W@sdZddlmZmZmZmZddlZddlZddlm Z m Z m Z m Z m Z mZmZddlmZddlmZmZmZddlmZmZmZdd lmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)dd l*m+Z+m,Z,Gd d d e'Z-Gd dde(Z.GdddeZ/Gddde'Z0Gddde'Z1Gddde'Z2GdddZ3Gddde$e3Z4Gddde#e3Z5GdddeZ6Gdd d e"Z7Gd!d"d"e"Z8Gd#d$d$e'Z9Gd%d&d&e'Z:Gd'd(d(e'Z;Gd)d*d*e'Z<Gd+d,d,e'Z=Gd-d.d.e"Z>Gd/d0d0eZ?Gd1d2d2eZ@Gd3d4d4e'ZAGd5d6d6e'ZBGd7d8d8e'ZCGd9d:d:e)ZDGd;d<d<e"ZEGd=d>d>ee'ZFGd?d@d@e'ZGGdAdBdBe'ZHGdCdDdDe'ZIGdEdFdFe'ZJGdGdHdHe"ZKGdIdJdJee'ZLGdKdLdLe'ZMdS)Ma' ASN.1 type classes for public and private keys. Exports the following items: - DSAPrivateKey() - ECPrivateKey() - EncryptedPrivateKeyInfo() - PrivateKeyInfo() - PublicKeyInfo() - RSAPrivateKey() - RSAPublicKey() Other type classes are defined that help compose the types listed above. )unicode_literalsdivisionabsolute_importprint_functionN)SECP192R1_BASE_POINTSECP224R1_BASE_POINTSECP256R1_BASE_POINTSECP384R1_BASE_POINTSECP521R1_BASE_POINT PrimeCurve PrimePoint)unwrap) type_namestr_clsbyte_cls)_ForceNullParametersDigestAlgorithmEncryptionAlgorithm)Any Asn1Value BitStringChoiceIntegerIntegerOctetStringNullObjectIdentifierOctetBitString OctetStringParsableOctetStringParsableOctetBitStringSequence SequenceOfSetOf)int_from_bytes int_to_bytesc@s7eZdZdZdefdefdefgZdS)OtherPrimeInfoz= Source: https://tools.ietf.org/html/rfc3447#page-46 primeZexponent coefficientN)__name__ __module__ __qualname____doc__r_fieldsr.r.1/usr/lib/python3/dist-packages/asn1crypto/keys.pyr&6s   r&c@seZdZdZeZdS)OtherPrimeInfosz= Source: https://tools.ietf.org/html/rfc3447#page-46 N)r)r*r+r,r& _child_specr.r.r.r/r0Bs r0c@s(eZdZdZddddiZdS)RSAPrivateKeyVersionzX Original Name: Version Source: https://tools.ietf.org/html/rfc3447#page-45 rz two-primerZmultiN)r)r*r+r,_mapr.r.r.r/r2Js r2c @seZdZdZdefdefdefdefdefdefdefd efd efd ed d ifg ZdS) RSAPrivateKeyz= Source: https://tools.ietf.org/html/rfc3447#page-45 versionmoduluspublic_exponentZprivate_exponentZprime1Zprime2Z exponent1Z exponent2r(Zother_prime_infosoptionalTN)r)r*r+r,r2rr0r-r.r.r.r/r4Vs          r4c@s.eZdZdZdefdefgZdS) RSAPublicKeyz= Source: https://tools.ietf.org/html/rfc3447#page-44 r6r7N)r)r*r+r,rr-r.r.r.r/r9is  r9c@sReZdZdZdefdefdefdefdefdefgZdS) DSAPrivateKeya& The ASN.1 structure that OpenSSL uses to store a DSA private key that is not part of a PKCS#8 structure. Reversed engineered from english-language description on linked OpenSSL documentation page. Original Name: None Source: https://www.openssl.org/docs/apps/dsa.html r5pqg public_key private_keyN)r)r*r+r,rr-r.r.r.r/r:ts      r:c@s4eZdZdZeddZddZdS)_ECPointa  In both PublicKeyInfo and PrivateKeyInfo, the EC public key is a byte string that is encoded as a bit string. This class adds convenience methods for converting to and from the byte string to a pair of integers that are the X and Y coordinates. cCsttjtj|dd}ttjtj|dd}t||}d}|t|d|7}|t|d|7}||S)a