introduction to cryptography multimedia security
TRANSCRIPT
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Introduction to Cryptography
Multimedia Security
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Outline
• Cryptography basics
• Cryptographic systems
• Conventional Cryptosystems
• DES
• AES
• Diffie Hellman’s public-key cryptosystem
• RSA
• Multimedia encryption
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Cryptography
• Cryptography is the science of secret writing.– A cipher is a secret method of writing, where by
plaintext (cleartext) is transformed into a ciphertext. – The process of transforming plaintext into ciphertext is
called encipherment or encryption. – The reverse process of transforming ciphertext into
plaintext is called decipherment or decryption. – Encryption and decryption are controlled by
cryptographic keys.
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Secret Writing
Encryption
Decryption
Plaintext Ciphertext Key
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Attacks against Ciphers
• Cryptanalysis is the science and study of methods of breaking ciphers.
• A cipher is breakable if it is possible to determine the plaintext or key from the ciphertext, or to determine the key from plaintext-ciphertext pairs.
• Attacks– Ciphertext-only attack– Known-plaintext attack– Chosen-plaintext attack
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Cryptographic Systems
• A cryptographic system has five components:– A plaintext message space, M– A ciphertext message space, C– A key space, K– A familiy of enciphering transformations
Ek:MC
– A family of deciphering transformations
Dk:CM
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Cryptographic Systems (cont.)
M Ek C Dk M
plaintext plaintextciphertext
Dk(Ek(m))=m ,for a key k
• Cryptosystem requirements:– Efficient enciphering/deciphering– Systems must be easy to use– The security of the system depends only
on the keys, not the secrecy of E or D
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Secure Cipher
• Unconditionally secure– A cipher is unconditionally secure if no matter
how much ciphertext is intercepted, there is not enough information in the ciphertext to determine the plaintext uniquely.
• Computationally secure– A cipher is computationally infeasible to
break.
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Secrecy Requirements
• It should be computationally infeasible to systematically determine the deciphering transformation Dk from intercepted c, even if corresponding m is known.
• It should be computationally infeasible to systematically determine m from intercepted c.
Ek C Dk MM
Mdisallowed
protected
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Authenticity requirements
• It should be computationally infeasible to systematically determine the enciphering transformation given c, even if corresponding m is known.
• It should be computationally infeasible to systematically find c’ such that Dk(c’) is a valid plaintext in M.
Ek C Dk MM
Mdisallowed
protected
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Key-distribution cryptosystem
• Encrypting &decrypting are closely tied together.• The sender and the receiver must agree on the use of a
common key before any message transmission takes place.
• A safe communication channel must exist between sender and receiver
Message Source
PEncryption
CDecryption
PReceiver
Secure key transmission
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Public-key Cryptosystem
In a public key cryptosystem, each participant is assigned a pair of inverse keys E and D.
• Different functions are used for enciphering and deciphering, one of the two keys can be made public, provided that it is impossible to generate one key from the other.
• E can be made public, but D is kept secret.• The normal key transmission between senders and receivers can be
replaced by an open directory of enciphering keys, containing the keys E for all participants.
Message Source
PEncryption
CDecryption
PReceiver
Key source 1Ek
Key source 2Dk
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Using Public-Key Cryptosystem to Transfer Messages Secretly
• When a person A wishes to send a message to a person B, the receiver’s enciphering key EB is
used to generate the ciphertext EB(m). Since the
key EB is freely available, anyone can then
encipher a message destined for B. However, only the receivers B with access to the decipher key DB can regenerate the original text by
performing the inverse transform DB(EB(m)).
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Most Common Solution
• Combine symmetric systems with public key cryptography.
• The plaintext is encrypted using a fast symmetric key scheme.
• Only the secret key used for symmetric encryption is encrypted with the slow public key scheme.
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Digital Signature
• Guaranteeing authenticity.• Let B be the recipient of a message m signed
by A. Then A’s signature must satisfy:1. B must be able to validate A’s signature on m.
2. It must be impossible to forge A’s signature.
3. If A disavow signing a message, a third party must be able to resolve the distribute.
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Using Public-key Systems to Implement Digital Signatures
1. A signs m by computing c=DA(m)2. B validates A’s signature by checking
EA(c) =m3. A dispute can be judged by checking
whether EA(c) restores M in the same ways as B.
• Requirements:– Dk(Ek(m))=Ek(Dk(m))=m
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Secrecy and Authenticity in A Public-Key System
• EA(DB(C))=EA(DB(EB(DA(M))))
=EA(DA(M))
=M
DA(m)=S EB(S)=C DB(C)=S EA(S)=mm m
Transformations applied by sender
Transformations applied by receiver
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Reference
• Cryptography and Data Security, D. Elizabeth and R. Denning, Purdue University, 1998
• FAQ about Today’s Cryptography, RSA Laboratory, (found in www.rsa.com)
• The reference listed in course handout.
