问题
This question is related to Opening and checking a Pem file in SWI-Prolog
Once I have downloaded and opened the certificates how do I verify the signature chain? I have:
:-use_module(library(http/http_client)).
url('https://s3.amazonaws.com/echo.api/echo-api-cert-4.pem').
url_data1(Url,Certs):-
http_open(Url,Stream,[]),
all_certs(Stream,Certs),
forall(member(C,Certs),my_validate(C)),
close(Stream).
all_certs(Stream,[C1|Certs]):-
catch(load_certificate(Stream,C1),_,fail),
all_certs(Stream,Certs),!.
all_certs(_Stream,[]).
my_validate(C):-
memberchk(to_be_signed(Signed),C),
memberchk(key(Key),C),
memberchk(signature(Signature),C),
memberchk(signature_algorithm(A),C),
algo_code(A,Code),
rsa_verify(Key,Signed,Signature,[type(Code)]).
algo_code('RSA-SHA256',sha256).
algo_code('RSA-SHA1',sha1).
This currently fails.
回答1:
Preliminaries
Verifying digital signatures and entire certificate chains is extremely easy with Prolog.
However, you need to have a basic understanding of how certificates are signed. A certificate chain is a sequence of certificates C0, C1, ..., CN. I am using CN to denote the root certificate. Depending on the used convention, you may mutatis mutandis reverse the order of course.
Importantly, certificate Ck is signed using the private key corresponding to the public key of Ck+1.
Thus, one of the issues with your code is that you are mistakenly using the public key of C to verify the signature of C even though the certificate was signed with the private key corresponding to a different certificate.
A different issue stems from some confusion about what is being signed. We are signing the hash of the to-be-signed part of a certificate, not the data itself. Thus, we must verify the signature against that hash.
Concrete example
To make this answer self-contained, I post here the relevant data from your use case, i.e., the relevant attributes of the certificates that the file contains at the time of this writing.
Data
First certificate
From the first certificate in the chain, we need the signature and the to-be-signed portion, which are:
signature("7B86A6E7A86B192579380108B7EADA1C25E288AB46120117DC6A80635324C89713C70206EF3FE13CCA5EDFF43601972CB96658826ADCD68B0FB3AE7F5607D036D6AE8AF824CD96D7F1B4DB58E714343031F292B17E6EEF83872A0FD586CC0D1DA85A677E4AB4C6540E9132B5BC5644533E0388F830B1B6757B7DB88AB82846F08B3B6DCEC7F24319AB7EA56F86592DDDEC4522CAF331C8B81A4E543FBDBF4D661B534BAE546465DB88A525BC82A7B4127F0AFF4A55525927A66A09055743F109E30D90CA074D258166F0E472CB7CCDB0747ADE74F7040CFEEB9A78C3483864C5106D542556C874AF768005A6EC83ADEB2EE32F8E6F7182A362775C2BF40AFA20").
to_be_signed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
Second certificate
From the second certificate, we only need the public key to verify the signature that was issued for the previous certificate:
key(public_key(rsa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
Verification
Computing the hash
As I said, a hash is what was actually signed. Critically, I don't mean the hash of the whole certificate, but the hash of the to-be-signed portion. This difference is important, because the hash of the whole certificate also comprises the signature, and that is of course not yet available when the certificate is being signed.
In SWI-Prolog, we can obtain the hash of the to-be-signed portion using library(crypto):
?- to_be_signed(TBS), hex_bytes(TBS, Bytes), crypto_data_hash(Bytes, Hash, [algorithm(sha256), encoding(octet)]). TBS = "3082...EB3B62", Bytes = [48, 130, 4, 102, 160, 3, 2, 1, 2|...], Hash = '651bdcdd90251f71a47a5d1bbc6f28486c94d2dc3739dcd58ecb09b3f224ee05'.
I am using sha256 because the first certificate indicates (RSA and) SHA256 in its signature_algorithm/1 field.
Verifying the signature using CLP(FD) constraints
One of the easiest ways to verify an RSA signature is to use CLP(FD) constraints. We only need to compute SigExp mod p. We plug in our concrete numbers, using (#=)/2 to evaluate the arithmetic expression over integers:
?- X #= 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x010001
mod 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
It yields:
X = 986236757547332986472011617696226561292849812918563355472727826767720188564083584387121625107510786855734801053524719833194566624465665316622563244215340671405971599343902468620306327831715457360719532421388780770165778156818229863337344187575566725786793391480600129482653072861971002459947277805295727097226389568776499707662505334062639449916265137796823793276300221537201727072401742985542559596685092673521228140822200236743113743661549252453726123450722876929538747702356573783116197523966334991563351853851212597377279504828784716104866621888265058037501385433453379649364782998949981722124880992983641605.
Excursion: On efficiency and use of CLP(FD).
You may now say: "Well, I don't really need (#=)/2, I can always use (is)/2 which I learned decades ago." But, if you are using (is)/2 in such examples, you easily end up with code that is thousands of times less efficient. As a simple benchmark, consider the predicate:
signature_pow(Sig, Exp, P, Pow) :-
Pow #= Sig^Exp mod P.
Now we have, for the query:
?- time(signature_pow(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x010001, 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ow)).
the timing:
% 16 inferences, 0.000 CPU in 0.000 seconds (99% CPU, 130624 Lips)
In contrast, if we regress in Prolog language development and replace (#=)/2 by (is)/2, we get:
% 3 inferences, 1.847 CPU in 1.852 seconds (100% CPU, 2 Lips)
Reason: In SWI-Prolog, certain goals involving (#=)/2 automatically use specialized arithmetic predicates. You do not need to learn these predicates to use them. CLP(FD) does it for you.
Recommendation: Use CLP(FD) constraints for reasoning over integers in Prolog. They typically make your predicates more general, and sometimes vastly more efficient. clpfd
Now, what about X? To see what it is, consider its hexadecimal encoding:
?- format("~16r", [$X]).
1fffffff...fff003031300d060960864801650304020105000420651bdcdd90251f71a47a5d1bbc6f28486c94d2dc3739dcd58ecb09b3f224ee05
This sounds familiar: At the end, you see that the hash of the to-be-signed portion of the certificate appears. This means that the signature checks out!
Verifying the signature with rsa_verify/4
Alternatively, we can use rsa_verify/4 from library(crypto) to verify the signature.
Here is the full query:
?- to_be_signed(TBS), hex_bytes(TBS, Bytes), crypto_data_hash(Bytes, Hash, [algorithm(sha256), encoding(octet)]), signature(Sig), key(Key), rsa_verify(Key, Hash, Sig, [type(sha256)]).
Since this succeeds, we know that the private key corresponding to Key was used to produce the signature.
Closing remarks
I have one important remark: Normally, this is all of course completely unnecessary!
The SWI-Prolog SSL infrastructure automatically verifies the certificate chain and thus all signatures every single time you use http_open/3 and related predicates to make a connection via TLS. But it is interesting to make these calculations yourself. Sometimes it is even necessary, if, as in this example, you are reasoning over certificates you have stored somewhere.
One small additional remark: Please use setup_call_cleanup/3 in your code. Otherwise, you risk leaking file descriptors if anything goes wrong before close/1, which is in fact even the case in your example.
来源：https://stackoverflow.com/questions/44507213/verifying-a-signature-chain-swi-prolog