keeping your bits private! tony c smith dept. computer science university of waikato science of...
TRANSCRIPT
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Keeping your bits private!
Tony C Smith
Dept. Computer Science
University of Waikato
Science of cryptography = Art of keeping secrets
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terminology
plaintext (the message)
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terminology
plaintext
sender (cryptographer)
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terminology
plaintext
sender receiver
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terminology
plaintext
sender
encrypt
receiver
ciphertext
(transmission)
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terminology
plaintext
sender
encrypt decrypt
receiver
ciphertext
plaintext
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terminology
is insecure!Transmission medium
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terminology
plaintext
sender
encrypt decrypt
receiver
plaintextcryptanalyst
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goal: deciphering the ciphertext is ashard as just guessing the plaintext message.
encryption process: transform plaintext into ciphertext
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plaintext and ciphertext are in 27 letter English:
26 letters of the alphabet, plus space
also, letters can be treated as numbers:
space is 0A is 1B is 2C is 3
…Z is 26
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because we can treat letters as numbers, we can do arithmetic with them:
B + C = E2 + 3 = 5
if the sum of two numbers goes beyond 26 thenwe wrap around back to the beginning of the alphabet
W + H = ? 23 + 8 = 31
Z + E = ?26 + 5 = 31
… same as ...
five letters beyond the end = fifth from start
… so, W + H = E
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plaintext
sender
encrypt decrypt
receiver
plaintextcryptanalyst
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plaintext
encrypt decrypt
plaintextknows the encryption scheme
key keyguessing the key is as hard as
guessing the message
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Caesar Cipher
Used by Julius Caesar to communicate with his army.
Thought to be the first general use of encryption, 75 B.C..
replace each letter with the k-th letter after it in the alphabet
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Caesar Cipher
E.g. k = 3
space + 3 = C A + 3 = D B + 3 = E … W + 3 = Z X + 3 = space Y + 3 = A Z + 3 = B
ATTACK AT DAWN … becomes ...
DWWDFNCDWCGDZQciphertext:
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plaintext
encrypt decrypt
plaintextknows the encryption scheme
key keyguessing the key is as hard as
guessing the message
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Caesar Cipher
Easily attacked!
Simply try every possible value for k … from 1 to 26
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Caesar Cipher
Easily attacked!
Simply try every possible value for k … from 1 to 26
ciphertext = DWWDFNCDWCGDZQ
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Caesar Cipher
Easily attacked!
Simply try every possible value for k … from 1 to 26
k = 1 ? CVVCEMBCVBFCYP
DWWDFNCDWCGDZQ
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Caesar Cipher
Easily attacked!
Simply try every possible value for k … from 1 to 26
k = 1 ? CVVCEMBCVBFCYP
k = 2 ? BUUBDLABUAEBXO
DWWDFNCDWCGDZQ
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Caesar Cipher
Easily attacked!
Simply try every possible value for k … from 1 to 26
k = 1 ? CVVCEMBCVBFCYP
k = 2 ? BUUBDLABUAEBXO
k = 3 ? ATTACK AT DAWN
DWWDFNCDWCGDZQ
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Keyed Substitution
A more general substitution scheme.
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Keyed Substitution
A more general substitution scheme.
Replaces each letter with another.
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Keyed Substitution
A more general substitution scheme.
Replaces each letter with another.
Any letter can stand in for any other letter.
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Keyed Substitution
A more general substitution scheme.
Replaces each letter with another.
Any letter can stand in for any other letter.
Each letter in ciphertext resolves to a unique letter in plaintext.
plaintext: _ABCDEFGHIJKLMNOPQRSTUVWXYZ
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Keyed Substitution
A more general substitution scheme.
Replaces each letter with another.
Any letter can stand in for any other letter.
Each letter in ciphertext resolves to a unique letter in plaintext.
plaintext: _ABCDEFGHIJKLMNOPQRSTUVWXYZsubstitution: SJKEIOAHWDPMGRNVT_QLZBFYCXU
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Keyed Substitution
A random substitution is hard to remember or validate.
Solution? Use a key phrase to set the substitution alphabet.
