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scryer-prolog/src/prolog/lib/crypto.pl
Markus Triska 1108c99688 document that lists of integers can be specified if encoding(octet) is used 
This seems to be a good compromise: The API now strongly encourages
lists of characters, which are ideally suited to represent text, and
also allows lists of bytes if the encoding(octet) option is used.
2020-05-21 13:41:57 +02:00

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/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Written May 2020 by Markus Triska (triska@metalevel.at)
Part of Scryer Prolog.
Predicates for cryptographic applications.
This library assumes that the Prolog flag double_quotes is set to chars.
In Scryer Prolog, lists of characters are very efficiently represented,
and strings have the advantage that the atom table remains unmodified.
Especially for cryptographic applications, it as an advantage that
using strings leaves little trace of what was processed in the system.
For predicates that accept an encoding/1 option to specify the encoding
of the input data, if encoding(octet) is used, then the input can also
be specified as a list of bytes, i.e., integers between 0 and 255.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
:- module(crypto,
[hex_bytes/2, % ?Hex, ?Bytes
crypto_n_random_bytes/2, % +N, -Bytes
crypto_data_hash/3, % +Data, -Hash, +Options
crypto_data_hkdf/4, % +Data, +Length, -Bytes, +Options
crypto_password_hash/2, % +Password, ?Hash
crypto_password_hash/3, % +Password, -Hash, +Options
crypto_data_encrypt/6, % +PlainText, +Algorithm, +Key, +IV, -CipherText, +Options
crypto_data_decrypt/6, % +CipherText, +Algorithm, +Key, +IV, -PlainText, +Options
ed25519_new_keypair/1, % -KeyPair
ed25519_keypair_public_key/2, % +KeyPair, +PublicKey
ed25519_sign/4, % +KeyPair, +Data, -Signature, +Options
ed25519_verify/4, % +PublicKey, +Data, +Signature, +Options
crypto_name_curve/2, % +Name, -Curve
crypto_curve_order/2, % +Curve, -Order
crypto_curve_generator/2, % +Curve, -Generator
crypto_curve_scalar_mult/4 % +Curve, +Scalar, +Point, -Result
]).
:- use_module(library(error)).
:- use_module(library(lists)).
:- use_module(library(between)).
:- use_module(library(dcgs)).
:- use_module(library(clpz)).
:- use_module(library(arithmetic)).
:- use_module(library(format)).
:- use_module(library(charsio)).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
hex_bytes(?Hex, ?Bytes) is det.
Relation between a hexadecimal sequence and a list of bytes. Hex
is a string of hexadecimal numbers. Bytes is a list of *integers*
between 0 and 255 that represent the sequence as a list of bytes.
At least one of the arguments must be instantiated.
Example:
?- hex_bytes("501ACE", Bs).
Bs = [80,26,206]
; false.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
hex_bytes(Hs, Bytes) :-
( ground(Hs) ->
must_be(list, Hs),
maplist(must_be(atom), Hs),
( phrase(hex_bytes(Hs), Bytes) ->
true
; domain_error(hex_encoding, Hs, hex_bytes/2)
)
; must_be_bytes(Bytes, hex_bytes/2),
phrase(bytes_hex(Bytes), Hs)
).
hex_bytes([]) --> [].
hex_bytes([H1,H2|Hs]) --> [Byte],
{ char_hexval(H1, High),
char_hexval(H2, Low),
Byte is High*16 + Low },
hex_bytes(Hs).
bytes_hex([]) --> [].
bytes_hex([B|Bs]) --> [C0,C1],
{ High is B>>4,
Low is B /\ 0xf,
char_hexval(C0, High),
char_hexval(C1, Low)
},
bytes_hex(Bs).
char_hexval(C, H) :- nth0(H, "0123456789abcdef", C), !.
char_hexval(C, H) :- nth0(H, "0123456789ABCDEF", C), !.
must_be_bytes(Bytes, Context) :-
must_be(list, Bytes),
maplist(must_be(integer), Bytes),
( member(B, Bytes), \+ between(0, 255, B) ->
type_error(byte, B, Context)
; true
).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Cryptographically secure random numbers
=======================================
crypto_n_random_bytes(+N, -Bytes) is det
Bytes is unified with a list of N cryptographically secure
pseudo-random bytes. Each byte is an integer between 0 and 255. If
the internal pseudo-random number generator (PRNG) has not been
seeded with enough entropy to ensure an unpredictable byte
sequence, an exception is thrown.
