DSA Signature Algorithm - A simple implementation in Python
The key generation is a crucial part in cryptography. Although it is possible to write it in pure Python, the implementation may be flawed or the key is not based on cryptographic secure random numbers.
Because of this, I've omitted the keygen method and would recommend building the key outside of Python.
I've included two sample keypairs. One 512 bit real world keypair and an example keypair that could be used to manually verify the code.
If you want to try some more keys, here are additional samples:
# DSA key, 512 bits { "Q": 1260021755928513788571599504438886461377936881217, "P": 13215802529071855551943313349879770394691927370711522722842622001745077211972890580640990748291114169465597253458597759821541714594668205612405531098743733, "G": 455276047485817069916277446743189730425377195217680631038889953605607728791921521615547377293778074804992911578317438998802842046309729006598780666658326, "pub": 3036404803411196033070069256170232409942989851179350334254820349265197216569566209172676966085463154256974657976616817584164365206502207073907472859238476, "priv": 279024187637732322086413868627746442116145320938 } # DSA key, 512 bits { "Q": 1341900549555124873064130204963147708769253581301, "P": 7432359888316154771263218275724280901131924575536161876179642361275610721524385726490308633552457445185120040662322772977088152988634728101226863046136581, "G": 1492257850168835134070466045257688315376150892012978487853819129156120580866745506490145142655023635369583736954729944890019656413604867081875127370443086, "pub": 7005989449884126047896047657721672005749055903600955133790719437011671925262647266511803606052447901765438966482199200282068327634086087235072658984799660, "priv": 775898251443508702569746196737915407724647185115 } # DSA key, 1024 bits prime { "Q": 1461461359677056032138425664688969714401096527653, "P": 113003610536769662365475438074349202902393371149098932488829763899759693942182221311951893491037065838678290591836787867236266829425427477322203921585701270997375076009060429934105831431797790713235693561718253840225010037389994367689434248899226231330475152082648849936270434981210830874017521600353881618277, "G": 96504423597250666602463350548382591669983630413397284533161601799828504875913402437338367980529992940898864793759282567968196860849581229764805627921115713088555922323634319263032762806965222542087676328725218634401760700374749451348066585982534624077588633442696948741889609514070233035695255374063221721717, "pub": 108995193903934240798564100451045627210748695124974357268916707208528553000170266840505861201457239168618690453605371832512801286701989019522907305372175334396049194915209672515965212302226018817730175446251842830527761730120646366217675171871247849970396570237026190763013764161366386690833417893072059869763, "priv": 936678825459923885095535567029229102235556154286 } The following example will demonstrate the usage of this module.
import hashlib from pydsa import dsa dsa_key = { 'Q': 1218442816993522937915646204915776994404649089503L, 'P': 11220611807188583130302963536190351192186270126479330588604287699892081267588448305835704397593153801135202051719876685351614175538253684346816652027037363L, 'G': 11189361631195852088154673407566885728548496486362662112597687161142104619469702160215294558351391466982303919803857229515093575816938371433954759500448775L, 'pub': 4572510396595314270786423212039255215498677297795049756997099191729339616558419010431226927123876238239229467750410441342637393785565872285607741290303779L, 'priv': 148102768779017960166999813987055538077373228390L} text = """lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.""" m = hashlib.sha1() m.update(text) message = int("0x" + m.hexdigest(), 0) sig = dsa.dsa_sign(dsa_key["Q"], dsa_key["P"], dsa_key["G"], dsa_key["priv"], message) print "=" * 80 print "DSA SIGNATURE EXAMPLE" print "=" * 80 print "DSA Keypair:" for k in dsa_key.keys(): print k, ':', str(dsa_key[k]) print "-" * 80 print "Text:" print text print "-" * 80 print "SHA-1:", print message print "-" * 80 print "DSA Signature:", print sig print "-" * 80 print "Verify:", print dsa.dsa_verify(sig[0], sig[1], dsa_key["G"], dsa_key["P"], dsa_key["Q"], dsa_key["pub"], message) print "-" * 80 ================================================================================ DSA SIGNATURE EXAMPLE ================================================================================ DSA Keypair: Q : 1218442816993522937915646204915776994404649089503 P : 11220611807188583130302963536190351192186270126479330588604287699892081267588448305835704397593153801135202051719876685351614175538253684346816652027037363 pub : 4572510396595314270786423212039255215498677297795049756997099191729339616558419010431226927123876238239229467750410441342637393785565872285607741290303779 G : 11189361631195852088154673407566885728548496486362662112597687161142104619469702160215294558351391466982303919803857229515093575816938371433954759500448775 priv : 148102768779017960166999813987055538077373228390 -------------------------------------------------------------------------------- Text: lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. -------------------------------------------------------------------------------- SHA-1: 15756661315799901065974520410262757362863199659 -------------------------------------------------------------------------------- DSA Signature: (1083487672663272963123471937064532340846466682277L, 325593530571084514925270065278707164203430125451L) -------------------------------------------------------------------------------- Verify: True -------------------------------------------------------------------------------- In order to test the module, I've included simple doctests.
Please note that DSA signatures change each time as a random number gets picked. Therefore I do only check the length of the returning tuple.
python pydsa/dsa.py -v Trying: import hashlib Expecting nothing ok Trying: import dsa Expecting nothing ok Trying: m = hashlib.sha1() Expecting nothing ok Trying: m.update("ABCDE") Expecting nothing ok Trying: message = int("0x" + m.hexdigest(), 0) Expecting nothing ok Trying: dsa_key = { 'Q': 11, 'P': 23, 'G': 4, 'pub': 8, 'priv': 7} Expecting nothing ok Trying: sig = dsa.dsa_sign(dsa_key["Q"], dsa_key["P"], dsa_key["G"], dsa_key["priv"], message) Expecting nothing ok Trying: print len(sig) Expecting: 2 ok Trying: import hashlib Expecting nothing ok Trying: import dsa Expecting nothing ok Trying: m = hashlib.sha1() Expecting nothing ok Trying: m.update("ABCDE") Expecting nothing ok Trying: message = int("0x" + m.hexdigest(), 0) Expecting nothing ok Trying: dsa_key = { 'Q': 11, 'P': 23, 'G': 4, 'pub': 8, 'priv': 7} Expecting nothing ok Trying: sig = (2,3) Expecting nothing ok Trying: print dsa.dsa_verify(sig[0], sig[1], dsa_key["G"], dsa_key["P"], dsa_key["Q"], dsa_key["pub"], message) Expecting: True ok 5 items had no tests: __main__ __main__._digits_of_n __main__._mod_inverse __main__._random_s __main__.modexp_lr_k_ary 2 items passed all tests: 8 tests in __main__.dsa_sign 8 tests in __main__.dsa_verify 16 tests in 7 items. 16 passed and 0 failed. Test passed.