A New Idea for RSA Backdoors
Department of Civil Engineering and Computer Science Engineering (DICII), University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy
Cryptography 2023, 7(3), 45; https://doi.org/10.3390/cryptography7030045
Submission received: 19 July 2023
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Revised: 16 September 2023
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Accepted: 18 September 2023
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Published: 21 September 2023
Abstract
This article proposes a new method to inject backdoors in RSA (the public-key cryptosystem invented by Rivest, Shamir, and Adleman) and other cryptographic primitives based on the integer factorization problem for balanced semi-primes. The method relies on mathematical congruences among the factors of the semi-primes based on a large prime number, which acts as a “designer key” or “escrow key”. In particular, two different backdoors are proposed, one targeting a single semi-prime and the other one a pair of semi-primes. This article also describes the results of tests performed on a SageMath implementation of the backdoors.
Keywords:
RSA; backdoor; escrow key; implicit factorization problem; integer factorization
Share and Cite
MDPI and ACS Style
Cesati, M. A New Idea for RSA Backdoors. Cryptography 2023, 7, 45. https://doi.org/10.3390/cryptography7030045
AMA Style
Cesati M. A New Idea for RSA Backdoors. Cryptography. 2023; 7(3):45. https://doi.org/10.3390/cryptography7030045
Chicago/Turabian StyleCesati, Marco. 2023. "A New Idea for RSA Backdoors" Cryptography 7, no. 3: 45. https://doi.org/10.3390/cryptography7030045
APA StyleCesati, M. (2023). A New Idea for RSA Backdoors. Cryptography, 7(3), 45. https://doi.org/10.3390/cryptography7030045
