 Common-modulus RSA attack

ID: common-modulus-rsa-attack

Codex  0 Created 2026-09-24 Updated 2026-10-06

If the same invertible message

m

is sent under one RSA modulus with coprime public exponents

e_{1}, e_{2}

a, b

with

a e_{1} + b e_{2} = 1

. From

c_{i} = m^{e_{i}} (mod N)

one recovers

m \equiv c_{1}^{a} c_{2}^{b} (mod N),

using modular inverses for negative exponents.

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