):  do IO<Maybe<&2, Keypair>>:    seed : List<&2, U32> <- random_bytes(8n, Nil{})    return generate_keypair(seed)def sign_if(+sk: List<&2, U32>, +msg: List<&2, U32>, ok: Bool) -> Maybe<&2, List<&2, U32>>:  match ok:    case True{}:      Some{E.sign_raw(sk, msg)}    case False{}:      None{}def sign(+sk: List<&2, U32>, +msg: List<&2, U32>) -> Maybe<&2, List<&2, U32>>:  sign_if(sk, msg, X.valid_bytes(32n, sk))def verify_if(+pk: List<&2, U32>, +msg: List<&2, U32>, +sig: List<&2, U32>, ok: Bool) -> Bool:  match ok:    case True{}:      E.verify_raw(pk, msg, sig)    case False{}:      False{}def verify(+pk: List<&2, U32>, +msg: List<&2, U32>, +sig: List<&2, U32>) -> Bool:  verify_if(pk, msg, sig, Bool.and(X.valid_bytes(32n, pk), X.valid_bytes(64n, sig)))