Definition ∞ RSA assumptions are mathematical hypotheses that underpin the security of the RSA cryptographic algorithm. These assumptions assert the computational difficulty of certain number-theoretic problems, specifically the factoring of large composite numbers and the RSA problem, which involves finding the nth root modulo a composite number. The security of RSA, a widely used public-key cryptosystem, relies on the belief that these problems cannot be solved efficiently by classical computers. These foundational assumptions are critical for the trustworthiness of digital signatures and secure communication.
Context ∞ RSA assumptions are fundamental to much of modern cryptography, though in the digital asset space, elliptic curve cryptography (ECC) is more prevalent for signatures. Discussions sometimes touch upon the long-term security of current cryptographic standards against advancements in quantum computing, which could potentially break these assumptions. While not directly crypto-specific, the integrity of such mathematical underpinnings remains relevant for the broader digital security landscape and potential future protocol designs.
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