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CertficateChain.spthy
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theory CertificateChain
begin
builtins: signing
functions:
create_certificate/3,
verify_certificate/2,
get_public_key_certificate/1,
get_signature_certificate/1,
get_tbsInfo_certificate/1
equations:
/*
Input :
SubjectTBSCertificateInfo = TBS Certificate info as expalined in https://datatracker.ietf.org/doc/html/rfc5280
SubjectPub : Subject public key
Issuer: Issuer Secret key , For signing the certificate
*/
create_certificate(SubjectTBSCertificateInfo,SubjectPup,IssuerSk)
= < SubjectTBSCertificateInfo, SubjectPup, sign(<SubjectTBSCertificateInfo, SubjectPup>,IssuerSk) >,
/*
Input :
Certificate.1 = Certificate of the subject need to verifed
Certificate.2 = Certificate of the issuer to verfiy the subject certificate
The certificate take the forms of :
<TBSCertificateInfo, publicKey, signature >
where:
TBSCertificateInfo = TBS Certificate info as expalined in https://datatracker.ietf.org/doc/html/rfc5280
publicKey = The certificate public key data
signature : signature of the Subject's TBSCertificateInfo and publicKey signed via Issuer private key
Note if IssuerSk = IssuerRootSk, then the issuer certficate is self signed certificate
*/
verify_certificate(
< SubjectTBSCertificateInfo, pk(SubjectSk), sign(<SubjectTBSCertificateInfo, pk(SubjectSk)>,IssuerSk) >
, < IssuerTBSCertificateInfo, pk(IssuerSk), sign(<IssuerTBSCertificateInfo, pk(IssuerSk)>,IssuerRootSk) >
) = true,
/*
Get public key of a certificate
Input :
Certificate
Return:
Public key of the certificate
*/
get_public_key_certificate(
< SubjectTBSCertificateInfo, pk(SubjectSk), sign(<SubjectTBSCertificateInfo, pk(SubjectSk)>,IssuerSk) >
) = pk(SubjectSk),
/*
Get Signature a certificate
Input :
Certificate
Return:
Signature
*/
get_signature_certificate(
< SubjectTBSCertificateInfo, pk(SubjectSk), sign(<SubjectTBSCertificateInfo, pk(SubjectSk)>,IssuerSk) >
) = sign(<SubjectTBSCertificateInfo, pk(SubjectSk)>,IssuerSk),
/*
Get TBS Info
Input :
Certificate
Return:
Signature
*/
get_tbsInfo_certificate(
< SubjectTBSCertificateInfo, pk(SubjectSk), sign(<SubjectTBSCertificateInfo, pk(SubjectSk)>,IssuerSk) >
) = SubjectTBSCertificateInfo
rule testGetPublicKey:
let
//creating CA Root certificate (self-signed)
CARootCertificate = create_certificate('TBSCertificateInfo',pk(~rootSk),~rootSk)
//Create a certificate issued by CA Root certificate
SubjectCertificate = create_certificate('TBSCertificateInfo',pk(~subjectSk),~rootSk)
//Extract Public key
SubjectCertificatePup = get_public_key_certificate(SubjectCertificate)
in
[
Fr(~rootSk),Fr(~subjectSk)
]
--[AssertGetPublicKey(pk(~subjectSk),SubjectCertificatePup)]->
[]
rule testChainCertificate:
let
//creating CA Root certificate (self-signed)
CARootCertificate = create_certificate('TBSCertificateInfo',pk(~rootSk),~rootSk)
//Create a certificate issued by CA Root certificate
SubjectCertificate = create_certificate('TBSCertificateInfo',pk(~subjectSk),~rootSk)
//verify self-signed certificate
verfication1 = verify_certificate(CARootCertificate,CARootCertificate)
//verify certificate chain
verfication2 = verify_certificate(SubjectCertificate,CARootCertificate)
in
[
Fr(~rootSk),Fr(~subjectSk)
]
--[AssertChainCertificate(verfication1,verfication2)]->
[]
rule testVerifyTamperedCertificate:
let
//creating CA Root certificate (self-signed)
CARootCertificate = create_certificate('TBSCertificateInfo',pk(~rootSk),~rootSk)
//Create a certificate issued by CA Root certificate
SubjectCertificate = create_certificate('TBSCertificateInfo',pk(~subjectSk),~rootSk)
//Craft certificate with invalid TBS info
//Extract Public key
SubjectCertificatePup = get_public_key_certificate(SubjectCertificate)
//Extract Signature
SubjectCertificateSignature = get_public_key_certificate(SubjectCertificate)
//Craft the fake certificate
fakeCertificate = <'FakeInfoTBSCertificateInfo', SubjectCertificatePup,SubjectCertificateSignature>
//Verfiy the certificate using issuer certificate
verfication = verify_certificate(fakeCertificate,CARootCertificate)
in
[
Fr(~rootSk),Fr(~subjectSk)
]
--[AssertVerifyTamperedCertificate(verfication)]->
[]
rule testChainCertficateWithExtensions:
let
//creating CA Root certificate (self-signed)
CARootCertificate = create_certificate(<'TBSCertificateInfo',~root_id>,pk(~rootSk),~rootSk)
//Create a certificate issued by CA Root certificate
SubjectCertificate = create_certificate(<'TBSCertificateInfo',~subject_id>,pk(~subjectSk),~rootSk)
//verify self-signed certificate
verfication1 = verify_certificate(CARootCertificate,CARootCertificate)
//verify certificate chain
verfication2 = verify_certificate(SubjectCertificate,CARootCertificate)
in
[
Fr(~rootSk),Fr(~subjectSk),
Fr(~root_id),Fr(~subject_id)
]
--[AssertChainCertficateWithExtensions(verfication1,verfication2)]->
[]
lemma testChainCertificate: exists-trace "Ex #i . AssertChainCertificate(true,true) @i "
lemma testGetPublicKey: exists-trace "Ex ppk #i . AssertGetPublicKey(ppk,ppk) @i "
lemma testVerifyTamperedCertificate: exists-trace "not Ex #i . AssertVerifyTamperedCertificate(true) @i "
lemma testChainCertficateWithExtensions: exists-trace "Ex #i . AssertChainCertficateWithExtensions(true,true) @i "
end
==============================================================================
summary of summaries:
analyzed: CertficateChain.spthy
testChainCertificate (exists-trace): verified (2 steps)
testGetPublicKey (exists-trace): verified (2 steps)
testVerifyTamperedCertificate (exists-trace): verified (3 steps)
testChainCertficateWithExtensions (exists-trace): verified (2 steps)
==============================================================================