crypto.md

TJCTF 2023 - Crypto Challenges

#1: baby-rsa

Description/Sources:

output.txt

n = 10888751337932558679268839254528888070769213269691871364279830513893837690735136476085167796992556016532860022833558342573454036339582519895539110327482234861870963870144864609120375793020750736090740376786289878349313047032806974605398302398698622431086259032473375162446051603492310000290666366063094482985737032132318650015539702912720882013509099961316767073167848437729826084449943115059234376990825162006299979071912964494228966947974497569783878833130690399504361180345909411669130822346252539746722020515514544334793717997364522192699435604525968953070151642912274210943050922313389271251805397541777241902027

e = 3

c = 2449457955338174702664398437699732241330055959255401949300755756893329242892325068765174475595370736008843435168081093064803408113260941928784442707977000585466461075146434876354981528996602615111767938231799146073229307631775810351487333

• Since e = 3 is very small, and c is considerably smaller than n such that m^e mod n = m^e = c, --> m = c ** (1/3). Hence we can just take the cube root of c and convert it to plaintext.

Flag

tjctf{thr33s_4r3_s0_fun_fb23d5ed}

#2: ezdlp

Description/Sources

numbers.txt

g = 8999 
s = 11721478752747238947534577901795278971298347908127389421908790123 
p = 12297383901740584470151577318651150337988716807049317851420298478128932232846789427512414204247770572072680737351875225891650166807323215624748551744377958007176198392481481171792078565005580006750936049744616851983231170824931892761202881982041842121034608612146861881334101500003915726821683000760611763097

g^x = s mod p
flag = tjctf{x}

• This is a Discrete Logarithm Problem (as suggested by the name dlp). I used this website to help me calculate the value of x.
  

Flag

tjctf{26104478854569770948763268629079094351020764258425704346666185171631094713742516526074910325202612575130356252792856014835908436517926646322189289728462011794148513926930343382081388714077889318297349665740061482743137948635476088264751212120906948450722431680198753238856720828205708702161666784517}