E#iH,SrSSKJr SSKJr "SS\5r"SS\5r"SS \5r"S S \5r S r S r Sr Sr SrSrSrSrSr\R&"\S\5r\R*"\\\\5rSrSrSrSrSr\R&"\S\5r\R*"\\\\5rSrSrSrSrSr\R&"\S\5r\R*"\\\\5rS rS!rS"rS#rS$r\R&"\S\5r\R*"\\\\5rS%rS&rS'rS(rS)r\R&"\S\5r\R*"\\\\5rS*rS+rS,rS-rS.rS/r\R&"\\\5r \R*"\ \\\5r!g0)1a Implementation of Elliptic-Curve Digital Signatures. Classes and methods for elliptic-curve signatures: private keys, public keys, signatures, NIST prime-modulus curves with modulus lengths of 192, 224, 256, 384, and 521 bits. Example: # (In real-life applications, you would probably want to # protect against defects in SystemRandom.) from random import SystemRandom randrange = SystemRandom().randrange # Generate a public/private key pair using the NIST Curve P-192: g = generator_192 n = g.order() secret = randrange( 1, n ) pubkey = Public_key( g, g * secret ) privkey = Private_key( pubkey, secret ) # Signing a hash value: hash = randrange( 1, n ) signature = privkey.sign( hash, randrange( 1, n ) ) # Verifying a signature for a hash value: if pubkey.verifies( hash, signature ): print_("Demo verification succeeded.") else: print_("*** Demo verification failed.") # Verification fails if the hash value is modified: if pubkey.verifies( hash-1, signature ): print_("**** Demo verification failed to reject tampered hash.") else: print_("Demo verification correctly rejected tampered hash.") Version of 2009.05.16. Revision history: 2005.12.31 - Initial version. 2008.11.25 - Substantial revisions introducing new classes. 2009.05.16 - Warn against using random.randrange in real applications. 2009.05.17 - Use random.SystemRandom by default. Written in 2005 by Peter Pearson and placed in the public domain. ) ellipticcurve) numbertheoryc\rSrSrSrg) RSZeroError<N)__name__ __module__ __qualname____firstlineno____static_attributes__r^/home/james-whalen/.local/lib/python3.13/site-packages/ccxt/static_dependencies/ecdsa/ecdsa.pyrr<srrc$\rSrSrSrSrSrSrg) Signature@zECDSA signature. c(XlX lX0lg)N)rsrecovery_param)selfrrrs r__init__Signature.__init__Ds,rcUR5nUR5nURnURnUnUn[ USUR 55UR 5U--UR5-UR 5-n [R"XR 55n U S-S:XaU OUR 5U - n [R"X8X5n [R"XT5Xl-U*U-U---n [X-5n[R"X8U *U5n[R"XT5Xo-U*U-U---n[UU5nUU/$)z~Returns two public keys for which the signature is valid hash is signed hash generator is the used generator of the signature )curveorderrrpowpabrsquare_root_mod_primerPoint inverse_mod Public_key)rhash generatorrnrrexalphabetayR1Q1Pk1R2Q2Pk2s rrecover_public_keysSignature.recover_public_keysIs? ! OO  FF FF  Q5779%Q7%'')CuwwyP11%C1HMDuwwy4'7 1 0  % %a +qv!a98L/L M' A2q 1  % %a +qv!a98L/L MB'Szr)rrrN)r r r r __doc__rr6r rrrrr@s- rrc$\rSrSrSrSrSrSrg)r'gzPublic key for ECDSA. c~UR5UlXlX lUR5nU(d [ S5eX2-[ R :Xd [ S5eUR5S:d:X2R5::d'UR5S:dX2R5::a [ S5eg)zagenerator is the Point that generates the group, point is the Point that defines the public key. z Generator point must have order.zGenerator point order is bad.rz(Generator point has x or y out of range.N) rr)pointr RuntimeErrorrINFINITYr,r/)rr)r<r*s rrPublic_key.__init__ks __& " OO AB ByM222>? ? 779q=ANeggi!mqGGI~IJ J@NrcBURnUR5nURnURnUS:dXTS- :agUS:dXdS- :ag[R "Xd5nX-U-nXW-U-n X-XR --n U R5U-n X:H$)z[Verify that signature is a valid signature of hash. Return True if the signature is valid. rF)r)rrrrr&r<r,) rr( signatureGr*rrcu1u2xyvs rverifiesPublic_key.verifies{s NN GGI KK KK q5AAI q5AAI  $ $Q *h!^eq[ Vb::o % DDFQJv r)rr)r<N)r r r r r8rrHr rrrr'r'gsK rr'c$\rSrSrSrSrSrSrg) Private_keyzPrivate key for ECDSA. cXlX lg)zIpublic_key is of class Public_key; secret_multiplier is a large integer. N public_keysecret_multiplier)rrOrPs rrPrivate_key.__init__s %!2rcURRnUR5nX$-nXS-nUR5U-nUS:Xa [ S5e[ R "XT5XRU-U---U-nUS:Xa [ S5eUR5S-=(d UR5U:XaSOSn [XxU 5$)a{Return a signature for the provided hash, using the provided random nonce. It is absolutely vital that random_k be an unpredictable number in the range [1, self.public_key.point.order()-1]. If an attacker can guess random_k, he can compute our private key from a single signature. Also, if an attacker knows a few high-order bits (or a few low-order bits) of random_k, he can compute our private key from many signatures. The generation of nonces with adequate cryptographic strength is very difficult and far beyond the scope of this comment. May raise RuntimeError, in which case retrying with a new random value k is in order. rz!amazingly unlucky random number rz!amazingly unlucky random number sr) rOr)rr,rrr&rPr/r) rr(random_krBr*kp1rrrs rsignPrivate_key.signs OO % % GGI L U DDFQJ 6AB B  % %a +,,q0A557:; < 6AB B!@RTTVq[a~..rrNN)r r r r r8rrVr rrrrKrKs3/rrKcUS:deUS:Xag/nU(a9US-nUR[RUSS55 US-nU(aM9UR5 SR U5$)z7Convert integer x into a string of bytes, as per X9.62.rrbigr)appendintto_bytesreversejoin)r,resultordinals r int_to_stringrdsl 6M6Av F d( cll7Au56 a !  NN 88F rclSnUH+n[U[5(d [U5nSU-U-nM- U$)z8Convert a string of bytes into an integer, as per X9.62.r) isinstancer^ord)rrbrCs r string_to_intris< F !S!!AAv! 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