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Conventional Cryptosystems
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Conventional Cryptosystems
• Using substitution transform and permutation transform– Substitution Ciphers– Running Key Ciphers– Permutation Ciphers– Stream Ciphers– Product Cipher
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Substitution Ciphers
• Replace bits, characters, or blocks of characters with substitutes.– Example: Caesar cipher
• which shift each letter in the English forward by K positions (shifts past Z cycle back to A)
• A simple substitution cipher is easy to solve by performing a frequency analysis.
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Running Key Ciphers
• The security of a substitution cipher generally increases with the key length. In a running key cipher, the key length is equal to the plaintext message.(not using a fixed key alphabet) – E.g. use the text in a book as the key sequence.
• The cipher may be breakable by Friedman’s method based on the observation that both plaintext and key letters are high frequency ones in natural language.
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Permutation Ciphers
• Rearrange bits or characters in the data.
• What is the key?• Attacks: frequency analysis of characters.
INFORMATION TECHNIQUES FOR IPR
I R I T N E R N O M T O E H I U S O I R F A N C Q F P
IRITNERNOMTOEHIUSOIRFANCQFP
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Stream Ciphers
• A random number generator (typically LFSR) may be used to generate a stream of key characters, each character of the key being added to a character of the input stream to produce an output character.
⊕ Cipher stream
Message stream
Key stream⊕
Shift register
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Product Cipher
• A product cipher is the composition of functions F1,…,Ft, where each Fi may be a substitution or permutation.
• Examples of product ciphers – DES
P P
S
S
S
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DES
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Data Encryption Standard (DES)
• The National Bureau of Standards announced DES to be used in unclassified U.S. Government applications.
• DES enciphers 64-bit blocks with a 56-bit key.
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DES
• An input block T is first transposed under an initial permutation IP, giving T0=IP(T).
– E.g. t1t2…t64 t58t50…t7
• Then T0 is passed through 16 iterations of function f.
• Finally, it is transposed under the inverse permutation IP-1 to give the final result.
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DES (cont.)
• Let Ti denote the result of the i-th iteration, and let Li and Ri denote the left and right halves of Ti. Then
Li=Ri-1
Ri=Li-1 f(R⊕ i-1, Ki)where is the exclusive-or operation and K ⊕is a 48-bit key.
• After the last iteration, the left and right halves are not changed , but instead passed to IP-1.
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DES (cont.)
• Calculate the function F(Ri-1, Ki):1. Using bit-selection Table E to
expand 32-bit Ri-1 to a 48-bit block E(Ri-1). (Similar to permutation)
2. Calculate the exclusive-or of E(Ri-1) and Ki. Then break the result into 8 6-bit blocks B1, …, B8.
3. Use each 6-bit Bj b1b2b3b4b5b6 as input to a selection (substitution) and return a 4-bit block Sj(Bj).
b1b6row
b2b3b4b5column
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DES (cont.)
• Key calculation– Each iteration i uses a different 48-bit
key Ki derived from the initial key K, which is input as a 64-bit block with 8 parity bits in positions 8, 16, …, 64.
– PC1 discards the parity bits and transposes the remaining 56-bit bits to obtain PC1(K).
– PC1(K) is then split to C and D of 28-bits each, and circular shifted by LS.
Ci=LSi(Ci-1), Di=LSi (Di-1)– Ki=PC2(CiDi).
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DES (cont.)
• Deciphering – The same algorithm is used, except that the
order of key for each iteration is reversed. E.g. K16 is used in 1st
iteration, K15 is used in 2nd iteration….
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Disputes about DES
• 56-bit key length should be doubled?– A special purpose machine containing a million LSI
chips could try 256 keys in 1 day. The cost of this machine is about $ 20 million. Amortized over 5 years, the cost per day would be $10,000.
– The same level of security could be obtained using multiple encryption scheme.
• The S-box may have hidden trapdoors.– The analysis is still classified.
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Triple DES
• Triple DES is a block cipher formed from the DES cipher by using it three times.
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AES
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Advanced Encryption Standard (AES)
• A block cipher adopted as an encryption standard by the U.S. Government.
• AES enciphers 128-bit blocks with a 128-bit, 192-bit, or 256-bit key.
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AES
• Initial Round– AddRoundKey
• Rounds– SubBytes– ShiftRows – MixColumns – AddRoundKey
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AES (cont.)
• SubBytes
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AES (cont.)
• ShiftRows
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AES (cont.)
• MixColumns
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AES (cont.)
• AddRoundKey
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Security
• AES has 10 rounds for 128-bit keys, 12 rounds for 192-bit keys, and 14 rounds for 256-bit keys.
