diff --git a/ssh.h b/ssh.h
index 2aaa679b..7b256cd1 100644
--- a/ssh.h
+++ b/ssh.h
@@ -665,6 +665,7 @@ struct ssh_hashalg {
     void (*final)(ssh_hash *, unsigned char *); /* ALSO FREES THE ssh_hash! */
     void (*free)(ssh_hash *);
     int hlen; /* output length in bytes */
+    int blocklen; /* length of the hash's input block, or 0 for N/A */
     const char *text_name;
 };
 
diff --git a/sshhmac.c b/sshhmac.c
index 8f2577a6..31e15ea8 100644
--- a/sshhmac.c
+++ b/sshhmac.c
@@ -14,7 +14,6 @@ struct hmac {
 
 struct hmac_extra {
     const ssh_hashalg *hashalg;
-    size_t blklen;
     const char *suffix;
 };
 
@@ -23,6 +22,15 @@ static ssh2_mac *hmac_new(const ssh2_macalg *alg, ssh_cipher *cipher)
     struct hmac *ctx = snew(struct hmac);
     const struct hmac_extra *extra = (const struct hmac_extra *)alg->extra;
 
+    /*
+     * HMAC is not well defined as a wrapper on an absolutely general
+     * hash function; it expects that the function it's wrapping will
+     * consume data in fixed-size blocks, and it's partially defined
+     * in terms of that block size. So we insist that the hash we're
+     * given must have defined a meaningful block size.
+     */
+    assert(extra->hashalg->blocklen);
+
     ctx->h_outer = ctx->h_inner = ctx->h_live = NULL;
     ctx->digest = snewn(extra->hashalg->hlen, uint8_t);
 
@@ -67,7 +75,7 @@ static void hmac_key(ssh2_mac *mac, ptrlen key)
     size_t klen;
     strbuf *sb = NULL;
 
-    if (key.len > extra->blklen) {
+    if (key.len > extra->hashalg->blocklen) {
         /*
          * RFC 2104 section 2: if the key exceeds the block length of
          * the underlying hash, then we start by hashing the key, and
@@ -98,13 +106,13 @@ static void hmac_key(ssh2_mac *mac, ptrlen key)
     ctx->h_outer = ssh_hash_new(extra->hashalg);
     for (size_t i = 0; i < klen; i++)
         put_byte(ctx->h_outer, PAD_OUTER ^ kp[i]);
-    for (size_t i = klen; i < extra->blklen; i++)
+    for (size_t i = klen; i < extra->hashalg->blocklen; i++)
         put_byte(ctx->h_outer, PAD_OUTER);
 
     ctx->h_inner = ssh_hash_new(extra->hashalg);
     for (size_t i = 0; i < klen; i++)
         put_byte(ctx->h_inner, PAD_INNER ^ kp[i]);
-    for (size_t i = klen; i < extra->blklen; i++)
+    for (size_t i = klen; i < extra->hashalg->blocklen; i++)
         put_byte(ctx->h_inner, PAD_INNER);
 
     if (sb)
@@ -153,7 +161,7 @@ static const char *hmac_text_name(ssh2_mac *mac)
     return ctx->text_name->s;
 }
 
-const struct hmac_extra ssh_hmac_sha256_extra = { &ssh_sha256, 64, "" };
+const struct hmac_extra ssh_hmac_sha256_extra = { &ssh_sha256, "" };
 const ssh2_macalg ssh_hmac_sha256 = {
     hmac_new, hmac_free, hmac_key,
     hmac_start, hmac_genresult, hmac_text_name,
@@ -161,7 +169,7 @@ const ssh2_macalg ssh_hmac_sha256 = {
     32, 32, &ssh_hmac_sha256_extra,
 };
 
-const struct hmac_extra ssh_hmac_md5_extra = { &ssh_md5, 64, "" };
+const struct hmac_extra ssh_hmac_md5_extra = { &ssh_md5, "" };
 const ssh2_macalg ssh_hmac_md5 = {
     hmac_new, hmac_free, hmac_key,
     hmac_start, hmac_genresult, hmac_text_name,
@@ -169,7 +177,7 @@ const ssh2_macalg ssh_hmac_md5 = {
     16, 16, &ssh_hmac_md5_extra,
 };
 
