diff --git a/dkim/__init__.py b/dkim/__init__.py
index 861a501..3ff305c 100644
--- a/dkim/__init__.py
+++ b/dkim/__init__.py
@@ -1,11 +1,11 @@
 # This software is provided 'as-is', without any express or implied
 # warranty.  In no event will the author be held liable for any damages
 # arising from the use of this software.
-# 
+#
 # Permission is granted to anyone to use this software for any purpose,
 # including commercial applications, and to alter it and redistribute it
 # freely, subject to the following restrictions:
-# 
+#
 # 1. The origin of this software must not be misrepresented; you must not
 #    claim that you wrote the original software. If you use this software
 #    in a product, an acknowledgment in the product documentation would be
@@ -13,8 +13,9 @@
 # 2. Altered source versions must be plainly marked as such, and must not be
 #    misrepresented as being the original software.
 # 3. This notice may not be removed or altered from any source distribution.
-# 
+#
 # Copyright (c) 2008 Greg Hewgill http://hewgill.com
+# Copyright (c) 2011 William Grant <me@williamgrant.id.au>
 
 import base64
 import hashlib
@@ -23,6 +24,14 @@ import time
 
 import dns.resolver
 
+from dkim.crypto import (
+    DigestTooLargeError,
+    parse_private_key,
+    parse_public_key,
+    RSASSA_PKCS1_v1_5_sign,
+    RSASSA_PKCS1_v1_5_verify,
+    UnparsableKeyError,
+    )
 from dkim.util import (
     InvalidTagValueList,
     parse_tag_value,
@@ -99,29 +108,6 @@ def _remove(s, t):
     assert i >= 0
     return s[:i] + s[i+len(t):]
 
-
-def EMSA_PKCS1_v1_5_encode(digest, modlen, hashid):
-    """Encode a digest with EMSA-PKCS1-v1_5.
-
-    Defined in RFC3447 section 9.2.
-
-    @param digest: A digest value to encode.
-    @param modlen: The desired message length.
-    @param hashid: The ID of the hash used to generate the digest.
-    """
-    dinfo = asn1_build(
-        (SEQUENCE, [
-            (SEQUENCE, [
-                (OBJECT_IDENTIFIER, hashid),
-                (NULL, None),
-            ]),
-            (OCTET_STRING, digest),
-        ]))
-    if len(dinfo)+3 > modlen:
-        raise ParameterError("Hash too large for modulus")
-    return "\x00\x01"+"\xff"*(modlen-len(dinfo)-3)+"\x00"+dinfo
-
-
 def hash_headers(hasher, canonicalize_headers, headers, include_headers,
                  sigheaders, sig):
     """Sign message header fields."""
@@ -146,22 +132,6 @@ def hash_headers(hasher, canonicalize_headers, headers, include_headers,
         hasher.update(x[1])
 
 
-def parse_public_key(data):
-    """Parse an RSA public key.
-
-    @param data: A DER-encoded X.509 subjectPublicKeyInfo
-        containing an RFC3447 RSAPublicKey.
-    """
-    x = asn1_parse(ASN1_Object, data)
-    # Not sure why the [1:] is necessary to skip a byte.
-    pkd = asn1_parse(ASN1_RSAPublicKey, x[0][1][1:])
-    pk = {
-        'modulus': pkd[0][0],
-        'publicExponent': pkd[0][1],
-    }
-    return pk
-
-
 def validate_signature_fields(sig, debuglog=None):
     """Validate DKIM-Signature fields.
 
