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as is so often true in cryptography it is easy to weaken a seemingly strong scheme by small modifications assume a
let the two primes p 41 and q 17 be given as set-up parameters for rsa1 which of the parameters e1 32e2 49 is a
computing modular exponentiation efficiently is inevitable for the practicability of rsa compute the following
we now analyze the security of des double encryption 2des by doing a cost-estimate1 first let us assume a pure key
verify the rsa with crt example in the chapter by computing yd 15103 mod 143 using the square-and-multiply
propose an ofb mode scheme which encrypts one byte of plaintext at a time eg for encrypting key strokes from a remote
keeping the iv secret in ofb mode does not make an exhaustive key search more complex describe how we can perform a
in a company all files which are sent on the network are automatically encrypted by using aes-128 in cbc mode a fixed
the level of security in terms of the corresponding bit length directly influences the performance of the respective
using the extended euclidean algorithm compute the greatest common divisor and the parameters st of1 198 and 2432 1819
understanding the functionality of groups cyclic groups and subgroups is important for the use of public-key
in this exercise you are asked to attack an rsa encrypted message imagine being the attacker you obtain the ciphertext
in this exercise we illustrate the problem of using nonprobabilistic cryptosystems such as schoolbook rsa imprudently
advanced problem there are ways to improve the square-and-multiply algorithm that is to reduce the number of operations
as we have seen in this chapter public-key cryptography can be used for encryption and key exchange furthermore it has
in this problem we want to compare the computational performance of symmetric and asymmetric algorithms assume a fast
verify that eulers theorem holds in zm m 69 for all elements a for which gcdam 1 also verify that the theorem does
we now show how an attack with chosen ciphertext can be used to break an rsa encryption1 show that the multiplicative
in sect 1013 we state that sender or message authentication always implies data integrity why is the opposite true too
we investigate the weaknesses that arise in elgamal encryption if a public key of small order is used we look at the
after the dhke alice and bob possess a mutual secret point r xy the modulus of the used elliptic curve is a 64-bit
given is a dhke algorithm the modulus p has 1024 bit and alpha is a generator of a subgroup where ordalpha asymp 21601
in the dhke protocol the private keys are chosen from the setwhy are the values 1 and p - 1 excluded describe the
one of the earlier applications of cryptographic hash functions was the storage of passwords for user authentication in
describe how exactly you would perform a collision search to find a pair x1 x2 such that hx1 hx2 for a given hash