Attacks on RSA

Cryptography · Axiom Academy

Understanding vulnerabilities in RSA cryptosystems and how to defend against them Mathematical attacks exploit weaknesses in RSA parameter selection or the underlying number theory. These attacks target the mathematical foundation of RSA rather than implementation details. 2. Common Modulus & Wiener's Attack Common Modulus Attack: When the same modulus N is used with different public exponents for different users, an attacker can recover plaintext without factoring N. Coppersmith's theorem is a powerful tool that finds small roots of polynomial equations modulo N. It has devastating applications against RSA when partial information about the message or key is known. Stereotyped Messages: If most of the message is known except for a small unknown portion Partial Key Exposure: If an attacker learns some bits of the private key d Related Message Attack: When encrypted messages have a known polynomial relationship Implementation attacks exploit the physical characteristics of cryptographic operations rather than mathematical weaknesses. These side-channel attacks can be devastating even when the mathematics is sound. Timing Attacks: Measure execution time of cryptographic operations. Different values of the private key cause different execution times, revealing key bits. Power Analysis: Monitor power consumption during computation. Simple Power Analysis (SPA) and Differential Power Analysis (DPA) can extract secret keys.

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