Encrypt & Check

Encrypt One Integer

RSA encryption is modular exponentiation with the public exponent and modulus. The ladder exposes each exact row for one tiny message integer.

highlighted = computed this step

Why encryption is modular exponentiation

RSA encryption raises one message integer to the public exponent and reduces modulo n. The ladder shows every square and multiply row instead of hiding the power.

c=me mod nc=m^e\bmod n
Encrypt one integerThe modular exponentiation ladder is recomputed from exact RSA inputs.Encrypt one integer - 7^3 mod 55stepbitpriorsquaremultiplyresult011177117491313

Use the public key

The message integer is 7, the public exponent is 3, and the modulus is 55.

m=7,e=3,n=55m=7,\quad e=3,\quad n=55
Encrypt one integerThe modular exponentiation ladder is recomputed from exact RSA inputs.Encrypt one integer - 7^3 mod 55stepbitpriorsquaremultiplyresult011177117491313

Read the ciphertext

The recomputed final ladder result is ciphertext 13. Anyone with n and e can do this operation.

73 mod 55=137^{3}\bmod{}55=13
Encrypt one integerThe modular exponentiation ladder is recomputed from exact RSA inputs.Encrypt one integer - 7^3 mod 55stepbitpriorsquaremultiplyresult011177117491313

Summary

Encryption maps message 7 to ciphertext 13. Exact arithmetic on deliberately tiny toy keys; real RSA uses 2048+ bit primes with padding, and timing/side-channels are not modeled here.

c=13c=13
Encrypt one integerThe modular exponentiation ladder is recomputed from exact RSA inputs.Encrypt one integer - 7^3 mod 55stepbitpriorsquaremultiplyresult011177117491313