Introduction

I am going to start out by creating a series of the basics of cryptography, each with its own challenges that can be solved with the information present in that post and at the end will be a single challenge that will not only be a lot harder than the rest but will be solvable through some combination of techniques used throughout any of the tutorials. As a result, each challenge will get incrementing rewards. Eventually it will build up to a point where I have no more tutorials and just offer challenges. My rewards that I offer will be in the form of cryptocrrencies.

Sourced as Public Domain

Caesar Cipher

Or more generally this tutorial will cover a substitution cipher and how it works. The Caesar Cipher is a very popular and basic encryption technique that is used to lure people into the idea of cryptography as 1: it is very easy to use and 2: it is eloquent. The general approach to the Caesar Cipher is to take a text, go through it character by character, and shift it by some number. For instance if we were to have a shift1 cipher (meaning we shift by 1 character) and our original text was "a" then we could have an output of "b".

Original	Billy bob loves his nuggets
Shift 0	Billy bob loves his nuggets
Shift 1	Cjmmz cpc mpwft ijt ovhhfut
Shift 2	Dknna dqd nqxgu jku pwiigvu
Shift 3	Eloob ere oryhv klv qxjjhwv
Shift 4	Fmppc fsf psziw lmw rykkixw
Shift 5	Gnqqd gtg qtajx mnx szlljyx
Shift 6	Horre huh rubky noy tammkzy
Shift 7	Ipssf ivi svclz opz ubnnlaz
Shift 8	Jqttg jwj twdma pqa vcoomba
Shift 9	Kruuh kxk uxenb qrb wdppncb
Shift 10	Lsvvi lyl vyfoc rsc xeqqodc
Shift 11	Mtwwj mzm wzgpd std yfrrped
Shift 12	Nuxxk nan xahqe tue zgssqfe
Shift 13	Ovyyl obo ybirf uvf ahttrgf
.	.
.	.
.	.
Shift 23	Yfiiv yly ilsbp efp krddbqp
Shift 24	Zgjjw zmz jmtcq fgq lseecrq
Shift 25	Ahkkx ana knudr ghr mtffdsr

I hope you do not mind but I cut out some rows from the table because I think you get the point. Now this looks simple, you can encrypt messages going 1 way very easily, but the question is how do you decrypt the message? This is very simple, you take the negative shift. So if you did a shift 5 to encrypt then you do a shift -5 (or more appropriately, a shift 21) and you will get the answer.

Sourced as Public Domain

What is a Substitution Cipher?

To put it quaintly, a substitution cipher is a cipher/encryption technique where you replace text or portions of text with something else and then you have the substitutions held as a key and only the sender and receiver should have the key and therefore be the only ones able to break it. On the right you will see a specific case of the Caesae Cipher (discussed above) named ROT13, or as we would put it Shift13. This is a special case because a Casar shift 13 can be undone by shifting another 13, with the English-Roman alphabet (For instance the Spanish-Roman alphabet has 27 letters and therefore has no shift that will undo itself as you cannot do a half shift, at least not using substitution methods.

Problems With Substitution Ciphers

One of the biggest problems is that most substitution methods (not all) suffer from a very blatant weakness which is letter frequency. For instance the frequency of usage of each letter in English (below) can be used to attack a cipher.

Sourced as Public Domain As we can see, certain letters are far far more likely to show up in certain texts. For instance, lets take the following encrypted text and find the letter of highest frequency and see what happens when we treat that letter as an E and shift each letter back as much as is required to make it an E.

Nby kocwe vliqh zir dogjyx ipyl nby futs mbyyj xia

Using this we can quickly see that there are more y's than anything (10 y's to be specific, with a total of 77 putting its frequency at around 12.98%, right where expected for E's) and since we know that if we shift E by 20 we will get Y we can determine that if we shift by -20 (or 6) we should get the original phrase.