• By 2006, the best known attacks were on 7 rounds for 128-bit keys, 8 rounds for 192-bit keys, and 9 rounds for 256-bit keys.
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Diffie Hellman’s public-key cryptosystem
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Cipher Based on Computationally Difficult Problems
• One-way function: C=f(P)
– exponentiation and logarithm– multiplication/factoring – review of number theory
• NP-complete problems– A systematic deterministic solution is likely to require
exponential time in the number of inputs.
f: computationally simple
f-1:computationally difficult except in special cases when supplementary information (keys) is available
P C
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Diffie Hellman’s public-key cryptosystem
• Each user i in the system has a pair of keys X i and Yi, where
Yi=αXi mod q , 1 X≦ i q-1, 1 α q-1, q: prime number≦ ≦ ≦
Xi is kept secret, but Yi is made public.• Sender i generates the key
Kij= YjXi mod q = αXiXj mod q
from receiver j’s public key Yj and his own private key Xi.
• Receiver j obtains Kij similarly from Yi and Xj.
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Example
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Security of Diffie Hellman’s System
• To generate the key Kij, one of the private keys Xi or Xj must be known.
• To generate the Kij from Yi and Yj, a form of logarithm below must be computed:Kij=Yi
(log Yj) mod q
which is computationally difficult.
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RSA
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The RSA Algorithm
• Each user selects two large prime numbers P and Q at random, and multiplies them to obtain N=P•Q. – N should be about 200 digits long and can be
made public – P and Q are kept secret.
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The RSA Algorithm (cont.)
• Using P and Q, the user computes the Euler totient function Φ(N), representing the number of positive integers relatively prime to N. – Φ(N)=Φ(P)Φ(Q) = (P-1) (Q-1)
• The user then chooses a quantity E less than N and relatively prime to Φ(N). The quantity E is made public.
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The RSA Algorithm (cont.)
• Given a message M to be enciphered, M is broken down into a sequence of quantities M1, M2, …, Mp, where each component Mi is
represented by an integer between 0 and N-1. The enciphering is now done separately on each block Mi using the public information E
and N to generate a cryptogram Ci as
– Ci=MiE mod N
– at most 2 . Log2(N) multiplications are required
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The RSA Algorithm (cont.)
• Using the secret informationΦ(N), the user can easily compute a quantity D such that E . D=1 modΦ(N) (deciphering key). I– E . D=1 modΦ(N)=KΦ(N)+1
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The RSA Algorithm (cont.)
• By Fermat’s theorem: MΦ(N)mod N =1 mod N, or MKΦ(N)+1 mod N =M mod N.
• Deciphering procedure: Ci
D mod N
= MiED mod N
= MiKΦ(N)+1 mod N
= Mi mod N
= Mi
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Example
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Example
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Using RSA
• Suppose user A want to send a message m to user B. User A creates the ciphertext c by c = mE
mod N, where E and N are user B’s public key. • User A sends c to user B.• User B decrypts c by calculate m = cD mod N.
The relation between D and E ensures that B correctly recovers m.
• Since only B knows D, only B can decrypt the message.
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Attacks against RSA
• Attacks to recover all messages for a given key – Factor the public modulus N to P and Q.With
P,Q, and E, the attacker can easily compute D.
• Attacks to recover a message– Guessed-plaintext attacks.– This attacks can be defeated by appending
random bits.
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Security of RSA
• The size of a key in the RSA algorithm typically refers to the size of the modulus N. The two primes P and Q should be roughly equal length.
• The longer the key size, the greater the security, but also the slower the RSA algorithm.
• The 512-bit RSA-155 was factored in seven month during 1999.
• The RSA lab currently recommends key sizes of 1024 bits for corporate use.
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Multimedia Encryption
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Multimedia Encryption
• Even the fastest symmetric schemes are computationally expensive for many real-time video and audio data.
• Exploit the format-specific properties of many standard video and audio formats in order to achieve the desired speed and enable real-time streaming.
• Carefully compare the cost of the multimedia information to be protected and the cost of the protection itself.
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Video Encryption Techniques
• Video Scrambling– The product of an immediate industrial need
by cable companies.– Seriously lack security and are extremely
easy to crack using modern computers.
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Video Encryption Techniques (Cont.)
• Selective Video Encryption– SECMPEG by Meyer and Gadegast, 1995
• Headers.• Most relevant parts of the I-blocks.• All I-frames and all I-blocks.• Whole MPEG-1 sequence.
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Video Encryption Techniques (Cont.)
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Conclusion
• Further research should be directed toward developing substantially secure encryption schemes for high bit rate and high-quality audiovisual data.
• The experts should investigate the security aspects of the newly proposed multimedia encryption techniques.