Creates an ECPoint object from the X and Y integer coordinates of the point :param x: The X coordinate, as an integer :param y: The Y coordinate, as an integer :return: An ECPoint object g @swidth)intmathceillogmaxr%)clsxyZx_bytesZy_bytesZ num_bytesZ byte_stringr.r.r/ from_coordss%%z_ECPoint.from_coordscCs|j}|dd}|dkr{|dd}t|d}t|d|}t||d}||fS|tddgkrttdttd dS) z Returns the X and Y coordinates for this EC point, as native Python integers :return: A 2-element tuple containing integers (X, Y) rrsNrAsszQ Invalid EC public key - first byte is incorrect z| Compressed representations of EC public keys are not supported due to patent US6252960 )nativelenr$set ValueErrorr)selfdataZ first_byteZ remainingZ field_lenrIrJr.r.r/ to_coordss    z_ECPoint.to_coordsN)r)r*r+r, classmethodrKrRr.r.r.r/r@s r@c@seZdZdS)ECPointN)r)r*r+r.r.r.r/rTs rTc@seZdZdS)ECPointBitStringN)r)r*r+r.r.r.r/rUs rUc@s.eZdZdZddddddiZdS) SpecifiedECDomainVersionz: Source: http://www.secg.org/sec1-v2.pdf page 104 rZecdpVer1rAZecdpVer2ZecdpVer3N)r)r*r+r,r3r.r.r.r/rVs rVc@s(eZdZdZddddiZdS) FieldTypezR Original Name: None Source: http://www.secg.org/sec1-v2.pdf page 101 z1.2.840.10045.1.1 prime_fieldz1.2.840.10045.1.2characteristic_two_fieldN)r)r*r+r,r3r.r.r.r/rXs rXc@s.eZdZdZddddddiZdS) CharacteristicTwoBasiszR Original Name: None Source: http://www.secg.org/sec1-v2.pdf page 102 z1.2.840.10045.1.2.1.1gn_basisz1.2.840.10045.1.2.1.2tp_basisz1.2.840.10045.1.2.1.3pp_basisN)r)r*r+r,r3r.r.r.r/r[s r[c@s7eZdZdZdefdefdefgZdS) Pentanomialz: Source: http://www.secg.org/sec1-v2.pdf page 102 Zk1Zk2Zk3N)r)r*r+r,rr-r.r.r.r/r_s   r_c@sUeZdZdZdefdefdefgZd Zde dede iZ dS) CharacteristicTwoz` Original Name: Characteristic-two Source: http://www.secg.org/sec1-v2.pdf page 101 mbasis parametersr\r]r^N)rbz parameters) r)r*r+r,rr[rr- _oid_pairrr_ _oid_specsr.r.r.r/r`s   r`c@sFeZdZdZdefdefgZdZdede iZ dS)FieldIDz: Source: http://www.secg.org/sec1-v2.pdf page 100 field_typercrYrZN)rgz parameters) r)r*r+r,rXrr-rdrr`rer.r.r.r/rfs  rfc@s@eZdZdZdefdefdeddifgZdS)Curvez: Source: http://www.secg.org/sec1-v2.pdf page 104 abseedr8TN)r)r*r+r,rrr-r.r.r.r/rh-s   rhc @smeZdZdZdefdefdefdefdefdedd ifd e dd ifgZ d S) SpecifiedECDomainz: Source: http://www.secg.org/sec1-v2.pdf page 103 r5field_idcurvebaseorderZcofactorr8ThashN) r)r*r+r,rVrfrhrTrrr-r.r.r.r/rl9s      rlcP@s eZdZdZdddddddd d d d d ddddddddddddddddddd d!d"d#d$d%d&d'd(d)d*d+d,d-d.d/d0d1d2d3d4d5d6d7d8d9d:d;d<d=d>d?d@dAdBdCdDdEdFdGdHdIdJdKdLdMdNdOdPdQi(ZdRS)S NamedCurvez Various named curves Original Name: None Source: https://tools.ietf.org/html/rfc3279#page-23, https://tools.ietf.org/html/rfc5480#page-5 z1.2.840.10045.3.0.1Z c2pnb163v1z1.2.840.10045.3.0.2Z c2pnb163v2z1.2.840.10045.3.0.3Z c2pnb163v3z1.2.840.10045.3.0.4Z c2pnb176w1z1.2.840.10045.3.0.5Z c2tnb191v1z1.2.840.10045.3.0.6Z c2tnb191v2z1.2.840.10045.3.0.7Z c2tnb191v3z1.2.840.10045.3.0.8Z