## Two issues in public key cryptography: RSA bit security and a new knapsack type systemThis book explores public key cryptographic systems, first investigating the question of cryptographic security of bits in the RSA encryption and then constructing a new knapsack type public key cryptosystem, based on arithmetic in finite fields.In Part I, two problems involving the RSA encryption of a message are proved to be equivalent. This equivalence implies that an adversary, given the ciphertext, can't do better than guessing unless s/he can break the RSA code. The results generated by the author's proof indicate that Rabin/RSA encryption can be directly used for pseudo random bit generation.A new knapsack type public key cryptosystem is introduced in Part II, along with a detailed description of its implementation. The system is based on a novel application of arithmetic in finite fields, following a construction by Bose and Chowla. By choosing appropriate parameters, the density of the resulting knapsack can be controlled. In particular, the density can be made high enough to foil low-density attacks against this new system. At present there are no known attacks capable of breaking the system in a reasonable amount of time.Ben-Zion Chor received his doctorate from MIT where he is currently a Post Doctoral Fellow in the Computer Science Laboratory. Two Issues in Public Key Cryptography: RSA Bit Security and a New Knapsack Type System is a 1985 ACM Distinguished Dissertation. |

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arithmetic bit of r,x bit security Blum Blum integers Boolean predicate Brickell Brute Force Attacks bx]n chapter Chor ciphertext composite number compute construction cryptanalyst degree h discrete logarithms dx-measurement dx]jv dx]n e(n)-oracle efficient En{x encryption function error probability finite fields gcd procedure GF(ph GF{p Given En(x Goldreich Goldwasser guess halfn implementation information rate input integers inverting algorithms inverting RSA iteration Jacobi symbol knapsack elements knapsack-type known Lagarias and Odlyzko Lagarias-Odlyzko lattice least significant bit log2 Low Density Attack Merkle-Hellman Micali mod ph modulo multiplicative outputs pairwise independent parity subroutine partial factorization plaintext Pohlig-Hellman algorithm polynomial-time probabilistic encryption probabilistic polynomial proposed parameters pseudo-random public-key cryptography public-key cryptosystem query the oracle Rabin Rabin encryption reduction relatively prime reliable oracles RSA Bit RSA encryption scheme security result sequence shortest vector simultaneous security special vector success probability thesis uniformly distributed Vazirani and Vazirani wraparound