One way to relate such a list of bytes to an _integer_ is to use
CLP(ℤ) constraints as follows:
:- use_module(library(clpz)).
:- use_module(library(lists)).
bytes_integer(Bs, N) :-
foldl(pow, Bs, 0-0, N-_).
pow(B, N0-I0, N-I) :-
B in 0..255,
N #= N0 + B*256^I0,
I #= I0 + 1.
With this definition, we can generate a random 256-bit integer
_from_ a list of 32 random _bytes_:
?- crypto_n_random_bytes(32, Bs),
bytes_integer(Bs, I).
Bs = [146,166,162,210,242,7,25,132,64,94|...],
I = 337420085690608915485...(56 digits omitted)
The above relation also works in the other direction, letting you
translate an integer _to_ a list of bytes. In addition, you can
use hex_bytes/2 to convert bytes to _tokens_ that can be easily
exchanged in your applications.
?- crypto_n_random_bytes(12, Bs),
hex_bytes(Hex, Bs).
Bs = [34,25,50,72,58,63,50,172,32,46|...], Hex = "221932483a3f32ac202 ..."
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
crypto_n_random_bytes(N, Bs) :-
must_be(integer, N),
length(Bs, N),
maplist(crypto_random_byte, Bs).
crypto_random_byte(B) :- '$crypto_random_byte'(B).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Hashing
=======
crypto_data_hash(+Data, -Hash, +Options)
Where Data is a list of characters, and Hash is the computed hash
as a list of hexadecimal characters.
Options is a list of:
- algorithm(+A)
where A is one of ripemd160, sha256, sha384, sha512, sha512_256,
sha3_224, sha3_256, sha3_384, sha3_512, blake2s256, blake2b512,
or a variable. If A is a variable, then it is unified with the
default algorithm, which is an algorithm that is considered
cryptographically secure at the time of this writing.
- encoding(+Encoding)
The default encoding is utf8. The alternative is octet,
to treat the input as a list of raw bytes.
Example:
?- crypto_data_hash("abc", Hs, [algorithm(sha256)]).
Hs = "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"
; false.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
SHA256 is the current default for several hash-related predicates.
It is deemed sufficiently secure for the foreseeable future. Yet,
application programmers must be aware that the default may change in
future versions. The hash predicates all yield the algorithm they
used if a Prolog variable is used for the pertaining option.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
crypto_data_hash(Data0, Hash, Options0) :-
must_be(list, Options0),
options_data_bytes(Options0, Data0, Data),
functor_hash_options(algorithm, A, Options0, _),
( hash_algorithm(A) -> true
; domain_error(hash_algorithm, A, crypto_data_hash/3)
),
'$crypto_data_hash'(Data, HashBytes, A),
hex_bytes(Hash, HashBytes).
options_data_bytes(Options, Data, Bytes) :-
option(encoding(Encoding), Options, utf8),
must_be(atom, Encoding),
encoding_bytes(Encoding, Data, Bytes).
default_hash(sha256).
functor_hash_options(F, Hash, Options0, [Option|Options]) :-
Option =.. [F,Hash],
( select(Option, Options0, Options) ->
( var(Hash) ->
default_hash(Hash)
; must_be(atom, Hash)
)
; Options = Options0,
default_hash(Hash)
).
hash_algorithm(ripemd160).
hash_algorithm(sha256).
hash_algorithm(sha512).
hash_algorithm(sha384).
hash_algorithm(sha512_256).
hash_algorithm(sha3_224).
hash_algorithm(sha3_256).
hash_algorithm(sha3_384).
hash_algorithm(sha3_512).
hash_algorithm(blake2s256).
hash_algorithm(blake2b512).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
crypto_data_hkdf(+Data, +Length, -Bytes, +Options) is det.
