Please keep the answers simple because I don't have any math background. (Also, I would prefer not to iterate, if possible.) I need to find integer k given any small integer e, and small primes p and q.
A number of Sage commands will be presented that help us to perform basic number theoretic operations such as greatest common divisor and Euler’s phi function. With p=13,q=7,e=5 then k = 2 (and therefore, d = 29). This tutorial uses Sage to study elementary number theory and the RSA public key cryptosystem. The value of k should be an integer (it must result in an integer value of d, the decryption exponent). Once I have picked e, p and q how do I find k? Once I have k, of course, finding d is trivial in my example. To me modInverse() is a "black box" and I'm trying to avoid those so that I can increase my understanding (although I'm working at a simple level of understanding). From e and you can compute d, which is the secret key exponent. Generation of RSA Key Pair Each person or a party who desires to participate in communication using encryption needs to generate a pair of keys, namely public key and private key.
#RSA CRYPTEXT D CALCULATOR MOD#
RSA key generation works by computing: n pq (p-1) (q-1) d (1/e) mod So given p, q, you can compute n and trivially via multiplication. We will see two aspects of the RSA cryptosystem, firstly generation of key pair and secondly encryption-decryption algorithms. I am trying to avoid calling any external functions. 1 Answer Sorted by: 15 Youve already been given everything you need to decrypt any messages. Assuming n is not too large, factorization should be relatively easy ( WolframAlpha may. It sounds like the task you have been set is essentially to break RSA by factoring n into its prime factors p and q, and then using these to calculate d. In particular I do not want to use something similar to the following method, which is what I find recommended on all the programming-related forums: BigInteger d = e.modInverse(totient) The security of RSA is derived from the difficulty in calculating d from e and n (the public key). I want to compute the RSA decryption exponent d, where d e1 mod (n). Im not trying to do anything that will have real world security. Why do I want to do it similar to that method? Although I am using the Java language, I am looking for a simple "hand calculation" method. Encryption: find d d if we know n n and e e Ask Question Asked 7 months ago Modified 7 months ago Viewed 697 times 2 If an R.S.A. 1 This is a simple exercise to help my personal understanding of RSA. I will use small primes (e.g., 7, 13) and I will also pick e to be something small like 5.
Where e is the RSA encryption exponent and p and q are randomly generated primes. I would prefer to make the calculation using a method similar to this: int d = (k * (p - 1) * (q - 1) + 1) / e I want to compute the RSA decryption exponent d, where d = e−1 mod φ(n).
I'm not trying to do anything that will have real world security. This is a simple exercise to help my personal understanding of RSA.
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