Write down each unique letter of the key phrase in order, thenappend the rest of the unused letters of the alphabet.
plaintext: _ABCDEFGHIJKLMNOPQRSTUVWXYZsubstitution: THE_QUICKBROWNFXJMPDAGLSVYZ
E.g. key phrase = THE QUICK BROWN FOX JUMPED
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Keyed Substitution
Security?Any letter can stand for any other letter. Thus there
are 27! possible different substitutions schema.
27 * 26 * 25 * … * 3 * 2 = 1029
At one permutation tested per second, it would takea million, million, million centuries to test them all.
Seems pretty secure …….. but ...
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ciphertext:
WSCZSDZHAKVSHQZAKZKE_ZDXXKZVHZKEXZBSHCQZSDZGSLXZOXZTXXKZEXAJ ZSPJZLSVYXQZOXZXHKJXAKZWSCZCXD XHCZSPJZDJXXZGAHCZ
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ciphertext:
WSCZSDZHAKVSHQZAKZKE_ZDXXKZVHZKEXZBSHCQZSDZGSLXZOXZTXXKZEXAJ ZSPJZLSVYXQZOXZXHKJXAKZWSCZCXD XHCZSPJZDJXXZGAHCZ
letter frequency:
Z 23
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ciphertext:
WSCZSDZHAKVSHQZAKZKE_ZDXXKZVHZKEXZBSHCQZSDZGSLXZOXZTXXKZEXAJ ZSPJZLSVYXQZOXZXHKJXAKZWSCZCXD XHCZSPJZDJXXZGAHCZ
letter frequency:
Z 23
probability in English:
space .20
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ciphertext:
WSC SD HAKVSHQ AK KE_ DXXK VH KEX BSHCQ SD GSLX OX TXXK EXAJ SPJ LSVYXQ OX XHKJXAK WSC CXD XHC SPJ DJXX GAHC
letter frequency:
Z 23
probability in English:
space .20
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ciphertext:
WSC SD HAKVSHQ AK KE_ DXXK VH KEX BSHCQ SD GSLX OX TXXK EXAJ SPJ LSVYXQ OX XHKJXAK WSC CXD XHC SPJ DJXX GAHC
letter frequency:
Z 23X 16
probability in English:
space .20
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ciphertext:
WSC SD HAKVSHQ AK KE_ DXXK VH KEX BSHCQ SD GSLX OX TXXK EXAJ SPJ LSVYXQ OX XHKJXAK WSC CXD XHC SPJ DJXX GAHC
letter frequency:
Z 23X 16
probability in English:
space .20 e .15
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ciphertext:
WSC SD HAKVSHQ AK KE_ DeeK VH KEe BSHCQ SD GSLe Oe TeeK EeAJ SPJ LSVYeQ Oe eHKJeAK WSC CeD eHC SPJ DJee GAHC
letter frequency:
Z 23X 16
probability in English:
space .20 e .15
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ciphertext:
WSC SD HAKVSHQ AK KE_ DeeK VH KEe BSHCQ SD GSLe Oe TeeK EeAJ SPJ LSVYeQ Oe eHKJeAK WSC CeD eHC SPJ DJee GAHC
letter frequency:
Z 23X 16S 10
probability in English:
space .20 e .15
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ciphertext:
WSC SD HAKVSHQ AK KE_ DeeK VH KEe BSHCQ SD GSLe Oe TeeK EeAJ SPJ LSVYeQ Oe eHKJeAK WSC CeD eHC SPJ DJee GAHC
letter frequency:
Z 23X 16S 10
probability in English:
space .20 e .15 o .09
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ciphertext:
WoC oD HAKVoHQ AK KE_ DeeK VH KEe BoHCQ oD GoLe Oe TeeK EeAJ oPJ LoVYeQ Oe eHKJeAK WoC CeD eHC oPJ DJee GAHC
letter frequency:
Z 23X 16S 10
probability in English:
space .20 e .15 o .09
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ciphertext:
WoC oD HAKVoHQ AK KE_ DeeK VH KEe BoHCQ oD GoLe Oe TeeK EeAJ oPJ LoVYeQ Oe eHKJeAK WoC CeD eHC oPJ DJee GAHC
letter frequency:
Z 23X 16S 10K 8
probability in English:
space .20 e .15 o .09
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ciphertext:
WoC oD HAKVoHQ AK KE_ DeeK VH KEe BoHCQ oD GoLe Oe TeeK EeAJ oPJ LoVYeQ Oe eHKJeAK WoC CeD eHC oPJ DJee GAHC
letter frequency:
Z 23X 16S 10K 8
probability in English:
space .20 e .15 o .09 t .08
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ciphertext:
WoC oD HAtVoHQ At tE_ Deet VH tEe BoHCQ oD GoLe Oe Teet EeAJ oPJ LoVYeQ Oe eHtJeAt WoC CeD eHC oPJ DJee GAHC
letter frequency:
Z 23X 16S 10K 8
probability in English:
space .20 e .15 o .09 t .08
