The Rabin cryptosystem revisited

The Rabin public-key cryptosystem is revisited with a focus on the problem of identifying the encrypted message unambiguously for any pair of primes. In particular, a deterministic scheme using quartic reciprocity is described that works for primes congruent 5 modulo 8, a case that was still open. Both theoretical and practical solutions are presented. The Rabin signature is also reconsidered and a deterministic padding mechanism is proposed.Comment: minor review + introduction of a deterministic scheme using quartic reciprocity that works for primes congruent 5 modulo

Approximate Two-Party Privacy-Preserving String Matching with Linear Complexity

Consider two parties who want to compare their strings, e.g., genomes, but do not want to reveal them to each other. We present a system for privacy-preserving matching of strings, which differs from existing systems by providing a deterministic approximation instead of an exact distance. It is efficient (linear complexity), non-interactive and does not involve a third party which makes it particularly suitable for cloud computing. We extend our protocol, such that it mitigates iterated differential attacks proposed by Goodrich. Further an implementation of the system is evaluated and compared against current privacy-preserving string matching algorithms.Comment: 6 pages, 4 figure

Cryptography from tensor problems

We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler

Identification of Quasi-Stationary Dynamic Objects with the Use of Derivative Disproportion Functions

This paper presents an algorithm for designing a cryptographic system, in which the derivative disproportion functions (key functions) are used. This cryptographic system is used for an operative identification of a differential equation describing the movement of quasi-stationary objects. The symbols to be transmitted are encrypted by the sum of at least two of these functions combined with random coefficients. A new algorithm is proposed for decoding the received messages making use of important properties of the derivative disproportion functions

Nonquadratic variation of the Blum-Blum-Shub Pseudorandom Number Generator

Cryptography is essential for secure online communications. Many different types of ciphers are implemented in modern-day cryptography, but they all have one common factor. All ciphers require a source of randomness, which makes them unpre-dictable. One such source of this randomness is a random number generator. This thesis focuses on Pseudorandom Number Generators (PRNG), specifically, a PRNG called Blum-Blum-Shub (BBS). In this thesis, we make two modifications to BBS, and test our modified generators for randomness using the National Institute of Standards and Technology (NIST) tests. The original BBS is a quadratic generator that generates bits based on the output of squaring terms in a sequence. The first modification replaces the quadratic generator with a cubic generator. The second modification generates bits faster by using more bits per iteration. Data collected in this thesis suggests that the cubic modification performs just as well as the original generator. In addition, data from this thesis suggests that taking more bits per iteration can speed up this process while retaining randomness. In addition, we propose a new cryptosystem based upon the modification of the BBS PRNG introduced in this thesis.http://archive.org/details/nonquadraticvari1094550570Second Lieutenant, United States ArmyApproved for public release; distribution is unlimited

Computational Indistinguishability between Quantum States and Its Cryptographic Application

We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is "secure" against any polynomial-time quantum adversary. Our problem, QSCDff, is to distinguish between two types of random coset states with a hidden permutation over the symmetric group of finite degree. This naturally generalizes the commonly-used distinction problem between two probability distributions in computational cryptography. As our major contribution, we show that QSCDff has three properties of cryptographic interest: (i) QSCDff has a trapdoor; (ii) the average-case hardness of QSCDff coincides with its worst-case hardness; and (iii) QSCDff is computationally at least as hard as the graph automorphism problem in the worst case. These cryptographic properties enable us to construct a quantum public-key cryptosystem, which is likely to withstand any chosen plaintext attack of a polynomial-time quantum adversary. We further discuss a generalization of QSCDff, called QSCDcyc, and introduce a multi-bit encryption scheme that relies on similar cryptographic properties of QSCDcyc.Comment: 24 pages, 2 figures. We improved presentation, and added more detail proofs and follow-up of recent wor