Concentrate possibly dispersed entropy of Data and then expand it
to the desired length. Data is a list of characters.
Bytes is unified with a list of bytes of length Length, and is
suitable as input keying material and initialization vectors to
symmetric encryption algorithms.
Admissible options are:
- algorithm(+Algorithm)
One of sha256, sha384 or sha512. If you specify a variable,
then it is unified with the algorithm that was used, which is a
cryptographically secure algorithm by default.
- info(+Info)
Optional context and application specific information,
specified as a list of characters. The default is [].
- salt(+List)
Optionally, a list of bytes that are used as salt. The
default is all zeroes.
- encoding(+Encoding)
The default encoding is utf8. The alternative is octet,
to treat the input as a list of raw bytes.
The `info/1` option can be used to generate multiple keys from a
single master key, using for example values such as "key" and
"iv", or the name of a file that is to be encrypted.
See crypto_n_random_bytes/2 to obtain a suitable salt.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
crypto_data_hkdf(Data0, L, Bytes, Options0) :-
functor_hash_options(algorithm, Algorithm, Options0, Options),
( hkdf_algorithm(Algorithm) -> true
; domain_error(hkdf_algorithm, Algorithm, crypto_data_hkdf/4)
),
must_be(integer, L),
L >= 0,
options_data_bytes(Options, Data0, Data),
option(salt(SaltBytes), Options, []),
must_be_bytes(SaltBytes, crypto_data_hkdf/4),
option(info(Info0), Options, []),
chars_bytes_(Info0, Info, crypto_data_hkdf/4),
'$crypto_data_hkdf'(Data, SaltBytes, Info, Algorithm, L, Bytes).
hkdf_algorithm(sha256).
hkdf_algorithm(sha384).
hkdf_algorithm(sha512).
option(What, Options, Default) :-
( member(V, Options), var(V) ->
instantiation_error(option/3)
; true
),
( member(What, Options) -> true
; What =.. [_,Default]
).
chars_bytes_(Cs, Bytes, Context) :-
must_be(list, Cs),
( maplist(integer, Cs) -> Bytes = Cs
; chars_utf8bytes(Cs, Bytes)
),
must_be_bytes(Bytes, Context).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The so-called modular crypt format (MCF) is a standard for encoding
password hash strings. However, there's no official specification
document describing it. Nor is there a central registry of
identifiers or rules. This page describes what is known about it:
https://pythonhosted.org/passlib/modular_crypt_format.html
As of 2016, the MCF is deprecated in favor of the PHC String Format:
https://github.com/P-H-C/phc-string-format/blob/master/phc-sf-spec.md
This is what we are using below. For the time being, it is best to
treat these hashes as opaque terms in applications. Please let me
know if you need to rely on any specifics of this format.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
crypto_password_hash(+Password, ?Hash) is semidet.
If Hash is instantiated, the predicate succeeds _iff_ the hash
matches the given password. Otherwise, the call is equivalent to
crypto_password_hash(Password, Hash, []) and computes a
password-based hash using the default options.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
crypto_password_hash(Password0, Hash) :-
( nonvar(Hash) ->
chars_bytes_(Password0, Password, crypto_password_hash/2),
must_be(list, Hash),
dollar_segments(Hash, [[],"pbkdf2-sha512",[t,=|CsIterations],SaltB64,HashB64]),
number_chars(Iterations, CsIterations),
bytes_base64(SaltBytes, SaltB64),
bytes_base64(HashBytes, HashB64),
'$crypto_password_hash'(Password, SaltBytes, Iterations, HashBytes)
; crypto_password_hash(Password0, Hash, [])
).
dollar_segments(Ls, Segments) :-
( append(Front, [$|Ds], Ls) ->
Segments = [Front|Rest],
dollar_segments(Ds, Rest)
; Segments = [Ls]
).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
crypto_password_hash(+Password, -Hash, +Options) is det.
Derive Hash based on Password. This predicate is similar to
crypto_data_hash/3 in that it derives a hash from given data.
