00:01
Okay, so the first thing i want to do is to review the rsa encryption.
00:04
So rsa encryption of a plain text message m using a public key n e results in a ciphertext c, which is computed as m e mod n, where n is the modulus, which is a product of two large primes, p and q, and e is the public exponent.
00:30
And for decryption, the private key d is used, which satisfies de equals 1 mod phi of n, where phi of n is equal to p -1, q -1, and is euler's torsion function.
00:56
Function.
00:57
As for eve's situation, so eve intercepts c1 and c2, where c1 equals me1 mod n, c2 equals course mode.
01:23
Now eve already knows n, e1, e2, c1, and c2.
01:43
Okay, so can eve compute the plaintext? so eve can potentially compute m without the private key under certain conditions by exploiting the fact that two different exponents were used for encryption.
02:10
Description, one method involves using the extended euclidean algorithm to find the integers x and y such that e1 times x plus e2 times y equals gcd of e1 and e2...