@@ -217,148 +187,10 @@ def validate_signature_fields(sig, debuglog=None):
             return False
     return True
 
-
-INTEGER = 0x02
-BIT_STRING = 0x03
-OCTET_STRING = 0x04
-NULL = 0x05
-OBJECT_IDENTIFIER = 0x06
-SEQUENCE = 0x30
-
-ASN1_Object = [
-    (SEQUENCE, [
-        (SEQUENCE, [
-            (OBJECT_IDENTIFIER,),
-            (NULL,),
-        ]),
-        (BIT_STRING,),
-    ])
-]
-
-ASN1_RSAPublicKey = [
-    (SEQUENCE, [
-        (INTEGER,),
-        (INTEGER,),
-    ])
-]
-
-ASN1_RSAPrivateKey = [
-    (SEQUENCE, [
-        (INTEGER,),
-        (INTEGER,),
-        (INTEGER,),
-        (INTEGER,),
-        (INTEGER,),
-        (INTEGER,),
-        (INTEGER,),
-        (INTEGER,),
-        (INTEGER,),
-    ])
-]
-
-def asn1_parse(template, data):
-    """Parse a data structure according to ASN.1 template.
-
-    @param template: A list of tuples comprising the ASN.1 template.
-    @param data: A list of bytes to parse.
-
-    """
-
-    r = []
-    i = 0
-    for t in template:
-        tag = ord(data[i])
-        i += 1
-        if tag == t[0]:
-            length = ord(data[i])
-            i += 1
-            if length & 0x80:
-                n = length & 0x7f
-                length = 0
-                for j in range(n):
-                    length = (length << 8) | ord(data[i])
-                    i += 1
-            if tag == INTEGER:
-                n = 0
-                for j in range(length):
-                    n = (n << 8) | ord(data[i])
-                    i += 1
-                r.append(n)
-            elif tag == BIT_STRING:
-                r.append(data[i:i+length])
-                i += length
-            elif tag == NULL:
-                assert length == 0
-                r.append(None)
-            elif tag == OBJECT_IDENTIFIER:
-                r.append(data[i:i+length])
-                i += length
-            elif tag == SEQUENCE:
-                r.append(asn1_parse(t[1], data[i:i+length]))
-                i += length
-            else:
-                raise KeyFormatError("Unexpected tag in template: %02x" % tag)
-        else:
-            raise KeyFormatError("Unexpected tag (got %02x, expecting %02x)" % (tag, t[0]))
-    return r
-
-def asn1_length(n):
-    """Return a string representing a field length in ASN.1 format."""
-    assert n >= 0
-    if n < 0x7f:
-        return chr(n)
-    r = ""
-    while n > 0:
-        r = chr(n & 0xff) + r
-        n >>= 8
-    return r
-
-def asn1_build(node):
-    """Build an ASN.1 data structure based on pairs of (type, data)."""
-    if node[0] == OCTET_STRING:
-        return chr(OCTET_STRING) + asn1_length(len(node[1])) + node[1]
-    if node[0] == NULL:
-        assert node[1] is None
-        return chr(NULL) + asn1_length(0)
-    elif node[0] == OBJECT_IDENTIFIER:
-        return chr(OBJECT_IDENTIFIER) + asn1_length(len(node[1])) + node[1]
-    elif node[0] == SEQUENCE:
-        r = ""
-        for x in node[1]:
-            r += asn1_build(x)
-        return chr(SEQUENCE) + asn1_length(len(r)) + r
-    else:
-        raise InternalError("Unexpected tag in template: %02x" % node[0])
-
 # These values come from RFC 3447, section 9.2 Notes, page 43.
 HASHID_SHA1 = "\x2b\x0e\x03\x02\x1a"
 HASHID_SHA256 = "\x60\x86\x48\x01\x65\x03\x04\x02\x01"
 
-def str2int(s):
-    """Convert an octet string to an integer. Octet string assumed to represent a positive integer."""
-    r = 0
-    for c in s:
-        r = (r << 8) | ord(c)
-    return r
-
-def int2str(n, length = -1):
-    """Convert an integer to an octet string. Number must be positive.
-
-    @param n: Number to convert.
-    @param length: Minimum length, or -1 to return the smallest number of bytes that represent the integer.
-
-    """
-
-    assert n >= 0
-    r = []
-    while length < 0 or len(r) < length:
-        r.append(chr(n & 0xff))
-        n >>= 8
-        if length < 0 and n == 0: break
-    r.reverse()
-    assert length < 0 or len(r) == length
-    return r
-
 def rfc822_parse(message):
     """Parse a message in RFC822 format.
 