However, it is tailored for the specific use case of _passwords_.
One essential distinction is that for this use case, the derivation
of a hash should be _as slow as possible_ to counteract brute-force
attacks over possible passwords.
Another important distinction is that equal passwords must yield,
with very high probability, _different_ hashes. For this reason,
cryptographically strong random numbers are automatically added to
the password before a hash is derived.
Hash is unified with a string that contains the computed hash and
all parameters that were used, except for the password. Instead of
storing passwords, store these hashes. Later, you can verify the
validity of a password with crypto_password_hash/2, comparing the
then entered password to the stored hash. If you need to export this
atom, you should treat it as opaque ASCII data with up to 255 bytes
of length. The maximal length may increase in the future.
Admissible options are:
- algorithm(+Algorithm)
The algorithm to use. Currently, the only available algorithm
is 'pbkdf2-sha512', which is therefore also the default.
- cost(+C)
C is an integer, denoting the binary logarithm of the number
of _iterations_ used for the derivation of the hash. This
means that the number of iterations is set to 2^C. Currently,
the default is 17, and thus more than one hundred _thousand_
iterations. You should set this option as high as your server
and users can tolerate. The default is subject to change and
will likely increase in the future or adapt to new algorithms.
- salt(+Salt)
Use the given list of bytes as salt. By default,
cryptographically secure random numbers are generated for this
purpose. The default is intended to be secure, and constitutes
the typical use case of this predicate.
Currently, PBKDF2 with SHA-512 is used as the hash derivation
function, using 128 bits of salt. All default parameters, including
the algorithm, are subject to change, and other algorithms will also
become available in the future. Since computed hashes store all
parameters that were used during their derivation, such changes will
not affect the operation of existing deployments. Note though that
new hashes will then be computed with the new default parameters.
See crypto_data_hkdf/4 for generating keys from Hash.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
crypto_password_hash(Password0, Hash, Options) :-
chars_bytes_(Password0, Password, crypto_password_hash/3),
must_be(list, Options),
option(cost(C), Options, 17),
Iterations is 2^C,
Algorithm = 'pbkdf2-sha512', % current default and only option
option(algorithm(Algorithm), Options, Algorithm),
( member(salt(SaltBytes), Options) ->
must_be_bytes(SaltBytes, crypto_password_hash/2)
; crypto_n_random_bytes(16, SaltBytes)
),
'$crypto_password_hash'(Password, SaltBytes, Iterations, HashBytes),
bytes_base64(HashBytes, HashB64),
bytes_base64(SaltBytes, SaltB64),
phrase(format_("$pbkdf2-sha512$t=~d$~s$~s", [Iterations,SaltB64,HashB64]), Hash).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Bidirectional Bytes <-> Base64 conversion
=========================================
This implements Base64 conversion *without padding*.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
n_base64(0 , 'A'). n_base64(1 , 'B'). n_base64(2 , 'C'). n_base64(3 , 'D').
n_base64(4 , 'E'). n_base64(5 , 'F'). n_base64(6 , 'G'). n_base64(7 , 'H').
n_base64(8 , 'I'). n_base64(9 , 'J'). n_base64(10, 'K'). n_base64(11, 'L').
n_base64(12, 'M'). n_base64(13, 'N'). n_base64(14, 'O'). n_base64(15, 'P').
n_base64(16, 'Q'). n_base64(17, 'R'). n_base64(18, 'S'). n_base64(19, 'T').
n_base64(20, 'U'). n_base64(21, 'V'). n_base64(22, 'W'). n_base64(23, 'X').
n_base64(24, 'Y'). n_base64(25, 'Z'). n_base64(26, 'a'). n_base64(27, 'b').
n_base64(28, 'c'). n_base64(29, 'd'). n_base64(30, 'e'). n_base64(31, 'f').
n_base64(32, 'g'). n_base64(33, 'h'). n_base64(34, 'i'). n_base64(35, 'j').
n_base64(36, 'k'). n_base64(37, 'l'). n_base64(38, 'm'). n_base64(39, 'n').
