FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Calculation of random pairs of primes whose product lies in a given short interval |
Bykovskii V.A. |
2020, issue 2, P. 150–154 DOI: https://doi.org/10.47910/FEMJ202016 |
Abstract |
| The paper proposes heuristic algorithms for constructing pairs of random primes, the product of which lies in a given interval $ \left (\Delta, \, \Delta + \delta \right). $ One algorithm refers to the case $ \delta = \sqrt {\Delta }, $ and the second to $ \delta = 30 \Delta^{1/3}. $ They allow in the well-known RSA cryptosystem to choose shorter public keys (twice for the first algorithm and three times for the second). |
Keywords: Number theory, cryptography, RSA cryptosystem |
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References |
| [1] Rivest R. L., Shamir A., Adleman L., “Method for Obtaining Digital Signatures and Public-Key Cryptosystems”, Commun. ACM, 21:2, (1978), 120–126. [2] Huxley M. N., “On the di?erence between consecutive primes”, Invent. math., 15, (1972), 164–170. |