The quick brown fox jumped over the lazy sheep dog

How I got 6 as the Shift (ROT) number

So the answer is very simple. To undo a caesar cipher you follow a simple formula: N-S_n=S
Where:
N is the number of letters in the alphabet
S_n is the shift number of the original shift
S is the shift required to undo it

Lets use this with the above example, N=26,S_n=20, 26-20=6, ergo if we shift the previous encryption forward by 6 it will give us our answer.

References
Frequency Counter (0)
Caesar Calculator (1)
Caesar Cipher (2)
Substitution Cipher (3)
Letter Frequency (4)
Stinson, Douglas R. Cryptography: Theory and Practice. Third Edition, Chapman & Hall/CRC, 2006, www.icst.pku.edu.cn/F/course/Cryptography/CryptographyTheoryandpractice(3ed).pdf.

Practice Problems

Find the original text to these encrypted messages, they all use a caesar cipher. State the original text and what shift was used: 1: Vs zbarl vf gur ebbg bs nyy rivy gura jul qb gurl nfx sbe vg ng puhepu
2: Je ru eh dej je ru, Jxqj yi jxu gkuijyed 3: Kimaiz kqxpmz qa wvm wn bpm wtlmab svwev mvkzgxbqwv umbpwla. Qb qa dmzg aquxtm - qb qa rcab apqnbqvo iv itxpijmb. Bzivanwzuibqwv qa bmzuml ZWBV, epmzm V qa apqnb ditcm ivl ZWB qa nzwu "ZWBIBM" jmkicam bpqa qa i kgktqk apqnb.
4: Mpwf uiz fofnz
5: A world which does not belong
Find the specific encryption to these messages (ROT3 means shift by 3): 6 ROT3: The world will never be enough
7 ROT13: Love thy neighbor as thy would love thyself
8 ROT22: Don't you stick it in your mouth, though it might look good to eat, and it might look good to taste. You could get sick, real ick, real sick, real quick.
9 ROT2: Why do sports fans always question why youtube gaming is popular? You guys just sit there watching others play games for entertainment too!

Answers:
1: ROT13(Shift13) If money is the root of all evil then why do they ask for it at chur
ch
3: ROT18 Caesar cipher is one of the oldest known encryption methods. It is very simple - it is just shifting an alphabet. Transformation is termed ROTN, where N is shift value and ROT is from "ROTATE" because this is a cyclic shift.
5: ROT0 (Shift0) A world which does not belong
7: Ybir gul arvtuobe nf gul jbhyq ybir gulfrys
9: Yja fq urqtvu hcpu cnycau swguvkqp yja aqwvwdg icokpi ku rqrwnct? Aqw iwau lwuv ukv vjgtg ycvejkpi qvjgtu rnca icogu hqt gpvgtvckpogpv vqq!

Challenge The challenge will be easy for this one so it will be worth very little. The difficulty rating is logarithmic in nature (exponential) so a difficulty rating of 2 is 10 times more difficult than 1, and a difficulty of 3 is 100 times more difficult than a rating of 1. As such the rewards will also scale with difficulty, though not at the same rate. The rewards for this challenge will be 1SBD + 50% of the SBD reward (or more closely as 18.75% of the final payout). The challenge must be solvable based off of information present in the post.

Find the original text: Hmh vjg usl moo ez sgd cow

To enter your answer (and be eligable) go to https://8gwifi.org/rsafunctions.jsp and enter in the public key below (delete the private key) and enter your answer into the clear text message. Make sure to have the encrypt message clicked. Then comment the output on this post.

Public key:

Example comment:

Here is my answer:

IS8G23WLHabrXBn7nL52GVEH9VIq7yXtzhtAWk+d8DGBOw8RY9y+murcsInWoRb7bQ/L1HULb9vAsdCc58EKBAFpxQrB4ju/gt+Tlw+pNl+U9xG7S5ujnROd+X/AwrLzQvWO5ik52jjzkpEC4z5Mc9I8OWLirRxWcMKCZ3Qy4jE=

The prize goes to the first person whom responds with the correct answer but the prize will be handed out no sooner than payout. If no correct answer has been handed in by payout then I will keep the prize for myself. There will be a bonus for second and third place people!

Cryptography Lesson1 Challenge 1