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Retrieving "Public Key Cryptography" from the archives

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  1. Modular Arithmetic

    Linked via "Public Key Cryptography"

    Applications in Cryptography
    Modular arithmetic is indispensable in modern Public Key Cryptography, particularly systems like RSA. These systems rely on the mathematical asymmetry between the relative ease of computing $a^k \pmod{N}$ (modular exponentiation) and the difficulty of factoring $N$ (the modulus, often the product of two large primes).
    To decrypt a message encrypted with a public exponent $e$, one must calculate the [modular multiplicative inverse](/entries/modular-multiplica…

  2. Quantum Information

    Linked via "public-key cryptography"

    Two foundational quantum algorithms illustrate the power of QI/):
    Shor's Algorithm: Provides an exponential speedup for integer factorization, posing a significant threat to commonly used public-key cryptography systems based on the difficulty of factoring large numbers.
    Grover's Algorithm: Offers a quadratic speedup for [unstructured search problems](/entries/unstructured-search-…