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ciphertext:
WoC oD HAtVoHQ At tE_ Deet VH tEe BoHCQ oD GoLe Oe Teet EeAJ oPJ LoVYeQ Oe eHtJeAt WoC CeD eHC oPJ DJee GAHC
letter frequency:
Z 23X 16S 10K 8H 7
probability in English:
space .20 e .15 o .09 t .08
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ciphertext:
WoC oD nAtVonQ At tE_ Deet Vn tEe BonCQ oD GoLe Oe Teet EeAJ oPJ LoVYeQ Oe entJeAt WoC CeD enC oPJ DJee GAnC
letter frequency:
Z 23X 16S 10K 8H 7
probability in English:
space .20 e .15 o .09 t .08 n .07
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ciphertext:
WoC oD nAtVonQ At tE_ Deet Vn tEe BonCQ oD GoLe Oe Teet EeAJ oPJ LoVYeQ Oe entJeAt WoC CeD enC oPJ DJee GAnC
letter frequency:
Z 23X 16S 10K 8H 7C 6
probability in English:
space .20 e .15 o .09 t .08 n .07
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ciphertext:
Wod oD nAtVonQ At tE_ Deet Vn tEe BondQ oD GoLe Oe Teet EeAJ oPJ LoVYeQ Oe entJeAt Wod deD end oPJ DJee GAnd
letter frequency:
Z 23X 16S 10K 8H 7C 6
probability in English:
space .20 e .15 o .09 t .08 n .07 d .06
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ciphertext:
Wod oD nAtVonQ At tE_ Deet Vn tEe BondQ oD GoLe Oe Teet EeAJ oPJ LoVYeQ Oe entJeAt Wod deD end oPJ DJee GAnd
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ciphertext:
Wod oD nAtVonQ At tE_ Deet Vn tEe BondQ oD GoLe Oe Teet
EeAJ oPJ LoVYeQ Oe entJeAt Wod deDend oPJ DJee GAnd
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ciphertext:
Wod oD nAtVonQ At tE_ Deet Vn tEe BondQ oD GoLe Oe Teet
EeAJ oPJ LoVYeQ Oe entJeAt Wod deDend oPJ DJee GAnd
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ciphertext:
Wod of nAtVonQ At tE_ feet Vn tEe BondQ of GoLe Oe Teet
EeAJ oPJ LoVYeQ Oe entJeAt Wod defend oPJ fJee GAnd
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ciphertext:
Wod of nAtVonQ At tE_ feet Vn tEe BondQ of GoLe Oe Teet
EeAJ oPJ LoVYeQ Oe entJeAt Wod defend oPJ fJee GAnd
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ciphertext:
Wod of nAtVonQ At tE_ feet Vn tEe BondQ of GoLe Oe Teet
EeAr oPr LoVYeQ Oe entreAt Wod defend oPr free GAnd
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ciphertext:
Wod of nAtVonQ At tE_ feet Vn tEe BondQ of GoLe Oe Teet
EeAr oPr LoVYeQ Oe entreAt Wod defend oPr free GAnd
![Page 53: Keeping your bits private! Tony C Smith Dept. Computer Science University of Waikato Science of cryptography = Art of keeping secrets](https://reader033.vdocuments.net/reader033/viewer/2022052603/56649e7f5503460f94b83f86/html5/thumbnails/53.jpg)
ciphertext:
Wod of natVonQ at tE_ feet Vn tEe BondQ of GoLe Oe Teet
Eear oPr LoVYeQ Oe entreat Wod defend oPr free Gand
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ciphertext:
Wod of natVonQ at tE_ feet Vn tEe BondQ of GoLe Oe Teet
Eear oPr LoVYeQ Oe entreat Wod defend oPr free Gand
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ciphertext:
Wod of nations at th_ feet in the Bonds of GoLe Oe Teet
hear oPr LoiYes Oe entreat Wod defend oPr free Gand
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ciphertext:
Wod of nations at th_ feet in the Bonds of GoLe Oe Teet
hear oPr LoiYes Oe entreat Wod defend oPr free Gand
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ciphertext:
God of nations at th_ feet in the bonds of love we meet
hear our voices we entreat God defend our free land
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plaintext:
God of nations at thy feet in the bonds of love we meet
hear our voices we entreat God defend our free land
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Strangely enough, it wasn’t until around the time ofQueen Elizabeth I that general substitution codes werefound breakable (1580).
