Rastislav Krivoš-Belluš

KRS1 - Kryptografické systémy a ich aplikácie (doc. RNDr. Jozef Jirásek, PhD.)

Lab 01

  1. Decipher (monoalphabetic substitution cipher):
    1. cipher in image
    2. Zgyzhs rh z hrnkov hfyhgrgfgrlm xrksvi uli gsv Svyivd zokszyvg.
  2. How many keys are there for enciphering in English/Slovak/Spanish alphabet?
    • monoalphabetic substitution cipher
    • affine cipher (Maple: ? numtheory[phi], Maxima: ? totient, Python: ? sympy.totient)
    • polygraphic substitution cipher of length 4
  3. Following ciphertext was encrypted using affine cipher. First two letters of plaintext are if. Decipher.
    NEJFX VPCOB PYUKN RUKPC TPUBP VKBO
zápis z cvičenia

Lab 02

  1. Decipher (shift cipher of english text)
    1. frequence analysis
    2. frequence coincidence
    Dolu fvb dlyl h ahkwvsl huk P dhz h mpzo Pu aol Whslvgvpj aptl, Huk zpkl if zpkl vu aol liipun apkl Dl zwyhdslk aoyvbno aol vvgl huk zsptl, Vy zrpaalylk dpao thuf h jhbkhs mspw aoyvbno aol klwaoz vm Jhtiyphu mlu Tf olhya dhz ypml dpao aol qvf vm spml, Mvy P svclk fvb lclu aolu.
    eng_freq = [ .082, .015, .028, .043, .127, .022, .020, .061, .070, .002, .008, .040, .024, .067, .075, .019, .001, .060, .063, .091, .028, .010, .023, .001, .020, .001]
  2. Decipher (english text, Vigenere)
    opkjcpcsrqtkhespzxxsjmuinieiovvryaaqaeicjnystxnemmbyzrvvvjo pwxzinqjibxzjdmjfsxnizvjiqidfzzymlxyeiljiqidfzzzaspwxcbnihe spzxxsjmuinbnijiehjzutsvrxdvmwmwkihaujharvzvgqsgfqhwtroqvsa bnijycrzzgfwpzxtxuxsrkmvtxmgorxopkxwqvsaxafzmteoquroruxcmic piirjbkwwwjyzqtavmtlopkzipeimihmzmkcvxviovvhnwlxkeiiqmxwwse wvzkmriexdnoirmwoiwcrhlzwdvlsfqrxdwtmgtiinmtxshfrgggwowlqhi xcqsdtgmzirikedtyefirzvqreppvjmwsxvijspziiwrumxizirmexcmkrr rfxzxriowvrjbkxvekiqmtmtxyihmzlchfjvbzeqoyenvuxpivrpbopwdvh jzgrsbgpjqzwqvztoqyrcxtymzkrhppadlkpmemedtgfzifropkmbxvvimz edskiiboezzlpimxepmcmognegfviiqjibxzjdmjydhrxzazswxvqnivtse imioordvvzdwawwwjyzaujqcsimvuxswrvztowhiumijuprrvadvlsfqrxd wtgcrkedvkhwrklzcvhoxvadtredtvemqtmhecmxqfirgfpjzkhhioxrpkv segtgqieppvxcmzeppvpdazwogmiicsfsvzrmmjavmtlxwxvswgsilyxcxy ixwsqcrmygvkvofzpdboigeehzfvsgyiinkbizmjxvkuqdmceoqurcjjxvv jefhzdzlteaijjjzbyzrvvvjopwxzinithcxyimqtjcvdeoqurgitymqzcs bgsncxig
    code
  3. LFSR
    • What is maximal period of LFSR (degree n)?
    • What can you say about the degree of LFSR if you know n bits of the generated sequence (e.g. 000101011101100)?
  4. Print next 50 bits of (Fibonacci) LFSR defined si+4 = si + si+1 + si+3 and inicialized with vector [1, 1, 0, 0]
  5. Compute the sequence, which you get by modular sum of two LFSRs. What is the period of resulting sequence?
    ai+5 = ai+1, IV = [0, 1, 1, 0, 1]
    bi+2 = bi + bi+1, IV = [0, 1]
    ci = ai + bi
  6. Find the minimal LFSR which generates the sequence from previous task (Berlekamp-Massey algorithm).
    7. code

Lab 03

code
  1. Show that pycryptodome implementations work correctly for test vectors:
    1. RC4 (RFC 6229)
    2. DES (Validating the Correctness of Hardware Implementations of the NBS Data Encryption Standard, data)
    3. 3DES (NIST Special Publication 800-67 Rev1 p. 19)
    4. ChaCha20 (RFC 7539)
    5. ChaCha20-Poly1305 (RFC 7539)
  2. Choose plaintext (the same for all ciphers from the previous task, e.g. 128 bits long). Compute how many bits of ciphertext are changed if you change just one bit of the plaintext.
RC4+DES code