c2onb191v4z1.2.840.10045.3.0.9Z c2onb191v5z1.2.840.10045.3.0.10Z c2pnb208w1z1.2.840.10045.3.0.11Z c2tnb239v1z1.2.840.10045.3.0.12Z c2tnb239v2z1.2.840.10045.3.0.13Z c2tnb239v3z1.2.840.10045.3.0.14Z c2onb239v4z1.2.840.10045.3.0.15Z c2onb239v5z1.2.840.10045.3.0.16Z c2pnb272w1z1.2.840.10045.3.0.17Z c2pnb304w1z1.2.840.10045.3.0.18Z c2tnb359v1z1.2.840.10045.3.0.19Z c2pnb368w1z1.2.840.10045.3.0.20Z c2tnb431r1z1.2.840.10045.3.1.2Z prime192v2z1.2.840.10045.3.1.3Z prime192v3z1.2.840.10045.3.1.4Z prime239v1z1.2.840.10045.3.1.5Z prime239v2z1.2.840.10045.3.1.6Z prime239v3z 1.3.132.0.1Z sect163k1z 1.3.132.0.15Z sect163r2z1.2.840.10045.3.1.1 secp192r1z 1.3.132.0.33 secp224r1z 1.3.132.0.26Z sect233k1z1.2.840.10045.3.1.7 secp256r1z 1.3.132.0.27Z sect233r1z 1.3.132.0.16Z sect283k1z 1.3.132.0.17Z sect283r1z 1.3.132.0.34 secp384r1z 1.3.132.0.36Z sect409k1z 1.3.132.0.37Z sect409r1z 1.3.132.0.35 secp521r1z 1.3.132.0.38Z sect571k1z 1.3.132.0.39Z sect571r1N)r)r*r+r,r3r.r.r.r/rrIsR rrc@s7eZdZdZdefdefdefgZdS)ECDomainParametersz: Source: http://www.secg.org/sec1-v2.pdf page 102 specifiednamed implicit_caN)r)r*r+r,rlrrrZ _alternativesr.r.r.r/rxs   rxc@s"eZdZdZddiZdS)ECPrivateKeyVersionzR Original Name: None Source: http://www.secg.org/sec1-v2.pdf page 108 rZ ecPrivkeyVer1N)r)r*r+r,r3r.r.r.r/r|s r|c @sjeZdZdZdefdefdeddddd d ifd edddd d d ifgZd S) ECPrivateKeyz: Source: http://www.secg.org/sec1-v2.pdf page 108 r5r?rctag_typeZexplicittagrr8Tr>rN) r)r*r+r,r|rrxrUr-r.r.r.r/r}s   r}c@s7eZdZdZdefdefdefgZdS) DSAParamsz Parameters for a DSA public or private key Original Name: Dss-Parms Source: https://tools.ietf.org/html/rfc3279#page-9 r;r<r=N)r)r*r+r,rr-r.r.r.r/rs   rc@s7eZdZdZdefdedeifgZdS) Attributezq Source: https://www.itu.int/rec/dologin_pub.asp?lang=e&id=T-REC-X.501-198811-S!!PDF-E&type=items page 8 typevaluesspecN)r)r*r+r,rr#rr-r.r.r.r/rs  rc@seZdZdZeZdS) Attributesz< Source: https://tools.ietf.org/html/rfc5208#page-3 N)r)r*r+r,rr1r.r.r.r/rs rc@s.eZdZdZddddddiZdS) PrivateKeyAlgorithmIdz These OIDs for various public keys are reused when storing private keys inside of a PKCS#8 structure Original Name: None Source: https://tools.ietf.org/html/rfc3279 z1.2.840.113549.1.1.1rsaz1.2.840.10040.4.1dsaz1.2.840.10045.2.1ecN)r)r*r+r,r3r.r.r.r/rs rc@sOeZdZdZdefdeddifgZd Zdede iZ dS) PrivateKeyAlgorithmzm Original Name: PrivateKeyAlgorithmIdentifier Source: https://tools.ietf.org/html/rfc5208#page-3 algorithmrcr8TrrN)z algorithmz parameters) r)r*r+r,rrr-rdrrxrer.r.r.r/rs  rc @s?eZdZdZdefdefdefdedddd d d ifgZd d Z de iZ dZ dZ dZ dZeddZddZddZeddZeddZeddZeddZeddZedd Zed!d"Zed#d$ZdS)%PrivateKeyInfoz< Source: https://tools.ietf.org/html/rfc5208#page-3 r5private_key_algorithmr?Z attributesr~Zimplicitrrr8TcCs+|ddj}dtdtdti|S)Nrrrrr)rLr4rr})rPrr.r.r/_private_key_specs  z PrivateKeyInfo._private_key_specNcCst|t r;t|t r;ttdt||dkrqt|tsetj|}t}n|dkrt|t