We select 7 as our public key eee, as 7 and 160 are relatively prime. It is computationally infeasible to determine the. Digital signatures were invented in the same seminal paper where Diffie and Hellman (1976) introduced the public key cryptography concept. In modular multiplication, a number kkk , has an inverse k′k'k′ such that k∗k′(modM)=1k * k' \pmod M = 1k∗k′(modM)=1. The sym… Finally, we calculate ddd: the multiplicative inverse of eee, (modϕ(n))\pmod{\phi(n)}(modϕ(n)). Given a modulus MMM, x∗y(modM)x * y \pmod Mx∗y(modM) is equal to the remainder of (x∗y)÷M(x * y) \div M(x∗y)÷M. Happy studying! Output c=(m1⊕b1,...,mn⊕bn,xn). If the prover's private input is just (pk) then the probability that a honest verifier accepts the conversation is noticeably less than 1. (4) Bob computes m = D(SK, c) to recover the original message. Parse pk=(param,y). From the very close analogy between the syntax of encryption schemes and signatures, some public key encryption schemes can be transformed into digital signature schemes by using Dec as the signature algorithm and using Enc in the verification of the signature. But the non-interactive protocol can be turned easily into a signature scheme by adding the message m to the argument of the hash function. The attacker intercepts ccc and performs the transformation c′=se∗cc' = s^e * cc′=se∗c. Parse pk=(i). Likewise, Trudy intercepts YBY_BYB that Bob sends to Alice and instead sends her own YXY_XYX to Alice, fooling Alice to believe that YXY_XYX is actually YBY_BYB. Choose a prime number q of λ bits. One issue with RSA is that the algorithm is deterministic. AAA selects a random integer XA