n_base64(40, 'o'). n_base64(41, 'p'). n_base64(42, 'q'). n_base64(43, 'r').
n_base64(44, 's'). n_base64(45, 't'). n_base64(46, 'u'). n_base64(47, 'v').
n_base64(48, 'w'). n_base64(49, 'x'). n_base64(50, 'y'). n_base64(51, 'z').
n_base64(52, '0'). n_base64(53, '1'). n_base64(54, '2'). n_base64(55, '3').
n_base64(56, '4'). n_base64(57, '5'). n_base64(58, '6'). n_base64(59, '7').
n_base64(60, '8'). n_base64(61, '9'). n_base64(62, '+'). n_base64(63, '/').
bytes_base64(Ls, Bs) :-
( list(Bs), maplist(atom, Bs) ->
maplist(n_base64, Is, Bs),
phrase(bytes_base64_(Ls), Is),
Ls ins 0..255
; phrase(bytes_base64_(Ls), Is),
Is ins 0..63,
maplist(n_base64, Is, Bs)
).
list(Ls) :-
nonvar(Ls),
( Ls = [] -> true
; Ls = [_|Rest],
list(Rest)
).
bytes_base64_([]) --> [].
bytes_base64_([A]) --> [W,X],
{ A #= W*4 + X//16,
X #= 16*_ }.
bytes_base64_([A,B]) --> [W,X,Y],
{ A #= W*4 + X//16,
B #= (X mod 16)*16 + Y//4,
Y #= 4*_ }.
bytes_base64_([A,B,C|Ls]) --> [W,X,Y,Z],
{ A #= W*4 + X//16,
B #= (X mod 16)*16 + Y//4,
C #= (Y mod 4)*64 + Z },
bytes_base64_(Ls).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
crypto_data_encrypt(+PlainText,
+Algorithm,
+Key,
+IV,
-CipherText,
+Options).
Encrypt the given PlainText, using the symmetric algorithm
Algorithm, key Key, and initialization vector (or nonce) IV, to
give CipherText.
PlainText must be a list of characters, Key and IV must be lists of
bytes, and CipherText is created as a list of characters.
Keys and IVs can be chosen at random (using for example
crypto_n_random_bytes/2) or derived from input keying material (IKM)
using for example crypto_data_hkdf/4. This input is often a shared
secret, such as a negotiated point on an elliptic curve, or the hash
that was computed from a password via crypto_password_hash/3 with a
freshly generated and specified _salt_.
Reusing the same combination of Key and IV typically leaks at least
_some_ information about the plaintext. For example, identical
plaintexts will then correspond to identical ciphertexts. For some
algorithms, reusing an IV with the same Key has disastrous results
and can cause the loss of all properties that are otherwise
guaranteed. Especially in such cases, an IV is also called a
_nonce_ (number used once).
It is safe to store and transfer the used initialization vector (or
nonce) in plain text, but the key _must be kept secret_.
Currently, the only supported algorithm is 'chacha20-poly1305', a
powerful and efficient _authenticated_ encryption scheme, providing
secrecy and at the same time reliable protection against undetected
_modifications_ of the encrypted data. This is a very good choice
for virtually all use cases. It is a stream cipher and can encrypt
data of any length up to 256 GB. Further, the encrypted data has
exactly the same length as the original, and no padding is used.
Options:
- encoding(+Encoding)
Encoding to use for PlainText. Default is utf8. The alternative
is octet to treat PlainText as raw bytes.
- tag(-List)
For authenticated encryption schemes, List is unified with a
list of _bytes_ holding the tag. This tag must be provided for
decryption.
Here is an example encryption and decryption, using the ChaCha20
stream cipher with the Poly1305 authenticator. This cipher uses a
256-bit key and a 96-bit nonce, i.e., 32 and 12 _bytes_,
respectively:
?- Algorithm = 'chacha20-poly1305',
crypto_n_random_bytes(32, Key),
crypto_n_random_bytes(12, IV),
crypto_data_encrypt("this text is to be encrypted", Algorithm,
Key, IV, CipherText, [tag(Tag)]),
crypto_data_decrypt(CipherText, Algorithm,
Key, IV, RecoveredText, [tag(Tag)]).
