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DES uses 16 rounds of feistel networks but not considered secure . Where Luby Rackoff constructions which are inspired by DES its proven by Patarin that 7 rounds is secure .

Is there a relation between number of rounds in DES and patarin's results ?

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I believe that result is just about indistinguishability under a chosen plaintext attack, it may not extend to other security properties required by block ciphers. Additionally, it makes the false assumption that F is randomly chosen, but in reality it depends on the round keys, and thus the key schedule is very important. –  Richie Frame Nov 9 '13 at 8:59
    
@RichieFrame any good references on what other properties are required by block cipher apart from CPA ? –  sashank Nov 9 '13 at 15:45
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Luby rackoff results are based on assuming the Round Function to be Secure Pseudo Random Functions. Where as the round functions of DES are not that secure enough which needs more rounds (Triple DES needs 48 rounds )

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