st j|}t }|d|d<|d|d<|d|d<|d}|d}nh|d kr2t|t st j|}n |j }|d }|d =nt td t|t}t||d <||d <|}||_td |d<||d<||d<|dkr||_|S)a' Wraps a private key in a PrivateKeyInfo structure :param private_key: A byte string or Asn1Value object of the private key :param algorithm: A unicode string of "rsa", "dsa" or "ec" :return: A PrivateKeyInfo object zX private_key must be a byte string or Asn1Value, not %s rrr;r<r=r>r?rrczU algorithm must be one of "rsa", "dsa", "ec", not %s rrr5r) isinstancerr TypeErrorrrr4loadrr:rr}copyrOreprrr _algorithmr _public_key)rHr?rparamsr>Zprivate_key_algo containerr.r.r/wrapsJ                   zPrivateKeyInfo.wrapc Cs|jdkrK|dd}tt|dj|djj|djS|jdkr|dj}td|dd |d iS|jd kr|j\}}|d krttd |d kr_|dddkrttdt |ddt |ddt |dd}|ddj dj \}}t |||}nU|dkr|dkrttd|dtdtdtdtdti|}||djdj} tj| j| jSdS)z Computes the public key corresponding to the current private key. :return: For RSA keys, an RSAPublicKey object. For DSA keys, an Integer object. For EC keys, an ECPointBitString. rrrcr=r?r;rr6r7rr{z Unable to compute public key for EC key using Implicit CA parameters ryrmrgrZz Unable to compute public key for EC key over a characteristic two field rnrirjrorzrsrtrurvrwz Unable to compute public key for EC named curve %s, parameters not currently included N)z secp192r1z secp224r1z secp256r1z secp384r1z secp521r1)rrpowrLparsedr9rnrOrr r$chosenrRr rrr r r rUrKrIrJ) rPrkeyZ curve_typeZdetailsrnZbase_xZbase_yZ base_pointZ public_pointr.r.r/_compute_public_keyLsN          !    z"PrivateKeyInfo._compute_public_keycCs|jdkr|djS|jdkr{|dd}tddd|dd |d d |d d |jd|djiS|jd kr|dj}|dd|d<|j|d <|Sd S)z Unwraps the private key into an RSAPrivateKey, DSAPrivateKey or ECPrivateKey object :return: An RSAPrivateKey, DSAPrivateKey or ECPrivateKey object rr?rrrcr5rr;r<r=r>rN)rrr:r>)rProutputr.r.r/rs        zPrivateKeyInfo.unwrapcCsr|jdkr-ttd|jj|dd}|j}|jdkr\d}n |j}|j|fS)a# Returns information about the curve used for an EC key :raises: ValueError - when the key is not an EC key :return: A two-element tuple, with the first element being a unicode string of "implicit_ca", "specified" or "named". If the first element is "implicit_ca", the second is None. If "specified", the second is an OrderedDict that is the native version of SpecifiedECDomain. If "named", the second is a unicode string of the curve name. rzK Only EC keys have a curve, this key is %s rrcr{N)rrOrupperrnamerL)rPrrvaluer.r.r/rns   zPrivateKeyInfo.curvecCsf|jdkr-ttd|jjtj|dddjdd}|dkrbd Sd S) z Returns the name of the family of hash algorithms used to generate a DSA key :raises: ValueError - when the key is not a DSA key :return: A unicode string of "sha1" or "sha2" rzt Only DSA keys are generated using a hash algorithm, this key is %s rrcr<rAsha1sha2)rrOrrrDrFrL)rPbyte_lenr.r.r/ hash_algos %zPrivateKeyInfo.hash_algocCs*|jdkr#|ddj|_|jS)zO :return: A unicode string of "rsa", "dsa" or "ec" Nrr)rrL)rPr.r.r/rszPrivateKeyInfo.algorithmcCs|jdkr|jdkr5|djdj}nJ|jdkr\|dddj}n#|jd kr|djdj}ttjtj|d |_|jd }|d kr|jd |7_|jS) zU :return: The bit size of the private key, as an integer Nrr?r6rrrcr;rrArr) _bit_sizerrrLrCrDrErF)rPr'r6r.r.r/bit_sizes$  zPrivateKeyInfo.bit_sizecCsttj|jdS)zV :return: The byte size of the private key, as an integer r)rCrDrEr)rPr.r.r/ byte_size szPrivateKeyInfo.byte_sizecCss|jdkrl|jdkr]|dj}|drK|dj|_ql|j|_n|j|_|jS)z :return: If an RSA key, an RSAPublicKey object. If a DSA key, an Integer object. If an EC key, an ECPointBitString object. Nrr?r>)rrruntagr)rPrr.r.r/r>s  zPrivateKeyInfo.public_keycCs0tdd|jd|ddid|jiS)z\ :return: A PublicKeyInfo object derived from this private key. rrcrr>) PublicKeyInforr>)rPr.r.r/public_key_info*s  zPrivateKeyInfo.public_key_infocCs|jdkr|dd}|dj}|jdkrZd|dj|djf}nH|jd kr|j}d |d j|d j|d j|jf}n|jdkr|dj}|dkr|jj}|jdkrd|jj}|jd}||7}n|jdkr*|}nx|jdkrd|jddj}|jd}|d|jddj7}|d|jddj7}||7}t|t r|jd}t j |j |_|jS)aZ Creates a fingerprint that can be compared with a public key to see if the two form a pair. This fingerprint is not compatiable with fingerprints generated by any other software. :return: A byte string that is a sha256 hash of selected components (based on the key type) Nrrcr?rz%d:%dr6r7rz %d:%d:%d:%dr;r<r=rr>rzz%s:zutf-8r{ryrm:rnrirj) _fingerprintrrrLr>rrencoderrhashlibsha256digest)rPrrto_hashr>r.r.r/ fingerprint9sD            zPrivateKeyInfo.fingerprint)r)r*r+r,rrrrr-r_spec_callbacksrrrrrSrrrpropertyrnrrrrr>rrr.r.r.r/rs,    $ D I "  rc@s.eZdZdZdefdefgZdS)EncryptedPrivateKeyInfoz< Source: https://tools.ietf.org/html/rfc5208#page-4 Zencryption_algorithmZencrypted_dataN)r)r*r+r,rrr-r.r.r.r/rvs  rc@s.eZdZdZdefdefgZdS)ValidationParmsz= Source: https://tools.ietf.org/html/rfc3279#page-10 rkZ pgen_counterN)r)r*r+r,rrr-r.r.r.r/rs  rc@s[eZdZdZdefdefdefdeddifdeddifgZd S) DomainParametersz= Source: https://tools.ietf.org/html/rfc3279#page-10 r;r=r<jr8TZvalidation_paramsN)r)r*r+r,rrr-r.r.r.r/rs    rc@s4eZdZdZdddddddd iZd S) PublicKeyAlgorithmIdzM Original Name: None Source: https://tools.ietf.org/html/rfc3279 z1.2.840.113549.1.1.1rz1.2.840.10040.4.1rz1.2.840.10045.2.1rz1.2.840.10046.2.1dhN)r)r*r+r,r3r.r.r.r/rs rc@sUeZdZdZdefdeddifgZd Zdede de iZ d S) PublicKeyAlgorithmzd Original Name: AlgorithmIdentifier Source: https://tools.ietf.org/html/rfc5280#page-18 rrcr8TrrrN)z algorithmz parameters) r)r*r+r,rrr-rdrrxrrer.r.r.r/rs  rc@seZdZdZdefdefgZddZdeiZdZ dZ dZ dZ dZ eddZd d Zed d Zed dZeddZeddZeddZeddZeddZeddZdS)rze Original Name: SubjectPublicKeyInfo Source: https://tools.ietf.org/html/rfc5280#page-17 rr>cCs7|ddj}dtdtdtdfdti|S)Nrrrrr)rLr9rrU)rPrr.r.r/_public_key_specs   zPublicKeyInfo._public_key_specNcCst|t r;t|t r;ttdt||dkrbttdt|t}t ||d algorithm must "rsa", not %s rrcr>)rrrrrrrOrrrrrdumpr )rHr>rZalgorr.r.r/rs"      zPublicKeyInfo.wrapcCs]|jdkr|djS|jj}|dkr;dnd}ttd||dS)z