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RSA algorithm uses the following procedure to generate public and private keys: Select two large prime numbers, p and q. Multiply these numbers to find n = p x q, where n is called the modulus for encryption and decryption. If n = p x q, then the public key is <e, n>.
Euclid algorithm and extended Euclid algorithm are the best algorithms to solve the public key and private key in RSA. Extended Euclid algorithm in IEEE P1363 is improved by eliminating the negative integer operation, which reduces the computing resources occupied by RSA, hence has an important application value.
Generation of RSA Key Pair Calculate n=p*q. For strong unbreakable encryption, let n be a large number, typically a minimum of 512 bits.
I'm a high school student writing a paper on RSA, and I'm doing an example with some very small prime numbers. I understand how the system works, but I can't for the life of me calculate the private key using the extended euclidean algorithm.
Here's what I have done so far:
Now I just have to calculate the private key d, which should satisfy ed=1 (mod 3168)
Using the Extended Euclidean Algorithm to find d such that de+tN=1 I get -887•25+7•3168=1. I throw the 7 away and get d=-887. Trying to decrypt a message, however, this doesn't work.
I know from my book that d should be 2281, and it works, but I can't figure out how they arrive at that number.
Can anyone help? I've tried solving this problem for the last 4 hours, and have looked for an answer everywhere. I'm doing the Extended Euclidean Algorithm by hand, but since the result works my calculations should be right.
Thanks in advance,
Mads
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