elliptic-shiho · July 10, 2023 06:29 · elliptic-shiho · Jul 10, 2023
diff --git a/solve.sage b/solve.sage
 from sage.all import *
 from Crypto.Util.number import long_to_bytes

 A = 6737149052150272134972940516590980024331491319339741317342183169802474656888386084365871287308045730462954100927849817850868865189752921007067826413968051476282853264469660023301658697080152738648906257793188559177506701773637608811467111764155767760049813836531589499517889064750007039677591074035963533567
 q = 15040222622096320078383580808680733765955114958694997949647342925417877088612792495485641348591026281373930569798925789027166056695954731923306109646611840570310396750856642056018981080439916663195842593441587057719678555907050674529272376248049062724657792390788687452049496308886252188791975094655675938807

 F = GF(q)
 PR.<x> = F[x]
 l = (x ^ 6 - A).roots()
 for a, b in l:
    print(long_to_bytes(ZZ(a)))
diff --git a/solve_log b/solve_log
 Sun Jul  9 16:46:32 JST 2023 ~/Downloads/risk 
 > time sage solve.sage
 b'\x15k\x01B<\xba\xbe\xd4\x96\xc9\xb4\xd9W\xc0f\xa0zH\xbd\x95v\x16\xb3\x92\xba\\\x15\x95)$\xce\xff/\xd6\xd2"\xbd\x98\xeb\xda\x91\n\xd6\xcap\rr\xb7\xfa\x12\xb6b\xe4ti\xd7\xad\xcc\xc3\xb4\xd3{\xbe\xf0a\xfd77\xd3\x11OO\xc7L\x1e\xc7b\x14\x17\xe5\x81p\xce\xb4\x85%\xa5Q%\xb0\x01D\x1e/\xe6:\x0f>\xe8\x16\x1f67]\x9ah\t\xe9&\xe7\x1d\xa1H\xf0\\\xccs\x9ej\xb9\x92\xdd\xe2c\x089\x16z'
 b'\x14\x96\x97\x9f\xeb\x0b\xbd\xe2\xd4\x82}\x7f\x00F\xcd\x13\xbd01&\xf8\x19\xd0I\xb8|bl+\x98+F\x98\xff:\x8f\xf5\xb2\x88\xfe\xd0T\xab\x05\xa7\xde/\xb2\x12\xe0\x01\x9e\xebK\t\xe6#Q\xa5\x92\xbf}\xf92\xa01X\x96\x10A\xd9\xbb[oh\x12\xd5#\xc5r\x1fn\xc3l\xcbIGi\xd1[\x86u"\xaf\tB\xdaY{\x9b-\x95\xf8-\xbf\xb31fZ\xc3$\x1ds(\xb9g\x05\xcbj*\x7fwo\xae\\\xbd\x7fi'
 b'\x14\x96\x97\x9f\xeb\x0b\xbd\xe2\xd4\x82}\x7f\x00F\xcd\x13\xbd01&\xf8\x19\xd0I\xb8|bl+\x98+F\x98\xff:\x8f\xf5\xb2\x88\xfe\xd0T\xab\x05\xa7\xde/\xb2\x12\xe0\x01\x9e\xebK\t\xe6#Q\xa5\x92\xbf}\xf92\xa01X\x96\x10A\xd9\xbb[og\xcf\x91\xcf~\xf6\xccMV\x1c\x9a\x03\xe8(\x99\xe7R\x11\xd7O\xd8\xd4{\x06\x0bU\xcad\x96\xe1\x92}\xbc\xf3\xe5_\xcf\xa8\x00\xf5u\x07\xb3x(\xcb\x0f%>@\xf7\x88]\xec'
 b'\xd4i\xa2Q\xaf\x00\xf1\xc2G7ZWy\x99\x8c\xbd\x18\x8cn}\xfc\xe3I\x01\xdf\xb3(\xfd\x8c\xa3\xb8\x96\xd7\x97\x92\xc7\xe6b\xdb\xc0\xb6+\xc4\xc8/C\x05\xe72\xb4\xc3\xf9)_\xf1\x8a{\x1e"\x13\xfd\xc5\xbd\xc1\xcb\xde\xa1\xc2\xcfu\x94k\xdc\xb7;\x13\x98\xdfj\x08D\xe5\xe8\x1cg\x1ci\xc3<\xe3\x95\x92?=\xd3\xf3\x8cM\x05\xb8\x03\x01\xc85\x1f\xc1g\xb6\xea\xa2n\xba.,$\x12y\x83M\xf4\n\xd5\x8fu\xe5\xda\x0b'
 b'\xd4i\xa2Q\xaf\x00\xf1\xc2G7ZWy\x99\x8c\xbd\x18\x8cn}\xfc\xe3I\x01\xdf\xb3(\xfd\x8c\xa3\xb8\x96\xd7\x97\x92\xc7\xe6b\xdb\xc0\xb6+\xc4\xc8/C\x05\xe72\xb4\xc3\xf9)_\xf1\x8a{\x1e"\x13\xfd\xc5\xbd\xc1\xcb\xde\xa1\xc2\xcfu\x94k\xdc\xb6\xf7\xd0D\x98\xee\xb5#x\x97\xeb!\xbd(\x8b\xc8\xaf2F\xe0\re\x948\xdc\xc0T\xd1\xa0|\x07\xeaL\xf5A\x87M\xf9G\xfa\xe7\xc4\xc0&A\xee\x83\xb8\xa4"\x10\xb0\xb8\x8e'
 b'CCTF{S!mP1E_A7t4cK_0n_SpEc1aL-5trucTur3D_RSA_pR1me5!}'

 real    0m6.584s
 user    0m6.354s
 sys     0m0.236s
	from sage.all import *
	from Crypto.Util.number import long_to_bytes