@@ -443,18 +275,10 @@ def sign(message, selector, domain, privkey, identity=None, canonicalize=(Simple
         raise KeyFormatError(str(e))
     if debuglog is not None:
         print >>debuglog, " ".join("%02x" % ord(x) for x in pkdata)
-    pka = asn1_parse(ASN1_RSAPrivateKey, pkdata)
-    pk = {
-        'version': pka[0][0],
-        'modulus': pka[0][1],
-        'publicExponent': pka[0][2],
-        'privateExponent': pka[0][3],
-        'prime1': pka[0][4],
-        'prime2': pka[0][5],
-        'exponent1': pka[0][6],
-        'exponent2': pka[0][7],
-        'coefficient': pka[0][8],
-    }
+    try:
+        pk = parse_private_key(pkdata)
+    except UnparsableKeyError, e:
+        raise KeyFormatError(str(e))
 
     if identity is not None and not identity.endswith(domain):
         raise ParameterError("identity must end with domain")
@@ -503,10 +327,12 @@ def sign(message, selector, domain, privkey, identity=None, canonicalize=(Simple
     if debuglog is not None:
         print >>debuglog, "sign digest:", " ".join("%02x" % ord(x) for x in d)
 
-    modlen = len(int2str(pk['modulus']))
-    encoded = EMSA_PKCS1_v1_5_encode(d, modlen, HASHID_SHA256)
-    sig2 = int2str(pow(str2int(encoded), pk['privateExponent'], pk['modulus']), modlen)
-    sig += base64.b64encode(''.join(sig2))
+    try:
+        sig2 = RSASSA_PKCS1_v1_5_sign(
+            d, HASHID_SHA256, pk['privateExponent'], pk['modulus'])
+    except DigestTooLargeError:
+        raise ParameterError("digest too large for modulus")
+    sig += base64.b64encode(sig2)
 
     return sig + "\r\n"
 
@@ -597,10 +423,12 @@ def verify(message, debuglog=None, dnsfunc=dnstxt):
         pub = parse_tag_value(s)
     except InvalidTagValueList:
         return False
-    pk = parse_public_key(base64.b64decode(pub['p']))
-    modlen = len(int2str(pk['modulus']))
-    if debuglog is not None:
-        print >>debuglog, "modlen:", modlen
+    try:
+        pk = parse_public_key(base64.b64decode(pub['p']))
+    except UnparsableKeyError, e:
+        if debuglog is not None:
+            print >>debuglog, "could not parse public key: %s" % e
+        return False
 
