(RSA public key cryptosystem)Bob chooses the secret primes p = 5 and q = 11.Bob chooses the encryption exponent e = 3.Bob publishes N = 55 and e = 3.If Bob receivers the ciphertext c = 24 from Alice, what is the plaintextm that Bob obtains by deciphering c?

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Answered: (RSA public key cryptosystem) = Bob…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter4: Polynomials

Section4.1: Exponents

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Rework Example 5 by breaking the message into two-digit blocks instead of three-digit blocks. What is the enciphered message using the two-digit blocks? Example 5: RSA Public Key Cryptosystem We first choose two primes (which are to be kept secret): p=17, and q=43. Then we compute m (which is to be made public): m=pq=1743=731. Next we choose e (to be made public), where e must be relatively prime to (p1)(q1)=1642=672. Suppose we take e=205. The Euclidean Algorithm can be used to verify that (205,672)=1. Then d is determined by the equation 1=205dmod672 Using the Euclidean Algorithm, we find d=613 (which is kept secret). The mapping f:AA, where A=0,1,2,...,730, defined by f(x)=x205mod731 is used to encrypt a message. Then the inverse mapping g:AA, defined by g(x)=x613mod731 can be used to recover the original message. Using the 27-letter alphabet as in Examples 2 and 3, the plaintext message no problem is translated into the message as follows: plaintext:noproblemmessage:13142615171401110412 The message becomes 13142615171401110412. This message must be broken into blocks mi, each of which is contained in A. If we choose three-digit blocks, each block mim=731. mi:13142615171401110412f(mi)=mi205mod731=ci:082715376459551593320 The enciphered message becomes 082715376459551593320 where we choose to report each ci with three digits by appending any leading zeros as necessary. To decipher the message, one must know the secret key d=613 and apply the inverse mapping g to each enciphered message block ci=f(mi): ci:082715376459551593320g(ci)=ci613mod731:13142615171401110412 Finally, by re-breaking the message back into two-digit blocks, one can translate it back into plaintext. Three-digitblockmessage:13142615171401110412Two-digitblockmessage:13142615171401110412Plaintext:noproblem The RSA Public Key Cipher is an example of an exponentiation cipher.
Suppose that in a long ciphertext message the letter occurred most frequently, followed in frequency by. Using the fact that in the -letter alphabet, described in Example, "blank" occurs most frequently, followed in frequency by, read the portion of the message enciphered using an affine mapping on. Write out the affine mapping and its inverse. Example 2 Translation Cipher Associate the letters of the "alphabet" with the integers. Let and define the mapping by where is the key, the number of positions from the plaintext to the ciphertext. If our alphabet consists of through, in natural order, followed by a blank, then we have "letters" that we associate with the integers as follows:
Suppose that in an RSA Public Key Cryptosystem, the public key is. Encrypt the message "pay me later” using two-digit blocks and the -letter alphabet from Example 2. What is the secret key? Example 2 Translation Cipher Associate the letters of the "alphabet" with the integers. Let and define the mapping by where is the key, the number of positions from the plaintext to the ciphertext. If our alphabet consists of through, in natural order, followed by a blank, then we have "letters" that we associate with the integers as follows:
only 6 please
Having chosen primes p and q, and suitable integers d and e, what is the public-key of our RSA cipher in this case? Select one: a. (φ(pq), e) b. (pq, e) c. (d. e) d. (p. q) Clear my choice
Encrypt the word "WATER" by using the cipher function f(p) = (3p+7)mod 26.
The following parameters are chosen to generate the public and private keys for the RSA cryptosystem. p = 13q = 11e = 37d = 13 If the ciphertext is c = 8, then what is the plaintext m?
Suppose the RSA system that is used for sending secret messages has private key (15, 3) and the cipher text "4" is received. What was the plain text sent? 12 0 8 6 4
Use the values below to encrypt the numerical message m = 55. Use the following cryptoscheme: Encryption (m + k) mod N = c Decryption (c - k) mod N = m N = 66 K = 20 Example:5
(5) Elgamal public key cryptosystem (decryption): Start with the prime p = 17 and the primitive root g = 3. Alice sends Bob the public key A = 5. Bob encrypts the message m and sends the pair of numbers (8,2) to Alice. Alice's secret key is a = 5. Using Elgamal public key decryption, Alice computes the plaintext message m from the ciphertext (8, 2). What is the number m that Alice obtains?
help
Suppose p 5 and q = 11. Which of the following is the private key of an RSA cryptosystem with public key (n, e) = (55, 7)? O (55,51) O (55, 23) O (55, 15) O (55, 39)

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(RSA public key cryptosystem) = Bob chooses the secret primes p = 5 and q Bob chooses the encryption exponent e = 3. Bob publishes N = 55 and e = 2= 3. If Bob receivers the ciphertext c = 24 from Alice, what is the plain m that Bob obtains by deciphering c? 11.