Unwraps an RSA public key into an RSAPublicKey object. Does not support DSA or EC public keys since they do not have an unwrapped form. :return: An RSAPublicKey object rr>ZECZanrizj Only RSA public keys may be unwrapped - this key is %s %s public key N)rrrrOr)rPkey_typeZa_anr.r.r/r s  zPublicKeyInfo.unwrapcCsr|jdkr-ttd|jj|dd}|j}|jdkr\d}n |j}|j|fS)a# Returns information about the curve used for an EC key :raises: ValueError - when the key is not an EC key :return: A two-element tuple, with the first element being a unicode string of "implicit_ca", "specified" or "named". If the first element is "implicit_ca", the second is None. If "specified", the second is an OrderedDict that is the native version of SpecifiedECDomain. If "named", the second is a unicode string of the curve name. rzK Only EC keys have a curve, this key is %s rrcr{N)rrOrrrrrL)rPrrrr.r.r/rn#s   zPublicKeyInfo.curvecCs|jdkr-ttd|jj|dd}|jdkrNdStj|djdd}|d kr{d Sd S) a# Returns the name of the family of hash algorithms used to generate a DSA key :raises: ValueError - when the key is not a DSA key :return: A unicode string of "sha1" or "sha2" or None if no parameters are present rzt Only DSA keys are generated using a hash algorithm, this key is %s rrcNr<rArrrr)rrOrrrLrDrF)rPrcrr.r.r/rEszPublicKeyInfo.hash_algocCs*|jdkr#|ddj|_|jS)zO :return: A unicode string of "rsa", "dsa" or "ec" Nr)rrL)rPr.r.r/rdszPublicKeyInfo.algorithmcCs|jdkr|jdkrCt|djddd|_n|jdkri|djdj}n$|jd kr|d d d j}ttjtj|d|_|jd}|d kr|jd|7_|jS)zT :return: The bit size of the public key, as an integer Nrr>rrArrr6rrrcr;r) rrrMrLrrCrDrErF)rPr'r6r.r.r/ros%$  zPublicKeyInfo.bit_sizecCsttj|jdS)zU :return: The byte size of the public key, as an integer r)rCrDrEr)rPr.r.r/rszPublicKeyInfo.byte_sizecCs8|jdkr1tjt|dj|_|jS)ze :return: The SHA1 hash of the DER-encoded bytes of this public key info Nr>)_sha1rrrr)rPr.r.r/rs"zPublicKeyInfo.sha1cCs8|jdkr1tjt|dj|_|jS)zh :return: The SHA-256 hash of the DER-encoded bytes of this public key info Nr>)_sha256rrrr)rPr.r.r/rs"zPublicKeyInfo.sha256cCs|jdkr|ddj}|dd}|dkrh|dj}d|dj|djf}n4|d kr|dj}d |d j|d j|d j|jf}n|dkr|d}|jdkrd|jj}|jd}||j7}n|jdkr!|j}n{|jdkrd|jddj}|jd}|d|jddj7}|d|jddj7}||j7}t|tr|jd}tj |j |_|jS)a[ Creates a fingerprint that can be compared with a private key to see if the two form a pair. This fingerprint is not compatiable with fingerprints generated by any other software. :return: A byte string that is a sha256 hash of selected components (based on the key type) Nrrcrr>z%d:%dr6r7rz %d:%d:%d:%dr;r<r=rrzz%s:zutf-8r{ryrmrrnrirj) rrLrrrrrrrrr)rPrrrrr.r.r/rsB            zPublicKeyInfo.fingerprint)r)r*r+r,rr r-rrrrrrrrSrrrrnrrrrrrrr.r.r.r/rs(   + "    r)Nr,Z __future__rrrrrrDZ_elliptic_curverrr r r r r Z_errorsrZ_typesrrrZalgosrrrZcorerrrrrrrrrrrr r!r"r#utilr$r%r&r0r2r4r9r:r@rTrUrVrXr[r_r`rfrhrlrrrxr|r}rrrrrrrrrrrrr.r.r.r/sV"  4 d   F     7