The catalyst was a plot by Queen Mary of Scotland andher loyal friends to depose Elizabeth and seize theEnglish throne. Mary was using a very clever substitutioncode which included “nulls” … irrelevant symbolsintroduced to alter the statistics of English.
The idea that language exhibited conspicuous statisticalregularities was just beginning to be exploited.
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The Vigenere Cipher (1600)
One way to alter the statistics of the ciphertext is tochange the substitution code often during encryption.
Instead of using a key phrase to create one substitution,use it to create many substitutions and rotate through themas each letter of the plaintext is encrypted.
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The Vigenere Cipher
plaintext: ATTACK AT DAWN
key: ABC
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The Vigenere Cipher
plaintext: ATTACK AT DAWN
key: ABC
ABCABCABCABCAB
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The Vigenere Cipher
plaintext: ATTACK AT DAWN +
key: ABC
ABCABCABCABCAB
BVWBENACWAFDXPciphertext:
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The Vigenere Cipher
plaintext: ATTACK AT DAWN
key: ABC
ABCABCABCABCAB
BVWBENACWAFDXPciphertext:
Notice that the same letter can encode differently.
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The Vigenere Cipher
plaintext: ATTACK AT DAWN
key: ABC
ABCABCABCABCAB
BVWBENACWAFDXPciphertext:
While A occurs four times and T three times in themessage, nothing occurs more than twice in the cipher.
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Attacking the Vigenere Cipher
ciphertext:
HQGAQIAPDUKROUCBVCUJAAHHFVCJPCUJHADROFVAQIANRWGCXGCNGHUBKFCUAQXSBYPKFFUCXGCFPWSGDUBJPFCEGIFPGAQXSBISGHANDOF
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Attacking the Vigenere Cipher
ciphertext:
HQGAQIAPDUKROUCBVCUJAAHHFVCJPCUJHADROFVAQIANRWGCXGCNGHUBKFCUAQXSBYPKFFUCXGCFPWSGDUBJPFCEGIFPGAQXSBISGHANDOF
Guess the length of key phrase and apply a statisticaltest to letters separated by that distance.
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Attacking the Vigenere Cipher
ciphertext:
HQGAQIAPDUKROUCBVCUJAAHHFVCJPCUJHADROFVAQIANRWGCXGCNGHUBKFCUAQXSBYPKFFUCXGCFPWSGDUBJPFCEGIFPGAQXSBISGHANDOF
Guess the length of key phrase and apply a statisticaltest to letters separated by that distance.
k = 3 ?
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Attacking the Vigenere Cipher
ciphertext:
HQGAQIAPDUKROUCBVCUJAAHHFVCJPCUJHADROFVAQIANRWGCXGCNGHUBKFCUAQXSBYPKFFUCXGCFPWSGDUBJPFCEGIFPGAQXSBISGHANDOF
Guess the length of key phrase and apply a statisticaltest to letters separated by that distance.
k = 3 ? A occurs 9 times
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Attacking the Vigenere Cipher
ciphertext:
HQG QI PDUKROUCBVCUJA HHFVCJPCUJH DROFV QI NRWGCXGCNGHUBKFCU QXSBYPKFFUCXGCFPWSGDUBJPFCEGIFPG QXSBISGH NDOF
Guess the length of key phrase and apply a statisticaltest to letters separated by that distance.
k = 3 ? A occurs 9 times = space?
