Visualization RSA algorithm - Encryption - Decryption

Modulo

a

a ∈ Z_c

b

c

Find a, b | a^b mod c = d

d

d = a^b mod c

Find coprime

n

Click to select Z_n

Coprime

All Coprime ∈ U(Z_n)

E * D mod n = 1

E, D ∈ U(Z_n)

Modular Multiplicative Inverse

Click to select Z_p

Z_p

p is prime

E

E ∈ U(Z_p)

D

D = E^-1 mod p

Big prime numbers

Click to copy/select _p

Modular Exponentiation in Z_p

p

p ∈ N^*

ϕ(n)

ϕ(n) = n.(1 - 1/p₁).(1 - 1/p₂)...

x

x ∈ Z_p

E

E ∈ U(Z_ϕ(n))

D

D ∈ Z_ϕ(n)

m = x^E mod p

x = m^D mod p

RSA

p

p is prime

q

q is prime

n

n = p * q

ϕ(n)

ϕ(n) = lcm(p − 1, q − 1)

x

x ∈ Z_p

E

E ∈ U(Z_ϕ(n))

D

D ∈ Z_ϕ(n)

m = x^E mod n

x = m^D mod n