PRELIMINARIES Mathematical background Algebraic structures in a nutshell Finite groups Summary and further reading Exercises Basics on complexity Complexity classes Asymptotic notation and examples Summary and further reading Exercises Cryptology: An introduction A short historical overview Historical encryption schemes Public-key cryptography Modern cryptology Summary and further reading Exercises PUBLIC-KEY ENCRYPTION Provable security guarantees Public-key encryption revisited Characterizing secure public-key encryption One-way functions and random oracles The general Bellare-Rogaway construction IND-CCA security with an Abelian group: RSA-OAEP One-way functions from non-Abelian groups? Summary and further reading Exercises Public-key encryption in the standard model The Crame-Shoup encryption scheme from 1998 Going beyond: Tools Projective hash families Subset membership problems Hash proof systems General Cramer-Shoup encryption scheme A concrete instantiation Projective hash families from (non-Abelian) groups Group action systems Group action projective hash families Summary and further reading Exercises Public-key encryption using infinite groups The word problem in finitely presented groups The encryption scheme of Wagner and Magyarik Polly Cracker A successor of the Wagner-Magyarik scheme Using a group that is not finitely presentable? Braid groups in cryptography Basics on braid groups Some computational problems in the braid group Bn Summary and further reading Exercises III SECRET-KEY ENCRYPTION Block ciphers Advanced Encryption Standard Specifying the round function Key schedule Encryption and decryption with AES Data Encryption Standard General structure of DES: A Feistel cipher Round function of DES Key schedule Permutation Group Mappings Modes of operation Electronic codebook (ECB) mode Cipher block chaining (CBC) mode Cipher feedback (CFB) mode Output feedback (OFB) mode Counter (CTR) mode Summary and further reading Exercises Cryptographic hash functions and message authentication codes Cryptographic hash functions Deriving a hash function from a block cipher Cayley hash functions Message authentication codes Keyed-Hash Message Authentication Code Cipher-based Message Authentication Code Summary and further reading Exercises OTHER CRYPTOGRAPHIC CONSTRUCTIONS Key establishment protocols Setting the stage Provable security for key exchange protocols A secure construction Anshel-Anshel-Goldfeld key exchange Braid-based key exchange Constructions over matrix groups Summary and further reading Exercises Signature and identification schemes Definitions and terminology RSA signatures: FDH and PSS Identification schemes Summary and further reading Exercises APPENDIX Solutions to selected exercises Solutions to selected exercises of Part I Solutions to selected exercises of Part II Solutions to selected exercises of Part III Solutions to selected exercises of Part IV References Index ding Exercises Public-key encryption in the standard model The Crame-Shoup encryption scheme from 1998 Going beyond: Tools Projective hash families Subset membership problems Hash proof systems General Cramer-Shoup encryption scheme A concrete instantiation Projective hash families from (non-Abelian) groups Group action systems Group action projective hash families Summary and further reading Exercises Public-key encryption using infinite groups The word problem in finitely presented groups The encryption scheme of Wagner and Magyarik Polly Cracker A successor of the Wagner-Magyarik scheme Using a group that is not finitely presentable? Braid groups in cryptography Basics on braid groups Some computational problems in the braid group Bn Summary and further reading Exercises III SECRET-KEY ENCRYPTION Block ciphers Advanced Encryption Standard Specifying the round function Key schedule Encryption and decryption with AES Data Encryption Standard General structure of DES: A Feistel cipher Round function of DES Key schedule Permutation Group Mappings Modes of operation Electronic codebook (ECB) mode Cipher block chaining (CBC) mode Cipher feedback (CFB) mode Output feedback (OFB) mode Counter (CTR) mode Summary and further reading Exercises Cryptographic hash functions and message authentication codes Cryptographic hash functions Deriving a hash function from a block cipher Cayley hash functions Message authentication codes Keyed-Hash Message Authentication Code Cipher-based Message Authentication Code Summary and further reading Exercises OTHER CRYPTOGRAPHIC CONSTRUCTIONS Key establishment protocols Setting the stage Provable security for key exchange protocols A secure construction Anshel-Anshel-Goldfeld key exchange Braid-based key exchange Constructions over matrix groups Summary and further reading Exercises Signature and identification schemes Definitions and terminology RSA signatures: FDH and PSS Identification schemes Summary and further reading Exercises APPENDIX Solutions to selected exercises Solutions to selected exercises of Part I Solutions to selected exercises of Part II Solutions to selected exercises of Part III Solutions to selected exercises of Part IV References Index me of Wagner and Magyarik Polly Cracker A successor of the Wagner-Magyarik scheme Using a group that is not finitely presentable? Braid groups in cryptography Basics on braid groups Some computational problems in the braid group Bn Summary and further reading Exercises III SECRET-KEY ENCRYPTION Block ciphers Advanced Encryption Standard Specifying the round function Key schedule Encryption and decryption with AES Data Encryption Standard General structure of DES: A Feistel cipher Round function of DES Key schedule Permutation Group Mappings Modes of operation Electronic codebook (ECB) mode Cipher block chaining (CBC) mode Cipher feedback (CFB) mode Output feedback (OFB) mode Counter (CTR) mode Summary and further reading Exercises Cryptographic hash functions and message authentication codes Cryptographic hash functions Deriving a hash function from a block cipher Cayley hash functions Message authentication codes Keyed-Hash Message Authentication Code Cipher-based Message Authentication Code Summary and further reading Exercises OTHER CRYPTOGRAPHIC CONSTRUCTIONS Key establishment protocols Setting the stage Provable security for key exchange protocols A secure construction Anshel-Anshel-Goldfeld key exchange Braid-based key exchange Constructions over matrix groups Summary and further reading Exercises Signature and identification schemes Definitions and terminology RSA.