43 lines
5.7 KiB
Plaintext
43 lines
5.7 KiB
Plaintext
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Þ½�jÌ
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ã óR — d Z ddlZddlmZmZ d„ Zd„ Zd„ Zd„ Zd„ Zd „ Zd d
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„Z d „ Z
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y)
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uz
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lib/crypto_utils.py — common CTF crypto helpers (RSA / lattice / misc).
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Patterns distilled from p4-team/ctf writeups.
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é N)ÚgcdÚisqrtc óX — |dk( r| ddfS t || |z « \ }}}|||| |z |z z
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fS )Nr é )Úegcd)ÚaÚbÚgÚxÚys úlib/crypto_utils.pyr r
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sD € ؈A‚vØ�1�aˆyÐÜ�1�a˜!‘e‹n�G€A€qˆ!Ø
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ˆq�!�q˜A‘v ‘lÑ"Ð #Ð#ó c óR — t | |z |« \ }}}|dk7 r t d« ‚||z S )Nr zmodinv: no inverse)r Ú
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ValueError)r Úmr
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r Ú_s r
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Úmodinvr s3 € Ü�1�q‘5˜!‹n�G€A€qˆ!؈A‚vÜÐ-Ó.Ð.Ø ˆq‰5€Lr c ó, — t j | « S ©N)Úmathr )Úns r
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r r s € Ü �:‰:�a‹=Ðr c óH — t dd« D ] }| |z dk( sŒ || |z fc S y)z)Tiny factor finder for small/weak moduli.é i r N)Úrange)r Úps r
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Úfactor_trivialr s6 € ä
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�1�gÓ
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ò ˆØ ˆq‰5�A‹:Ø�a˜1‘f�9Ò ð ð r c ó� ‡— ddl Šˆfd„}ˆfd„} || |« D ] } ||||« }|sŒ|c S y# t $ r t d« ‚w xY w)z¢
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From p4 'lost_modulus': we know e, d, ipmq=modinv(p,q), iqmp=modinv(q,p)
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but NOT n. Recover n via quadratic equation on phi. Returns (p, q) or None.
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r Nz&gmpy2 required for recover_n_from_keysc 3 ó¬ •K — | |z dz
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}|t |« dz z } ||z } ‰j | |« }||k( r|–— |dz
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}Œ'# t $ r Y Œw xY ww)Nr é )ÚintÚinvertÚ Exception)ÚeÚdÚkfiÚkÚfiÚd0Úgmpy2s €r
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Úfind_phiz%recover_n_from_keys.<locals>.find_phi0 sv øè ø€ Ø�!‰e�a‰iˆØ ”C˜“F˜Q‘JÑ ˆØؘ‘ˆBð
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Ø—\‘\ ! RÓ(�ؘ’7Ø ’Hð
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�‰FˆAð øô ò
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Ùð
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üs' ƒ A¤A ¿AÁ AÁAÁAÁAc ó6 •— |dz
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}| |z dz
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|z
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}| |z |z
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}||z d|z |z z
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}|dkD rm‰ j |d« \ }}|rV| |z
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d|z z | |z d|z z fD ]; } ‰ j | dz « sŒ| dz }
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|| z dz } t | « t |
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« fc S y )Nr r é r )ÚirootÚis_primer )
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ÚipmqÚiqmpÚ possible_phir r ÚcÚdeltaÚrÚcorrectr Úqr r) s
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€r
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Úsolvez"recover_n_from_keys.<locals>.solve= sÒ ø€ Ø �1‰HˆØ �4‰K˜!‰O˜lÑ *ˆØ �<Ñ ,Ñ .ˆØ�A‘˜˜A™ ™ Ñ!ˆØ �1Š9Ø Ÿ™ U¨AÓ.‰JˆAˆwÙØ ˜2 ™6 q¨1¡uÑ-°°°Q±¸AÀ¹EÑ/BÐCò .�AØ —~‘~ a¨!¡eÕ,Ø ™E˜Ø (¨AÑ -°Ñ 1˜Ü " 1›v¤s¨1£v˜~Ò-ð .ð
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r )r) r" Ú
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SystemExit) r# r$ r/ r0 r* r7 ÚphiÚresr) s @r
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