crypto8_new

crypto8_new - CIS 5371 Cryptography 8 Encryption-Asymmetric...

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CIS 5371 Cryptography 8. Encryption -- symmetric Techniques Asymmetric Techniques
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extbook encryption algorithms Textbook encryption algorithms this chapter security (confidentiality) is considered In this chapter, security (confidentiality) is considered in the following sense: All-or-nothing secrecy . Given the ciphertext y=E ( x ), K of plaintext x , the task of the attacker is to retrieve the whole of x . Otherwise he fails. hat is the adversary either gets r nothing – That is, the adversary either gets x or nothing. – Nothing means that the attacker does not have any knowledge about x before of after the attack. Passive attacker. The attacker does not manipulate or modify the ciphertext using data she/he has in possession and does not ask a key owner to provide encryption or yp y p decryption services .
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Textbook encryption algorithms All-or-nothing secrecy . applications plaintext data is likely to have In applications, plaintext data is likely to have partial information known to the attacker. assive attacker Passive attacker. One should never expect an attacker to be so ice and remain passive nice and remain passive.
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Textbook encryption algorithms security paradigms We regard the security offered by the All-or-nothing secrecy , and the assive attacker Passive attacker as models for our security paradigms .
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Public Key Cryptography li b Alice Bob Alice and Bob want to exchange a private key in public.
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ublic Key Cryptography Public Key Cryptography The Diffie-Hellman protocol Let p is a large prime and g Z * an element p that generates a group of large prime order. he order f a factor of – The order q of g is a factor of p- 1 . – If q = p- 1, then we say that g is a generator of Z p * – Usually we take q to be a prime.
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ublic Key Cryptography Public Key Cryptography The Diffie-Hellman protocol Alice g a mod p Bob g b mod p he private key is: od The private key is: g ab mod p where p is a prime and g is a generator of Z p *
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Example p = 43, g = 3 , • Alice and Bob share ( p,g ) = (43,3). • Alice picks at random her secret exponent a = 8 • Alice sends Bob: 3 8 25 (mod 43). • Bob picks at random his secret exponent b = 37 • Bob sends Alice: 3 37 20 (mod 43). • The secret key agreed between the two is: 9 20 8 25 37 (mod 43).
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an- - e- iddle attack Man in the middle attack • Alice picks a U Z p * and sends Malice (“Bob”): g a (mod p ) • Malice (“Alice”) picks m Z * and sends Bob: g m (mod p ) () p p ( • Bob picks b U Z p * and sends Malice (“Bob) Bob: g b (mod p ) • Malice (“Bob”) sends Alice: g m (mod p ) •A l i ce computes: m a mod ce co pu es: k 1 ( g ) (o d p ) • Bob computes: k 2 ( g m ) b (mod p )
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he Diffie- ellman Problem The Diffie Hellman Problem he Computational Diffie- ellman Problem -- DH The Computational Diffie Hellman Problem CDH • INPUT – The description of a finite cyclic group G of order q (say Z q * ) – A generator element g of G g a , g a G , for some integers 0 < a,b < q .
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This note was uploaded on 12/11/2011 for the course CIS 5371 taught by Professor Mascagni during the Fall '11 term at FSU.

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crypto8_new - CIS 5371 Cryptography 8 Encryption-Asymmetric...

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