Yielding:
Algorithm = 'chacha20-poly1305',
Key = [113,247,153,134,177,220,13,193,50,150|...],
IV = [135,20,149,153,63,35,68,114,247,171|...],
CipherText = "\x94\0Ej\x94\®Â\x95\óÑÆXÃn¾ð©b\x1c\ ...",
RecoveredText = "this text is to be ...",
Tag = [152,117,152,17,162,75,150,206,144,40|...]
In this example, we use crypto_n_random_bytes/2 to generate a key
and nonce from cryptographically secure random numbers. For
repeated applications, you must ensure that a nonce is only used
_once_ together with the same key. Note that for _authenticated_
encryption schemes, the _tag_ that was computed during encryption
is necessary for decryption. It is safe to store and transfer the
tag in plain text.
See also crypto_data_decrypt/6, and hex_bytes/2 for conversion
between bytes and hex encoding.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
crypto_data_encrypt(PlainText0, Algorithm, Key, IV, CipherText, Options) :-
options_data_bytes(Options, PlainText0, PlainText),
option(tag(Tag), Options, _),
( nonvar(Tag) ->
must_be_bytes(Tag, crypto_data_encrypt/6)
; true
),
must_be_bytes(Key, crypto_data_encrypt/6),
must_be_bytes(IV, crypto_data_encrypt/6),
must_be(atom, Algorithm),
( Algorithm = 'chacha20-poly1305' -> true
; domain_error('chacha20-poly1305', Algorithm, crypto_data_encrypt/6)
),
'$crypto_data_encrypt'(PlainText, Key, IV, Tag, CipherText).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
crypto_data_decrypt(+CipherText,
+Algorithm,
+Key,
+IV,
-PlainText,
+Options).
Decrypt the given CipherText, using the symmetric algorithm
Algorithm, key Key, and initialization vector IV, to give
PlainText. CipherText must be a list of characters, and Key and IV
must be lists of bytes. PlainText is created as a list of
characters.
Currently, the only supported algorithm is 'chacha20-poly1305',
a very secure, fast and versatile authenticated encryption method.
Options is a list of:
- encoding(+Encoding)
Encoding to use for PlainText. The default is utf8. The
alternative is octet, which is used if the data are raw bytes.
- tag(+Tag)
For authenticated encryption schemes, the tag must be specified as
a list of bytes exactly as they were generated upon encryption.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
crypto_data_decrypt(CipherText0, Algorithm, Key, IV, PlainText, Options) :-
option(tag(Tag), Options, []),
must_be_bytes(Tag, crypto_data_decrypt/6),
must_be_bytes(Key, crypto_data_decrypt/6),
must_be_bytes(IV, crypto_data_decrypt/6),
must_be(atom, Algorithm),
option(encoding(Encoding), Options, utf8),
must_be(atom, Encoding),
member(Encoding, [utf8,octet]),
must_be(list, CipherText0),
encoding_bytes(octet, CipherText0, CipherText1),
append(CipherText1, Tag, CipherText),
( Algorithm = 'chacha20-poly1305' -> true
; domain_error('chacha20-poly1305', Algorithm, crypto_data_decrypt/6)
),
'$crypto_data_decrypt'(CipherText, Key, IV, Encoding, PlainText).
encoding_bytes(octet, Bs0, Bs) :-
must_be(list, Bs0),
( maplist(integer, Bs0) ->
Bs0 = Bs
; maplist(char_code, Bs0, Bs)
),
must_be_bytes(Bs, crypto_encoding).
encoding_bytes(utf8, Cs, Bs) :-
must_be(list, Cs),
( maplist(atom, Cs) ->
chars_bytes_(Cs, Bs, crypto_encoding)
; domain_error(encryption_encoding, Cs, crypto)
).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Digital signatures with Ed25519
===============================
- ed25519_new_keypair(-Pair)
Yields a new Ed25519 key pair Pair, a list of characters. The
pair contains the private key and must be kept absolutely secret.
