Quelle: https://www.cryer.co.uk/glossary/r/rsa/mathematical_guts_of_rsa_encryption.html
The RSA algorithm was invented in 1978 by Ron Rivest, Adi Shamir, and Leonard Adleman.
Here's the relatively easy to understand math behind RSA public key encryption.
Your public key is the pair (PQ, E). Your private key is the number D (reveal it to no one). The product PQ is the modulus (often called N in the literature). E is the public exponent. D is the secret exponent.
You can publish your public key freely, because there are no known easy methods of calculating D, P, or Q given only (PQ, E) (your public key). P and Q need to be sufficiently long (>2048 bits), for this method to be considered secure.
Here is an example of RSA encryption:
P = 61 <- first prime number (destroy this after computing E and D) Q = 53 <- second prime number (destroy this after computing E and D) PQ = 3233 <- modulus (give this to others) E = 17 <- public exponent (give this to others) D = 2753 <- private exponent (keep this secret!) Your public key is (E,PQ). Your private key is D. The encryption function is: encrypt(T) = (T^E) mod PQ = (T^17) mod 3233 The decryption function is: decrypt(C) = (C^D) mod PQ = (C^2753) mod 3233 To encrypt the plaintext value 123, do this: encrypt(123) = (123^17) mod 3233 = 337587917446653715596592958817679803 mod 3233 = 855 To decrypt the ciphertext value 855, do this: decrypt(855) = (855^2753) mod 3233 = 123 One way to compute the value of 855^2753 mod 3233 is like this: 2753 = 101011000001 base 2, therefore 2753 = 1 + 2^6 + 2^7 + 2^9 + 2^11 = 1 + 64 + 128 + 512 + 2048 Consider this table of powers of 855: 855^1 = 855 (mod 3233) 855^2 = 367 (mod 3233) 855^4 = 367^2 (mod 3233) = 2136 (mod 3233) 855^8 = 2136^2 (mod 3233) = 733 (mod 3233) 855^16 = 733^2 (mod 3233) = 611 (mod 3233) 855^32 = 611^2 (mod 3233) = 1526 (mod 3233) 855^64 = 1526^2 (mod 3233) = 916 (mod 3233) 855^128 = 916^2 (mod 3233) = 1709 (mod 3233) 855^256 = 1709^2 (mod 3233) = 1282 (mod 3233) 855^512 = 1282^2 (mod 3233) = 1160 (mod 3233) 855^1024 = 1160^2 (mod 3233) = 672 (mod 3233) 855^2048 = 672^2 (mod 3233) = 2197 (mod 3233) Given the above, we know this: 855^2753 (mod 3233) = 855^(1 + 64 + 128 + 512 + 2048) (mod 3233) = 855^1 * 855^64 * 855^128 * 855^512 * 855^2048 (mod 3233) = 855 * 916 * 1709 * 1160 * 2197 (mod 3233) = 794 * 1709 * 1160 * 2197 (mod 3233) = 2319 * 1160 * 2197 (mod 3233) = 184 * 2197 (mod 3233) = 123 (mod 3233) = 123 If you have a computer program (such as the "bc" utility that comes with Linux), you can compute 855^2753 mod 3233 directly, like this: 855^2753 mod 3233 = 50432888958416068734422899127394466631453878360035509315554967564501 05562861208255997874424542811005438349865428933638493024645144150785 17209179665478263530709963803538732650089668607477182974582295034295 04079035818459409563779385865989368838083602840132509768620766977396 67533250542826093475735137988063256482639334453092594385562429233017 51977190016924916912809150596019178760171349725439279215696701789902 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305946326827861270203356980346143245697021484375 mod 3233 = 123