Lab 04

  1. Encipher some text, which length is not multiple of 8. Try different modes of padding.
    from Crypto.Util.Padding import pad, unpad
    from Crypto.Cipher import AES, DES
    from Crypto.Random import get_random_bytes
    from base64 import b64encode, b64decode

    #encryption
    data = b'TestUPJS'
    key = get_random_bytes(8)
    cipher = DES.new(key, DES.MODE_ECB)
    ct = cipher.encrypt(data)
    print(ct)
    print(b64encode(ct).decode('utf-8'))

    #decryption
    decipher = DES.new(key, DES.MODE_ECB)
    pt = decipher.decrypt(ct)
    print(pt)
  2. Display ciphertext encrypted in several modes ECB/CBC/OFB/CFB/CTR/OPENPGP using the same key. Find the differencies in decrypted text after changing one bit in ciphertext for several modes of block cipher. Use at least 3 blocks and change bit in the second one.
    def wrap(text, size=8):
      for i in range((len(text)+size-1) // size):
        print(text[i*size:(i+1)*size])
    DES.new(..., DES.MODE_CBC, iv=?)
    rb = get_random_bytes(8)
    cipher = DES.new(rb, DES.MODE_OPENPGP, iv=get_random_bytes(8))
    ct = cipher.encrypt(b'abcd1234')
    decipher = DES.new(rb, DES.MODE_OPENPGP, iv=ct[:10])
    pt = decipher.decrypt(ct[10:])
    from Crypto.Util import Counter

    rb = get_random_bytes(8)
    nonce = get_random_bytes(4)
    cipher = DES.new(rb, DES.MODE_CTR, counter=Counter.new(32, prefix=nonce))
    ct = cipher.encrypt(b'abcd1234')
    decipher = DES.new(rb, DES.MODE_CTR, counter=Counter.new(32, prefix=nonce))
    pt = decipher.decrypt(ct)
    Bonus*: Use modern modes of operation for AES.
code
Key Derivation Functions

Lab 05

  1. Find the prime of the length at least 420 bits (nextprime).
  2. Find the generator of the group Z*p (at least 35 digits long in the base 10) - you can use Lagrange theorem
    p = 9081321110693270343633073697474256143651
  3. Decipher text encrypted using RSA (the least significant byte of the number represents the ascii code of the first character):
    p = 19669081321110693270343633073697474256143563558458718976746753830538032062222257
    q = 74121768604305613921745580037409259811952655310075487163797179490457039169594213
    e = 2**16+1
    c = 457716555223273825704148364196947662526456383872312885913872033868857417571016723717157292001931658990661403522966925784509993828339567050645537597819658756771
code

Lab 06

  1. Implement Merkle-Hellman cryptosystem. First check using the example from wikipedia and then decipher (8-bit ASCII):
    w = [1, 2, 4, 9]

    q1 = 17
    r1 = 15
    c1 = [29, 25, 22, 16, 22, 28, 22, 16, 22, 16, 22, 44, 9, 16, 0, 24]

    q2 = 19
    r2 = 7
    c2 = [23, 7, 23, 20, 23, 21, 23, 21, 23, 36, 9, 0, 29, 14, 23, 7, 23, 20, 29, 9, 23, 20, 15, 36, 0, 16]
  2. OAEP is implemented in python as PKCS1_OAEP. Try to encrypt with several parameters PKCS1_OAEP.new.

Lab 07

  1. Encrypt and decrypt using El Gamal: p = 97, g > 50, m = 75
  2. Encrypt and decrypt using El Gamal text encoded into numbers (a -> 01, ... z -> 26, code each char as two subsequent digits). As a generator use at least 35 digits long decadic number.
    p = 9081321110693270343633073697474256143651
    d = 1026722818625797069602002237808990689994 #private key
  3. How many points are there for the following elliptic curves?
    1. E_11(1, 6)
    2. E_11(3, 5)
    3. E_1009(2, 4)
    4. E_10007(3, 10000)
code, code for dictionary of squares

Lab 08

  1. Which HASH algoritms are supported in Python / Java? hashlib in Python / Hash Algos in JDK
  2. HW: Compute HASHes (at least crc32, md5, sha1, sha224, ripemd128, whirlpool, tiger128.3, haval128.3, gost) [you can use online tool for HASHes] and create table with columns Algorithm/Length of the hash in bits/Number of changed bits in hash after changing just one charactes (Compute average from 5 different positions of changed character).
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  3. HW: Choose a password and check if it is possible to crack it from its MD5/SHA1 hash (HashKiller). Find a password which
    1. looks complicated, but can be cracked
    2. is not cracked yet, but is as simple as possible
  4. How would you store passwords (let say in your web app)?
    hashlib
    BCrypt Attacks
    Argon2 (winner of Password Hashing Competition)
    Argon2 Wikipedia
    Argon2 Online
code for bits

