Ciphers

Notes

• This is from Du: Computer and Internet Security
• A cipher is an encryption/decryption algorithm pair
• Du states that we know of ciphers existing as early as 1900 bc.
  • Taterka, Filip. "Ancient Egyptian Royal Cryptography in the Ramesside Period." ANTROPOLOGIA KOMUNIKACJI. (2015): 71.
  • A link to the article in English
  • It seems to rely on minor changes to words written in hieroglyphics
  • Which were very complex and few could read
  • And it took an "outstanding" scribe to figure out the real meaning
  • I don't know enough about hieroglyphics to completely understand.
  • But the paper says they would:
    1. Change the traditional shape of a hieroglyph
    2. Change the phonetic value of a hieroglyph
    3. Add additional signs
• More traditionally ciphers have been characterized as
  • Substitution Ciphers: change the meaning of a letter or group of letters
    • Caesar Cipher, to encrypt add 3 to each letter a->d, b->e
  • Transposition Ciphers: Rearrange the letters
    • Playfair Cipher: Build a code block, read the letters from that block.
• There is no reason to just have one of these methods.
• And we can do other things as well.
• The simplest is something like a substitution cipher
  • Ceaser Cipher
    • letter = (letter + 3) % 26, letter = (letter - 3) % 26
  • Rot13
    • Letter = (letter + 13) % 26
  • Keyword-Key Phrase Cipher

    • remove duplicate letters from the key
      write down the key
      for letter = a to z 
         if letter has not been written down write it down
      
      encrypt based on this code block

    • Keyword: edinboro

    • Plaintext Alphabet	a	b	c	d	e	f	g	h	i	j	k	l	m	n	o	p	q	r	s	t	u	v	w	x	y	z
      Ciphertext Alphabet	e	d	i	n	b	o	r	a	c	e	f	g	h	j	k	l	m	r	s	t	u	v	w	x	y	z

    • Plaintext: Attack at dawn!
    • Ciphertext: Etteif et newj!
  • Or even "The Dancing Man Code".
    • Used in a Sherlock Holmes Story, The Adventure of the Dancing Men
    • (From https://evil.fandom.com/wiki/The_Dancing_Men?file=Dancing_Men.jpg)
• These are all examples of monoalphabetic substitution ciphers
  • They are characterized by a simple substitution table.
  • Each letter is mapped to exactly one other letter.
  • They are, unfortunately, easy to break.
• Frequency analysis
  • We know that not all letters in English are used equally.
  • see This frequency table, which I reproduce

  • Letter	Count	Frequency	Letter	Count	Frequency
    E	21912	12.02	M	4761	2.61
    T	16587	9.10	F	4200	2.30
    A	14810	12	Y	3853	2.11
    O	14003	7.68	W	3819	2.09
    I	13318	7.31	G	3693	2.03
    N	12666	6.95	P	3316	1.82
    S	11450	6.28	B	2715	1.49
    R	10977	6.02	V	2019	1.11
    H	10795	5.92	K	1257	0.69
    D	7874	4.32	X	315	0.17
    L	7253	3.98	Q	205	0.11
    U	5246	2.88	J	188	0.10
    C	4943	2.71	Z	128	0.07

  • Or digraphs (From https://pi.math.cornell.edu/~mec/2003-2004/cryptography/subs/digraphs.html)

    Digraph	Count		Digraph	Frequency
    th	5532		th	1.52
    he	4657		he	1.28
    in	3429		in	0.94
    er	3420		er	0.94
    an	3005		an	0.82
    re	2465		re	0.68
    nd	2281		nd	0.63
    at	2155		at	0.59
    on	2086		on	0.57
    nt	2058		nt	0.56
    ha	2040		ha	0.56
    es	2033		es	0.56
    st	2009		st	0.55
    en	2005		en	0.55
    ed	1942		ed	0.53
    to	1904		to	0.52
    it	1822		it	0.50
    ou	1820		ou	0.50
    ea	1720		ea	0.47
    hi	1690		hi	0.46
    is	1660		is	0.46
    or	1556		or	0.43
    ti	1231		ti	0.34
    as	1211		as	0.33
    te	985		te	0.27
    et	704		et	0.19
    ng	668		ng	0.18
    of	569		of	0.16
    al	341		al	0.09
    de	332		de	0.09
    se	300		se	0.08
    le	298		le	0.08
    sa	215		sa	0.06
    si	186		si	0.05
    ar	157		ar	0.04
    ve	148		ve	0.04
    ra	137		ra	0.04
    ld	64		ld	0.02
    ur	60		ur	0.02

  • Or even higher
    • Most common bigrams: th, he, in, en, nt, re, er, an, ti, es, on, at, se, nd, or, ar, al, te, co, de, to, ra, et, ed, it, sa, em, ro.
    • Most common trigrams: the, and, tha, ent, ing, ion, tio, for, nde, has, nce, edt, tis, oft, sth, men
• Let's break a simple encryption
  • I like this working tool..
  • This tool would be helpful for computing ngrams.
  • I use this site quite frequently.
  • Here is a coded message:

    Oz Hfypfbc giuk cip fcksue, abk tbyk feu yftu fcg kpbtt,
    Oz dfpaue giuk cip duut oz feo, au afk ci yqtku cie sbtt,
    Pau kaby bk fchaieug kfdu fcg kiqcg, bpk jizflu htikug fcg gicu,
    Deio dufedqt peby pau jbhpie kaby hiouk bc sbpa iwmuhp sic;
          Unqtp I kaieuk, fcg ebcl I wuttk!
              Wqp B sbpa oiqecdqt peufg,
                   Sftx pau guhx oz Hfypfbc tbuk,
                           Dfttuc hitg fcg gufg.

• Can you break this coded message?

  • Nsjr-Waec
    V.I. Jputsgys
    
    A gsxst npu p uajv eiagz
    nbttc rbt aensjr
    P nopjj katv uajj vtbw rtblsg vspv rtbo p kbfzi
    uaeibfe sxst ipxagz rsje nbttc rbt aensjr 

    Not the message is much smaller
  • AND it does not use the common letter distribution.
• Here is a challenge:

  • Xr jr, pf ecx ww of, hyox la gis hiivbvpb:
    Nviwprs 'hzg rrjyff zb xkm zjbu hs vcsgsi
    Hlh ayjbxg eql nsffkw rn bvhiokhwht tffxxvr,
    Pf kc xdsr bfdg ejivogk o whi bg hicyetrt
    Oer fb wcqcjwrj mae hysq. Ww qjs-kc womrq,
    Bf asum; nor sm e vtrfd kc wdg jf ser
    Xkm ufoih-efpr bbu hlh bupijorg vnuiiop vpbdyj
    Hldb smsjv mv prjf kc: 'xla n dcegypunuwfb
    Hhdbvhcm xr jr xwjv'h. Ww qjs, kc womrq;
    Hf gphmc, qsiqldvpf hf rvhiz-bm, kvium'f uvv fye:

• Some other tools
  • a letter scrambler
  • A random replacement tool.