## Advances in Cryptology - CRYPTO '88: ProceedingsThe papers in this volume were presented at the CRYPTO '88 conference on theory and applications of cryptography, held in Santa Barbara, California, August 21-25, 1988. The papers were chosen for their perceived originality and often represent preliminary reports on continuing reserach. The main sections deal with the following topics: Zero-Knowledge, Number Theory, Pseudorandomness, Signatures, Complexity, Protocols, Security, Cryptoanalysis. As such, they will give the committed reader a unique insight into the very latest developments in the field. |

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### Contents

Weakening Security Assumptions and Oblivious Transfer | 2 |

Limits on the Provable Consequences of OneWay Permutations | 8 |

Generalized Secret Sharing and Monotone Functions | 27 |

Copyright | |

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### Common terms and phrases

abuse-free algorithm Alice assume assumption attack bits boolean Boolean circuit Chaum chooses chosen ciphertext coin complexity Computer Science construction controller CRYPTO cryptographic cryptosystem decryption defined definition denote digital signature discrete logarithm error Ethernet example exists factor finite fulfills the SAC given Goldreich Goldwasser IEEE input integer interactive proof system iteration Lemma length linear matrix Micali modulo node oblivious transfer one-way function one-way permutation oracle output pair participants perfect zero-knowledge pieces of information plaintext polynomial-time possible prime private pieces probabilistic encryption probabilistic polynomial probability space Proc protocol prove pseudo-random public key quadratic residues random number randomly result satisfies SECC scheme secret key secret sharing sends sequence Shamir shared secret schemes signature scheme smart card solve step string subset tape Theorem Theory threshold scheme transformation trapdoor trapdoor functions verifier viruses zero zero-knowledge proof