Answer:
1. Can you crack the RSA Encrypted value with the following parameters:
e: 65537
N: 896451247364832522335371462620300449
Cipher: 537346246383456572577077015701806879
We are using 60 bit primes
Additional information:
Details: [here]. Here is an example: Encryption parameters e: 65537 N: 1034776851837418228051242693253376923 Cipher: 582984697800119976959378162843817868 We are using 60 bit primes Now we have to crack N by finding the primes that make up the value. If we use this [link], we get: Factors ------- 1,034,776,851,837,418,228,051,242,693,253,376,923 = 1,086,027,579,223,696,553 x 952,809,000,096,560,291 p=1,086,027,579,223,696,553 q=952,809,000,096,560,291 Now we work out PHI, which is equal to (p−1)×(q−1): >>>p=1086027579223696553 >>>q=952809000096560291 >>> print (p-1)*(q-1) 1034776851837418226012406113933120080 Now we find e^−1 (mod PHI) (and where (d×e) (mod PHI)=1), such as using [link]: Inverse of 65537 mod 1034776851837418226012406113933120080 Result: 568411228254986589811047501435713 This is the decryption key. Finally we decrypt with Message=Cipher^d (mod N): >>> d=568411228254986589811047501435713 >>> cipher=582984697800119976959378162843817868 >>> N=1034776851837418228051242693253376923 >>> print pow(cipher,d,N) 345 The message is 345 Finally, let's check the answer. So we can recipher with the encryption key and we use Cipher=M^e (mod N): >>> m=345 >>> e=65537 >>> N=1034776851837418228051242693253376923 >>> print pow(m,e,N) 582984697800119976959378162843817868 This is the same as the cipher, so the encryption and decryption keys have worked. Thus the encryption key is [65537, 1034776851837418228051242693253376923] and the decryption key is [568411228254986589811047501435713, 1034776851837418228051242693253376923]
Ans:
1713