     include_headers = re.split(r"\s*:\s*", sig['h'])
     h = hasher()
@@ -609,17 +437,11 @@ def verify(message, debuglog=None, dnsfunc=dnstxt):
     d = h.digest()
     if debuglog is not None:
         print >>debuglog, "verify digest:", " ".join("%02x" % ord(x) for x in d)
+    signature = base64.b64decode(re.sub(r"\s+", "", sig['b']))
     try:
-        sig2 = EMSA_PKCS1_v1_5_encode(d, modlen, hashid)
-    except ParameterError:
+        return RSASSA_PKCS1_v1_5_verify(
+            d, hashid, signature, pk['publicExponent'], pk['modulus'])
+    except DigestTooLargeError:
+        if debuglog is not None:
+            print >>debuglog, "digest too large for modulus"
         return False
-    if debuglog is not None:
-        print >>debuglog, "sig2:", " ".join("%02x" % ord(x) for x in sig2)
-        print >>debuglog, sig['b']
-        print >>debuglog, re.sub(r"\s+", "", sig['b'])
-    v = int2str(pow(str2int(base64.b64decode(re.sub(r"\s+", "", sig['b']))), pk['publicExponent'], pk['modulus']), modlen)
-    if debuglog is not None:
-        print >>debuglog, "v:", " ".join("%02x" % ord(x) for x in v)
-    assert len(v) == len(sig2)
-    # Byte-by-byte compare of signatures
-    return not [1 for x in zip(v, sig2) if x[0] != x[1]]
diff --git a/dkim/asn1.py b/dkim/asn1.py
new file mode 100644
index 0000000..7aa4c00
--- /dev/null
+++ b/dkim/asn1.py
@@ -0,0 +1,128 @@
+# This software is provided 'as-is', without any express or implied
+# warranty.  In no event will the author be held liable for any damages
+# arising from the use of this software.
+#
+# Permission is granted to anyone to use this software for any purpose,
+# including commercial applications, and to alter it and redistribute it
+# freely, subject to the following restrictions:
+#
+# 1. The origin of this software must not be misrepresented; you must not
+#    claim that you wrote the original software. If you use this software
+#    in a product, an acknowledgment in the product documentation would be
+#    appreciated but is not required.
+# 2. Altered source versions must be plainly marked as such, and must not be
+#    misrepresented as being the original software.
+# 3. This notice may not be removed or altered from any source distribution.
+#
+# Copyright (c) 2008 Greg Hewgill http://hewgill.com
+# Copyright (c) 2011 William Grant <me@williamgrant.id.au>
+
+__all__ = [
+    'asn1_build',
+    'asn1_parse',
+    'ASN1FormatError',
+    'BIT_STRING',
+    'INTEGER',
+    'SEQUENCE',
+    'OBJECT_IDENTIFIER',
+    'OCTET_STRING',
+    'NULL',
+    ]
+
+INTEGER = 0x02
+BIT_STRING = 0x03
+OCTET_STRING = 0x04
+NULL = 0x05
+OBJECT_IDENTIFIER = 0x06
+SEQUENCE = 0x30
+
+
+class ASN1FormatError(Exception):
+    pass
+
+
+def asn1_parse(template, data):
+    """Parse a data structure according to an ASN.1 template.
+
+    @param template: tuples comprising the ASN.1 template
+    @param data: byte string data to parse
+    @return: decoded structure
+    """
+
+    r = []
+    i = 0
+    for t in template:
+        tag = ord(data[i])
+        i += 1
+        if tag == t[0]:
+            length = ord(data[i])
+            i += 1
+            if length & 0x80:
+                n = length & 0x7f
+                length = 0
+                for j in range(n):
+                    length = (length << 8) | ord(data[i])
+                    i += 1
+            if tag == INTEGER:
+                n = 0
+                for j in range(length):
+                    n = (n << 8) | ord(data[i])
+                    i += 1
+                r.append(n)
+            elif tag == BIT_STRING:
+                r.append(data[i:i+length])
+                i += length
+            elif tag == NULL:
+                assert length == 0
+                r.append(None)
+            elif tag == OBJECT_IDENTIFIER:
+                r.append(data[i:i+length])
+                i += length
+            elif tag == SEQUENCE:
+                r.append(asn1_parse(t[1], data[i:i+length]))