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Attacking the Vigenere Cipher
ciphertext:
HQG QI PDUKROUCBVCUJA HHFVCJPCUJH DROFV QI NRWGCXGCNGHUBKFCU QXSBYPKFFUCXGCFPWSGDUBJPFCEGIFPG QXSBISGH NDOF
Guess the length of key phrase and apply a statisticaltest to letters separated by that distance.
k = 3 ? A occurs 9 times = space?offset of every third letter is 1?
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Attacking the Vigenere Cipher
ciphertext:
gQG QI PDtKRnUCaVCtJA HHeVCiPCtJH DRnFV QI NRvGCwGCmGHtBKeCU QXrBYoKFeUCwGCePWrGDtBJoFCdGIePG QXrBIrGH NDnF
Guess the length of key phrase and apply a statisticaltest to letters separated by that distance.
k = 3 ? A occurs 9 times = space?offset of every third letter is 1?
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Vernam Cipher (1917)
Solution? make the keyphrase as long as the message!
message: ATTACK AT DAWN
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Vernam Cipher
Solution? make the keyphrase as long as the message!
message: ATTACK AT DAWN key: ABCDEFGHIJKLMN
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Vernam Cipher
Solution? make the keyphrase as long as the message!
message: ATTACK AT DAWN key: ABCDEFGHIJKLMN
ciphertext: BVWEHQGIBJOMIA
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Vernam Cipher
Solution? make the keyphrase as long as the message!
message: ATTACK AT DAWN key: ABCDEFGHIJKLMN
ciphertext: BVWEHQGIBJOMIA
Now any letter can encode as any other letter atany point in the message.
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Vernam Cipher
Solution? make the keyphrase as long as the message!
message: ATTACK AT DAWN key: ABCDEFGHIJKLMN
ciphertext: BVWEHQGIBJOMIA
Now any letter can encode as any other letter atany point in the message.
Solving a letter doesn’t help solve any others.
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Vernam Cipher
Solution? make the keyphrase as long as the message!
message: ATTACK AT DAWN key: ABCDEFGHIJKLMN
ciphertext: BVWEHQGIBJOMIA
Now any letter can encode as any other letter atany point in the message.
Solving a letter doesn’t help solve any others.
Only provably secure encryption scheme!
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Vernam Cipher
Two major problems:
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Vernam Cipher
Two major problems:
1. Can’t re-use keys, so how do we make them?(one-time pad)
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Vernam Cipher
Two major problems:
1. Can’t re-use keys, so how do we make them?(one-time pad)
2. How do we distribute them?
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Digital Vernam Cipher
Solution: generate keys
randomgenerator
message
encoder encoded message
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Digital Vernam Cipher
message = ‘V’ = 86 = 01010110
random number = 223 = 11100101
XOR = 10110011
random number = 223 = 11100101
XOR = 01010110 = ‘V’
= cipher
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Digital Vernam Cipher
Solution: generate keys
randomgenerator
message
encoder encoded message
Problem: distribute generator for decoding
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Public Key encryption
Solution: publish the encryption key
RSA:
1. generate 3 large prime numberss=97 x=47 y=79
which give N = x * y, or N=3713
2. find a unique value, p, satisfying(p*s) mod (x-1)*(y-1) = 1
which, in this case, gives p = 37
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RSA:
3. Encrypt a message segment, m, usingmp mod N
e.g. for m = 0120012037 mod 3713 = 1404
Public Key encryption
4. decrypt the coded segment, c, usingcs mod N
e.g.140497 mod 3713 = 0120
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RSA: publish some of the values (p, N)
Anyone wanting to send us a message can useour public key to encrypt it.
Public Key encryption
We decrypt the message with our secret key, (s, N)
Cracking our code is as hard as deriving s from (p, N)
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RSA: how secure is it
Anyone can crack our coded messages bymathematically deriving s from (p, N), which ispossible ….. but …
Public Key encryption
If N is very large, then finding its factors(i.e. x and y, from which we get p) takes a verylong time … too long to make it worth while.
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RSA: one way to crack it
Quantum computers can simultaneously testall possible factors …but …
So far, only 5-qubit quantum machines havebeen achieved … and …
We can use quantum computers to make newencryption schemes.
Public Key encryption
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Instead of encoding the information …
… hide it!
Bury our bits in image files in a way that no one can see them, or in audio files in a way no one can hear them.
Demo in the S Block foyer on state-of-the-art steganography research, by Kathryn Hempstalk
Steganography