-const struct hmac_extra ssh_hmac_sha1_extra = { &ssh_sha1, 64, "" };
+const struct hmac_extra ssh_hmac_sha1_extra = { &ssh_sha1, "" };
 
 const ssh2_macalg ssh_hmac_sha1 = {
     hmac_new, hmac_free, hmac_key,
@@ -178,7 +186,7 @@ const ssh2_macalg ssh_hmac_sha1 = {
     20, 20, &ssh_hmac_sha1_extra,
 };
 
-const struct hmac_extra ssh_hmac_sha1_96_extra = { &ssh_sha1, 64, "-96" };
+const struct hmac_extra ssh_hmac_sha1_96_extra = { &ssh_sha1, "-96" };
 
 const ssh2_macalg ssh_hmac_sha1_96 = {
     hmac_new, hmac_free, hmac_key,
@@ -188,7 +196,7 @@ const ssh2_macalg ssh_hmac_sha1_96 = {
 };
 
 const struct hmac_extra ssh_hmac_sha1_buggy_extra = {
-    &ssh_sha1, 64, " (bug-compatible)"
+    &ssh_sha1, " (bug-compatible)"
 };
 
 const ssh2_macalg ssh_hmac_sha1_buggy = {
@@ -199,7 +207,7 @@ const ssh2_macalg ssh_hmac_sha1_buggy = {
 };
 
 const struct hmac_extra ssh_hmac_sha1_96_buggy_extra = {
-    &ssh_sha1, 64, "-96 (bug-compatible)"
+    &ssh_sha1, "-96 (bug-compatible)"
 };
 
 const ssh2_macalg ssh_hmac_sha1_96_buggy = {
diff --git a/sshmd5.c b/sshmd5.c
index 4fcc906b..2a083f8d 100644
--- a/sshmd5.c
+++ b/sshmd5.c
@@ -271,5 +271,5 @@ static void md5_final(ssh_hash *hash, unsigned char *output)
 }
 
 const ssh_hashalg ssh_md5 = {
-    md5_new, md5_copy, md5_final, md5_free, 16, "MD5"
+    md5_new, md5_copy, md5_final, md5_free, 16, 64, "MD5"
 };
diff --git a/sshsh256.c b/sshsh256.c
index 940726bd..fbd8bdb2 100644
--- a/sshsh256.c
+++ b/sshsh256.c
@@ -252,7 +252,7 @@ static void sha256_final(ssh_hash *hash, unsigned char *output)
 }
 
 const ssh_hashalg ssh_sha256 = {
-    sha256_new, sha256_copy, sha256_final, sha256_free, 32, "SHA-256"
+    sha256_new, sha256_copy, sha256_final, sha256_free, 32, 64, "SHA-256"
 };
 
 #ifdef COMPILER_SUPPORTS_SHA_NI
diff --git a/sshsh512.c b/sshsh512.c
index 7e27d738..bacba0d4 100644
--- a/sshsh512.c
+++ b/sshsh512.c
@@ -13,7 +13,7 @@
 
 typedef struct {
     uint64_t h[8];
-    unsigned char block[128];
+    unsigned char block[BLKSIZE];
     int blkused;
     uint64_t lenhi, lenlo;
     BinarySink_IMPLEMENTATION;
@@ -343,7 +343,7 @@ static void sha512_final(ssh_hash *hash, unsigned char *output)
 }
 
 const ssh_hashalg ssh_sha512 = {
-    sha512_new, sha512_copy, sha512_final, sha512_free, 64, "SHA-512"
+    sha512_new, sha512_copy, sha512_final, sha512_free, 64, BLKSIZE, "SHA-512"
 };
 
 static ssh_hash *sha384_new(const ssh_hashalg *alg)
@@ -363,5 +363,5 @@ static void sha384_final(ssh_hash *hash, unsigned char *output)
 }
 
 const ssh_hashalg ssh_sha384 = {
-    sha384_new, sha512_copy, sha384_final, sha512_free, 48, "SHA-384"
+    sha384_new, sha512_copy, sha384_final, sha512_free, 48, BLKSIZE, "SHA-384"
 };
diff --git a/sshsha.c b/sshsha.c
index 9f4fb5c7..82f1c913 100644
--- a/sshsha.c
+++ b/sshsha.c
@@ -281,7 +281,7 @@ static void sha1_final(ssh_hash *hash, unsigned char *output)
 }
 
 const ssh_hashalg ssh_sha1 = {
-    sha1_new, sha1_copy, sha1_final, sha1_free, 20, "SHA-1"
+    sha1_new, sha1_copy, sha1_final, sha1_free, 20, 64, "SHA-1"
 };
 
 #ifdef COMPILER_SUPPORTS_SHA_NI