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By Maria Isabel Vasco, Spyros Magliveras, Rainer Steinwandt

Crew theoretic difficulties seem to be the main promising resource of tough computational difficulties for deploying new cryptographic buildings. This reference specializes in the specifics of utilizing nonabelian teams within the box of cryptography. It presents an creation to cryptography (mostly uneven) with a spotlight on staff theoretic buildings, making it the 1st ebook to exploit this strategy. The authors contain all the wanted cryptographic and staff theoretic suggestions. they provide routines on the finish of every bankruptcy, chosen ideas behind the publication, and proposals for scholar tasks that require using the pc or computing device algebra platforms.

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Five IND-CCA safeguard with an Abelian workforce: RSA-OAEP four. 6 One-way services from non-Abelian teams? . . . . . . four. 7 precis and extra studying . . . . . . . . . . . . . . 37 . . . . . . . . . . . . . . . . . . . . . 39 39 forty two fifty three fifty seven sixty two sixty four sixty eight vii viii Contents four. eight workouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . five Public-key encryption within the general version five. 1 The Cramer–Shoup encryption scheme from 1998 five. 2 Going past: instruments . . . . . . . . . . . . . . . . five. 2. 1 Projective hash households . . . . . . . . . . . five. 2. 2 Subset club difficulties . . . . . . . . five. 2. three Hash evidence structures . . . . . . . . . . . . . . five. three normal Cramer–Shoup encryption scheme . . . . five. four A concrete instantiation . . . . . . . . . . . . . . . five. five Projective hash households from (non-Abelian) teams five. five. 1 team motion structures . . . . . . . . . . . . five. five. 2 staff motion projective hash households . . . five. 6 precis and additional interpreting . . . . . . . . . . . five. 7 workouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Public-key encryption utilizing endless teams 6. 1 The be aware challenge in finitely awarded teams . . . . . 6. 1. 1 The encryption scheme of Wagner and Magyarik 6. 1. 2 Polly Cracker . . . . . . . . . . . . . . . . . . . . 6. 1. three A successor of the Wagner–Magyarik scheme . . 6. 2 utilizing a bunch that's not finitely presentable? . . . . . 6. three Braid teams in cryptography . . . . . . . . . . . . . . . 6. three. 1 fundamentals on braid teams . . . . . . . . . . . . . . . 6. three. 2 a few computational difficulties within the braid crew 6. four precis and additional analyzing . . . . . . . . . . . . . . 6. five routines . . . . . . . . . . . . . . . . . . . . . . . . . . III . . . . . . . . . . . . . . . . . . . . . . . . seventy three seventy three eighty eighty eighty three eighty four eighty five 87 88 88 ninety two ninety four ninety five . . . . . . . . . . . . . . Bn . . . . . . . . . . . . . . ninety seven ninety seven ninety eight 102 103 a hundred and five 108 108 111 117 118 . . . . . . . . . . . . Secret-Key Encryption 7 Block ciphers 7. 1 complicated Encryption usual . . . . . . . . . . 7. 1. 1 Specifying the around functionality . . . . . . . . 7. 1. 2 Key agenda . . . . . . . . . . . . . . . . . 7. 1. three Encryption and decryption with AES . . . 7. 2 information Encryption average . . . . . . . . . . . . . 7. 2. 1 common constitution of DES: A Feistel cipher . 7. 2. 2 around functionality of DES . . . . . . . . . . . 7. 2. three Key agenda . . . . . . . . . . . . . . . . . 7. three Permutation crew Mappings . . . . . . . . . . . 7. four Modes of operation . . . . . . . . . . . . . . . . . 7. four. 1 digital codebook (ECB) mode . . . . . . 7. four. 2 Cipher block chaining (CBC) mode . . . . . 7. four. three Cipher suggestions (CFB) mode . . . . . . . . 7. four. four Output suggestions (OFB) mode . . . . . . . sixty nine 121 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 124 124 126 126 129 129 132 134 a hundred thirty five 137 137 138 138 139 ix Contents 7. five 7. 6 7. four. five Counter (CTR) mode . . . . . . . . . . . . . . . . . . precis and extra studying . . . . . . . . . . . . . . . . . workouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . one hundred forty 141 142 eight Cryptographic hash services and message authentication codes a hundred forty five eight. 1 Cryptographic hash services . . . . . . . . . . . . . . . . . . a hundred forty five eight. 2 Deriving a hash functionality from a block cipher . . . . . . . . . 147 eight. three Cayley hash features . . . . . . . . . . . . . . . . . . . . . . 149 eight. four Message authentication codes . . . . . . . . . . . . . . . . . . 151 eight. four. 1 Keyed-Hash Message Authentication Code . . . . . . . 152 eight. four. 2 Cipher-based Message Authentication Code . . . . . . 153 eight. five precis and additional examining . . . . . . . . . . . . . . . . . 154 eight. 6 routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . one hundred fifty five IV different Cryptographic buildings 157 nine Key institution protocols nine.

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