+                i += length
+            else:
+                raise ASN1FormatError(
+                    "Unexpected tag in template: %02x" % tag)
+        else:
+            raise ASN1FormatError(
+                "Unexpected tag (got %02x, expecting %02x)" % (tag, t[0]))
+    return r
+
+
+def asn1_length(n):
+    """Return a string representing a field length in ASN.1 format.
+
+    @param n: integer field length
+    @return: ASN.1 field length
+    """
+    assert n >= 0
+    if n < 0x7f:
+        return chr(n)
+    r = ""
+    while n > 0:
+        r = chr(n & 0xff) + r
+        n >>= 8
+    return r
+
+
+def asn1_build(node):
+    """Build a DER-encoded ASN.1 data structure.
+
+    @param node: (type, data) tuples comprising the ASN.1 structure
+    @return: DER-encoded ASN.1 byte string
+    """
+    if node[0] == OCTET_STRING:
+        return chr(OCTET_STRING) + asn1_length(len(node[1])) + node[1]
+    if node[0] == NULL:
+        assert node[1] is None
+        return chr(NULL) + asn1_length(0)
+    elif node[0] == OBJECT_IDENTIFIER:
+        return chr(OBJECT_IDENTIFIER) + asn1_length(len(node[1])) + node[1]
+    elif node[0] == SEQUENCE:
+        r = ""
+        for x in node[1]:
+            r += asn1_build(x)
+        return chr(SEQUENCE) + asn1_length(len(r)) + r
+    else:
+        raise ASN1FormatError("Unexpected tag in template: %02x" % node[0])
diff --git a/dkim/crypto.py b/dkim/crypto.py
new file mode 100644
index 0000000..29d734a
--- /dev/null
+++ b/dkim/crypto.py
@@ -0,0 +1,221 @@
+# This software is provided 'as-is', without any express or implied
+# warranty.  In no event will the author be held liable for any damages
+# arising from the use of this software.
+#
+# Permission is granted to anyone to use this software for any purpose,
+# including commercial applications, and to alter it and redistribute it
+# freely, subject to the following restrictions:
+#
+# 1. The origin of this software must not be misrepresented; you must not
+#    claim that you wrote the original software. If you use this software
+#    in a product, an acknowledgment in the product documentation would be
+#    appreciated but is not required.
+# 2. Altered source versions must be plainly marked as such, and must not be
+#    misrepresented as being the original software.
+# 3. This notice may not be removed or altered from any source distribution.
+#
+# Copyright (c) 2008 Greg Hewgill http://hewgill.com
+# Copyright (c) 2011 William Grant <me@williamgrant.id.au>
+
+__all__ = [
+    'DigestTooLargeError',
+    'parse_private_key',
+    'parse_public_key',
+    'RSASSA_PKCS1_v1_5_sign',
+    'RSASSA_PKCS1_v1_5_verify',
+    'UnparsableKeyError',
+    ]
+
+from dkim.asn1 import (
+    ASN1FormatError,
+    asn1_build,
+    asn1_parse,
+    BIT_STRING,
+    INTEGER,
+    SEQUENCE,
+    OBJECT_IDENTIFIER,
+    OCTET_STRING,
+    NULL,
+    )
+
+
+ASN1_Object = [
+    (SEQUENCE, [
+        (SEQUENCE, [
+            (OBJECT_IDENTIFIER,),
+            (NULL,),
+        ]),
+        (BIT_STRING,),
+    ])
+]
+
+ASN1_RSAPublicKey = [
+    (SEQUENCE, [
+        (INTEGER,),
+        (INTEGER,),
+    ])
+]
+
+ASN1_RSAPrivateKey = [
+    (SEQUENCE, [
+        (INTEGER,),
+        (INTEGER,),
+        (INTEGER,),
+        (INTEGER,),
+        (INTEGER,),
+        (INTEGER,),
+        (INTEGER,),
+        (INTEGER,),
+        (INTEGER,),
+    ])
+]
+
+
+class DigestTooLargeError(Exception):
+    """The digest is too large to fit within the requested length."""
+    pass
+
+
+class UnparsableKeyError(Exception):
+    """The data could not be parsed as a key."""
+    pass
+
+
+def parse_public_key(data):
+    """Parse an RSA public key.
+
+    @param data: DER-encoded X.509 subjectPublicKeyInfo
+        containing an RFC3447 RSAPublicKey.
+    @return: RSA public key
+    """
+    try:
+        # Not sure why the [1:] is necessary to skip a byte.
+        x = asn1_parse(ASN1_Object, data)