	A = 6737149052150272134972940516590980024331491319339741317342183169802474656888386084365871287308045730462954100927849817850868865189752921007067826413968051476282853264469660023301658697080152738648906257793188559177506701773637608811467111764155767760049813836531589499517889064750007039677591074035963533567
	q = 15040222622096320078383580808680733765955114958694997949647342925417877088612792495485641348591026281373930569798925789027166056695954731923306109646611840570310396750856642056018981080439916663195842593441587057719678555907050674529272376248049062724657792390788687452049496308886252188791975094655675938807

	F = GF(q)
	PR.<x> = F[x]
	l = (x ^ 6 - A).roots()
	for a, b in l:
	print(long_to_bytes(ZZ(a)))
	Sun Jul 9 16:46:32 JST 2023 ~/Downloads/risk
	> time sage solve.sage
	b'\x15k\x01B<\xba\xbe\xd4\x96\xc9\xb4\xd9W\xc0f\xa0zH\xbd\x95v\x16\xb3\x92\xba\\\x15\x95)$\xce\xff/\xd6\xd2"\xbd\x98\xeb\xda\x91\n\xd6\xcap\rr\xb7\xfa\x12\xb6b\xe4ti\xd7\xad\xcc\xc3\xb4\xd3{\xbe\xf0a\xfd77\xd3\x11OO\xc7L\x1e\xc7b\x14\x17\xe5\x81p\xce\xb4\x85%\xa5Q%\xb0\x01D\x1e/\xe6:\x0f>\xe8\x16\x1f67]\x9ah\t\xe9&\xe7\x1d\xa1H\xf0\\\xccs\x9ej\xb9\x92\xdd\xe2c\x089\x16z'
	b'\x14\x96\x97\x9f\xeb\x0b\xbd\xe2\xd4\x82}\x7f\x00F\xcd\x13\xbd01&\xf8\x19\xd0I\xb8\|bl+\x98+F\x98\xff:\x8f\xf5\xb2\x88\xfe\xd0T\xab\x05\xa7\xde/\xb2\x12\xe0\x01\x9e\xebK\t\xe6#Q\xa5\x92\xbf}\xf92\xa01X\x96\x10A\xd9\xbb[oh\x12\xd5#\xc5r\x1fn\xc3l\xcbIGi\xd1[\x86u"\xaf\tB\xdaY{\x9b-\x95\xf8-\xbf\xb31fZ\xc3$\x1ds(\xb9g\x05\xcbj*\x7fwo\xae\\\xbd\x7fi'
	b'\x14\x96\x97\x9f\xeb\x0b\xbd\xe2\xd4\x82}\x7f\x00F\xcd\x13\xbd01&\xf8\x19\xd0I\xb8\|bl+\x98+F\x98\xff:\x8f\xf5\xb2\x88\xfe\xd0T\xab\x05\xa7\xde/\xb2\x12\xe0\x01\x9e\xebK\t\xe6#Q\xa5\x92\xbf}\xf92\xa01X\x96\x10A\xd9\xbb[og\xcf\x91\xcf~\xf6\xccMV\x1c\x9a\x03\xe8(\x99\xe7R\x11\xd7O\xd8\xd4{\x06\x0bU\xcad\x96\xe1\x92}\xbc\xf3\xe5_\xcf\xa8\x00\xf5u\x07\xb3x(\xcb\x0f%>@\xf7\x88]\xec'
	b'\xd4i\xa2Q\xaf\x00\xf1\xc2G7ZWy\x99\x8c\xbd\x18\x8cn}\xfc\xe3I\x01\xdf\xb3(\xfd\x8c\xa3\xb8\x96\xd7\x97\x92\xc7\xe6b\xdb\xc0\xb6+\xc4\xc8/C\x05\xe72\xb4\xc3\xf9)_\xf1\x8a{\x1e"\x13\xfd\xc5\xbd\xc1\xcb\xde\xa1\xc2\xcfu\x94k\xdc\xb7;\x13\x98\xdfj\x08D\xe5\xe8\x1cg\x1ci\xc3<\xe3\x95\x92?=\xd3\xf3\x8cM\x05\xb8\x03\x01\xc85\x1f\xc1g\xb6\xea\xa2n\xba.,$\x12y\x83M\xf4\n\xd5\x8fu\xe5\xda\x0b'
	b'\xd4i\xa2Q\xaf\x00\xf1\xc2G7ZWy\x99\x8c\xbd\x18\x8cn}\xfc\xe3I\x01\xdf\xb3(\xfd\x8c\xa3\xb8\x96\xd7\x97\x92\xc7\xe6b\xdb\xc0\xb6+\xc4\xc8/C\x05\xe72\xb4\xc3\xf9)_\xf1\x8a{\x1e"\x13\xfd\xc5\xbd\xc1\xcb\xde\xa1\xc2\xcfu\x94k\xdc\xb6\xf7\xd0D\x98\xee\xb5#x\x97\xeb!\xbd(\x8b\xc8\xaf2F\xe0\re\x948\xdc\xc0T\xd1\xa0\|\x07\xeaL\xf5A\x87M\xf9G\xfa\xe7\xc4\xc0&A\xee\x83\xb8\xa4"\x10\xb0\xb8\x8e'
	b'CCTF{S!mP1E_A7t4cK_0n_SpEc1aL-5trucTur3D_RSA_pR1me5!}'

	real 0m6.584s
	user 0m6.354s
	sys 0m0.236s