Pair can be used for signing. Its public key can be obtained
with ed25519_keypair_public_key/2.
- ed25519_keypair_public_key(+Pair, -PublicKey)
PublicKey is the public key of the given key pair. The public key
can be used for signature verification, and can be shared freely.
The public key is represented as a list of characters.
- ed25519_sign(+Key, +Data, -Signature, +Options)
Key and Data must be lists of characters. Key is a key pair in
PKCS#8 v2 format as generated by ed25519_new_keypair/1. Sign Data
with Key, yielding Signature as a list of hexadecimal characters.
- ed25519_verify(+Key, +Data, +Signature, +Options)
Key and Data must be lists of characters. Key is a public key.
Succeeds if Data was signed with the private key corresponding to
Key, where Signature is a list of hexadecimal characters as
generated by ed25519_sign/4. Fails otherwise.
Currently, the only option for signing and verifying is:
- encoding(+Encoding)
The default encoding of Data is utf8. The alternative is octet,
which treats Data as a list of raw bytes.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ed25519_new_keypair(Pair) :-
'$ed25519_new_keypair'(Pair).
ed25519_keypair_public_key(Pair0, PublicKey) :-
encoding_bytes(octet, Pair0, Pair),
'$ed25519_keypair_public_key'(Pair, PublicKey).
ed25519_sign(Key0, Data0, Signature, Options) :-
options_data_bytes(Options, Data0, Data),
encoding_bytes(octet, Key0, Key),
'$ed25519_sign'(Key, Data, Signature0),
hex_bytes(Signature, Signature0).
ed25519_verify(Key0, Data0, Signature0, Options) :-
options_data_bytes(Options, Data0, Data),
encoding_bytes(octet, Key0, Key),
hex_bytes(Signature0, Signature),
'$ed25519_verify'(Key, Data, Signature).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Modular multiplicative inverse.
Compute Y = X^(-1) mod p, using the extended Euclidean algorithm.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
multiplicative_inverse_modulo_p(X, P, Y) :-
eea(X, P, _, _, Y),
R #= X*Y mod P,
zcompare(C, 1, R),
must_be_one(C, X, P, Y).
must_be_one(=, _, _, _).
must_be_one(>, X, P, Y) :- throw(multiplicative_inverse_modulo_p(X,P,Y)).
must_be_one(<, X, P, Y) :- throw(multiplicative_inverse_modulo_p(X,P,Y)).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Extended Euclidean algorithm.
Computes the GCD and the Bézout coefficients S and T.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
eea(I, J, G, S, T) :-
State0 = state(1,0,0,1),
eea_loop(I, J, State0, G, S, T).
eea_loop(I, J, State0, G, S, T) :-
zcompare(C, 0, J),
eea_(C, I, J, State0, G, S, T).
eea_(=, I, _, state(_,_,U,V), I, U, V).
eea_(<, I0, J0, state(S0,T0,U0,V0), I, U, V) :-
Q #= I0 // J0,
R #= I0 mod J0,
S1 #= U0 - (Q*S0),
T1 #= V0 - (Q*T0),
eea_loop(J0, R, state(S1,T1,S0,T0), I, U, V).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Operations on Elliptic Curves
=============================
Sample use: Establishing a shared secret S, using ECDH key exchange.
?- crypto_name_curve(Name, C),
crypto_curve_generator(C, Generator),
PrivateKey = 10,
crypto_curve_scalar_mult(C, PrivateKey, Generator, PublicKey),
Random = 12,
crypto_curve_scalar_mult(C, Random, Generator, R),
crypto_curve_scalar_mult(C, Random, PublicKey, S),
crypto_curve_scalar_mult(C, PrivateKey, R, S).
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
An elliptic curve over a prime field F_p is represented as:
curve(P,A,B,point(X,Y),Order,Cofactor).
First, we define suitable accessors.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
curve_p(curve(P,_,_,_,_,_), P).
curve_a(curve(_,A,_,_,_,_), A).
curve_b(curve(_,_,B,_,_,_), B).
crypto_curve_order(curve(_,_,_,_,Order,_), Order).
crypto_curve_generator(curve(_,_,_,G,_,_), G).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Scalar point multiplication.