+        pkd = asn1_parse(ASN1_RSAPublicKey, x[0][1][1:])
+    except ASN1FormatError, e:
+        raise UnparsableKeyError(str(e))
+    pk = {
+        'modulus': pkd[0][0],
+        'publicExponent': pkd[0][1],
+    }
+    return pk
+
+
+def parse_private_key(data):
+    """Parse an RSA private key.
+
+    @param data: DER-encoded RFC3447 RSAPrivateKey.
+    @return: RSA private key
+    """
+    try:
+        pka = asn1_parse(ASN1_RSAPrivateKey, data)
+    except ASN1FormatError, e:
+        raise UnparsableKeyError(str(e))
+    pk = {
+        'version': pka[0][0],
+        'modulus': pka[0][1],
+        'publicExponent': pka[0][2],
+        'privateExponent': pka[0][3],
+        'prime1': pka[0][4],
+        'prime2': pka[0][5],
+        'exponent1': pka[0][6],
+        'exponent2': pka[0][7],
+        'coefficient': pka[0][8],
+    }
+    return pk
+
+
+def EMSA_PKCS1_v1_5_encode(digest, mlen, hashid):
+    """Encode a digest with RFC3447 EMSA-PKCS1-v1_5.
+
+    @param digest: digest byte string to encode
+    @param mlen: desired message length
+    @param hashid: ID of the hash used to generate the digest
+    @return: encoded digest byte string
+    """
+    dinfo = asn1_build(
+        (SEQUENCE, [
+            (SEQUENCE, [
+                (OBJECT_IDENTIFIER, hashid),
+                (NULL, None),
+            ]),
+            (OCTET_STRING, digest),
+        ]))
+    if len(dinfo)+3 > mlen:
+        raise DigestTooLargeError()
+    return "\x00\x01"+"\xff"*(mlen-len(dinfo)-3)+"\x00"+dinfo
+
+
+def str2int(s):
+    """Convert a byte string to an integer.
+
+    @param s: byte string representing a positive integer to convert
+    @return: converted integer
+    """
+    r = 0
+    for c in s:
+        r = (r << 8) | ord(c)
+    return r
+
+
+def int2str(n, length=-1):
+    """Convert an integer to a byte string.
+
+    @param n: positive integer to convert
+    @param length: minimum length
+    @return: converted bytestring, of at least the minimum length if it was
+        specified
+    """
+    assert n >= 0
+    r = []
+    while length < 0 or len(r) < length:
+        r.append(chr(n & 0xff))
+        n >>= 8
+        if length < 0 and n == 0:
+            break
+    r.reverse()
+    assert length < 0 or len(r) == length
+    return ''.join(r)
+
+
+def perform_rsa(message, exponent, modulus, mlen):
+    """Perform RSA signing or verification.
+
+    @param message: byte string to operate on
+    @param exponent: public or private key exponent
+    @param modulus: key modulus
+    @param mlen: desired output length
+    @return: byte string result of the operation
+    """
+    return int2str(pow(str2int(message), exponent, modulus), mlen)
+
+
+def RSASSA_PKCS1_v1_5_sign(digest, hashid, private_exponent, modulus):
+    """Sign a digest with RFC3447 RSASSA-PKCS1-v1_5.
+
+    @param digest: digest byte string to sign
+    @param hashid: ID of the hash used to generate the digest
+    @param private_exponent: private key exponent
+    @param modulus: key modulus
+    @return: signed digest byte string
+    """
+    modlen = len(int2str(modulus))
+    encoded_digest = EMSA_PKCS1_v1_5_encode(digest, modlen, hashid)
+    return perform_rsa(encoded_digest, private_exponent, modulus, modlen)
+
+
+def RSASSA_PKCS1_v1_5_verify(digest, hashid, signature, public_exponent,
+                             modulus):
+    """Verify a digest signed with RFC3447 RSASSA-PKCS1-v1_5.
+
+    @param digest: digest byte string to check
+    @param hashid: ID of the hash used to generate the digest
+    @param signature: signed digest byte string
+    @param public_exponent: public key exponent
+    @param modulus: key modulus
+    @return: True if the signature is valid, False otherwise
+    """
+    modlen = len(int2str(modulus))
+    encoded_digest = EMSA_PKCS1_v1_5_encode(digest, modlen, hashid)
+    signed_digest = perform_rsa(signature, public_exponent, modulus, modlen)
+    return encoded_digest == signed_digest