Lab 09

  1. Sign the message and check the validity of the signature.
    Quisque bibendum tincidunt ipsum at lobortis. Etiam euismod consequat arcu in facilisis. Nulla iaculis turpis sed sem efficitur fringilla. Maecenas pulvinar velit eget tempor aliquet. Nulla odio nisl, commodo sit amet pellentesque quis, molestie at nisl. Praesent vel urna orci. Morbi convallis ante vel augue consectetur cursus. Integer rhoncus tincidunt tincidunt. Aliquam elementum nisl et dui auctor venenatis. Morbi tincidunt erat magna, ac gravida odio tristique nec. Vestibulum nec ex at dolor pulvinar varius. Fusce id pharetra leo. Cras sit amet molestie eros. Sed euismod tempus odio id sagittis. Cras aliquam dui in mauris blandit, vel pharetra augue tristique. Nulla vel magna nulla. Nullam cursus nunc arcu, id ullamcorper lacus feugiat vel. Pellentesque lectus ipsum, maximus eu fermentum ac, tincidunt eu augue. Nam et pellentesque lectus, in elementum risus. Cras arcu mauris, dictum eget accumsan sit amet, pharetra nec lorem. Sed felis risus, molestie in est at, rutrum consequat mauris. Morbi ultricies nulla non nunc malesuada congue. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Donec consectetur arcu ac elit imperdiet fringilla. Aliquam sed leo est. Aenean sit amet nunc et ante posuere congue. Duis volutpat ante vitae massa viverra ultricies. Maecenas quis dictum nulla. Ut consectetur magna eget vulputate semper. Fusce non aliquam nulla. Morbi a sodales massa. Phasellus non lacus sed est aliquet lobortis vitae vel lectus. Maecenas mi purus, ornare eget tincidunt aliquet, sodales ac ligula. Donec vel neque vel orci rhoncus convallis. Aenean dolor nulla, tempus ac neque sed, facilisis hendrerit massa. Etiam est diam, pellentesque sed dapibus in, cursus volutpat odio. Suspendisse elementum cursus augue nec congue. Donec ac mi nulla. Vivamus fringilla sapien cursus euismod mattis. Fusce semper vel justo non ultricies. Donec dictum interdum urna, in tincidunt neque posuere fermentum. Morbi at suscipit nisi. Morbi eros dui, porttitor nec condimentum sed, euismod et nibh. Etiam eget bibendum ante, ac fermentum elit. In consequat sit amet nibh non feugiat. Etiam et nulla sed urna porttitor congue eget laoreet metus. Curabitur fringilla id tellus feugiat accumsan. Donec a dui vitae tellus aliquet gravida.
    Algorithm:
    1. Lamport signature scheme.
    2. Merkle signature scheme. You can use just any hash as initial one-time signature.
code for Lamport One-Time Scheme, code for Merkle signature visualisation

Lab 10

  1. Share the secret (4 digit PIN code) between 7 friends in such way, that any four of them could compute the PIN. Use Shamir scheme. Show that it is good scheme for four people, i.e. for one triple of keys show that the PIN could be 1111, 3210, or 6789.
  2. Divide keys between 1 CEO, 3 directors and 20 officers. Share secret 10 digits code for opening the safe deposit in following way for opening:
    1. CEO + 1 director
    2. 3 directors
    3. 5 officers
    Which other combinations of people could open the safe deposit in your arrangment of the keys?
    Find any other combination for dividing the keys and all minimal subsets of users.
code for Lagrange Interpolation, sympy exact

Lab 11

  1. Agree on a pairwise encryption key using Diffie-Hellman exchange. Use a group of at least 512-bit size (safe in the mid-80s [Cryptographic Key Length Recommendation]).
  2. Burmester-Desmedt key exchange Protocol. Show the negotiation of a shared key for four participants.
  3. Describe the sequence of messages for key agreement using Diffie-Hellman exchange for 4 participants (A, B, C, D) in such way, that A sends the least possible number of messages.
code

Lab 12

  1. Which certificates use web page www.upjs.sk and email server smtp.gmail.com? Find at least 3 webpages with different root certificates (show its ertificates' chains).
    openssl s_client -status -showcerts -connect www.upjs.sk:443
    openssl s_client -status -showcerts -starttls smtp -connect smtp.gmail.com:587

    openssl x509 [-in certificate] -text -noout
  2. Find sites with different results in SSL tests and compare them.
    1. SSL Observatory
    2. SSL Test
    3. SSL Configuration Generator
code