R = k*Q.
The Montgomery ladder method is used to mitigate side-channel
attacks such as timing attacks, since the number of multiplications
and additions is independent of the private key K. This method does
not even reveal the key's Hamming weight (number of 1s).
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
crypto_curve_scalar_mult(Curve, K, Q, R) :-
msb(K, Upper),
scalar_multiplication(Curve, K, Upper, ml(null,Q)-R),
must_be_on_curve(Curve, R).
scalar_multiplication(Curve, K, I, R0-R) :-
zcompare(C, -1, I),
scalar_mult_(C, Curve, K, I, R0-R).
scalar_mult_(=, _, _, _, ml(R,_)-R).
scalar_mult_(<, Curve, K, I0, ML0-R) :-
BitSet #= K /\ (1 << I0),
zcompare(C, 0, BitSet),
montgomery_step(C, Curve, ML0, ML1),
I1 #= I0 - 1,
scalar_multiplication(Curve, K, I1, ML1-R).
montgomery_step(=, Curve, ml(R0,S0), ml(R,S)) :-
curve_points_addition(Curve, R0, S0, S),
curve_point_double(Curve, R0, R).
montgomery_step(<, Curve, ml(R0,S0), ml(R,S)) :-
curve_points_addition(Curve, R0, S0, R),
curve_point_double(Curve, S0, S).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Doubling a point: R = A + A.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
curve_point_double(_, null, null).
curve_point_double(Curve, point(AX,AY), R) :-
curve_p(Curve, P),
curve_a(Curve, A),
Numerator #= (3*AX^2 + A) mod P,
Denom0 #= 2*AY mod P,
multiplicative_inverse_modulo_p(Denom0, P, Denom),
S #= (Numerator*Denom) mod P,
R = point(RX,RY),
RX #= (S^2 - 2*AX) mod P,
RY #= (S*(AX - RX) - AY) mod P,
must_be_on_curve(Curve, R).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Adding two points.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
curve_points_addition(Curve, P, Q, R) :-
curve_points_addition_(P, Curve, Q, R).
curve_points_addition_(null, _, P, P).
curve_points_addition_(P, _, null, P).
curve_points_addition_(point(AX,AY), Curve, point(BX,BY), R) :-
curve_p(Curve, P),
Numerator #= (AY - BY) mod P,
Denom0 #= (AX - BX) mod P,
multiplicative_inverse_modulo_p(Denom0, P, Denom),
S #= (Numerator * Denom) mod P,
R = point(RX,RY),
RX #= (S^2 - AX - BX) mod P,
RY #= (S*(AX - RX) - AY) mod P,
must_be_on_curve(Curve, R).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Validation.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
curve_contains_point(Curve, point(QX,QY)) :-
curve_a(Curve, A),
curve_b(Curve, B),
curve_p(Curve, P),
QY^2 mod P #= (QX^3 + A*QX + B) mod P.
must_be_on_curve(Curve, P) :-
\+ curve_contains_point(Curve, P),
throw(not_on_curve(P)).
must_be_on_curve(Curve, P) :- curve_contains_point(Curve, P).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Predefined curves
=================
List available curves:
$ openssl ecparam -list_curves
Show curve parameters for secp256k1:
$ openssl ecparam -param_enc explicit -conv_form uncompressed \
-text -no_seed -name secp256k1
You must remove the leading "04:" from the generator.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
crypto_name_curve(secp112r1,
curve(0x00db7c2abf62e35e668076bead208b,
0x00db7c2abf62e35e668076bead2088,
0x659ef8ba043916eede8911702b22,
point(0x09487239995a5ee76b55f9c2f098,
0xa89ce5af8724c0a23e0e0ff77500),
0x00db7c2abf62e35e7628dfac6561c5,
1)).
crypto_name_curve(secp256k1,
curve(0x00fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f,
0x0,
0x7,
point(0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,
0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8),
0x00fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141,
1)).
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