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# public key cryptography notes

First, we select two prime numbers, p=17p = 17p=17 and q=11q = 11q=11. This signature scheme is vulnerable in the same way as the basic RSA signature. For example, for M=10M = 10M=10 and k=3k = 3k=3, k′=7k' = 7k′=7 because 3∗7(mod10)=21(mod10)=13 * 7 \pmod{10} = 21 \pmod{10} = 13∗7(mod10)=21(mod10)=1. To create a signature sss for a message mmm, Alice uses her private key, d,n{d, n}d,n to compute md(modn)m^d \pmod nmd(modn). Whatever a honest verifier can compute after the protocol, can also be computed without interacting with a honest prover (implying that the verifier learns nothing about sk in a protocol execution). Indeed, signature schemes are sometimes used to sign random values instead of structured messages with high redundancy. Normally, public key is used for encryption and. public key PK and computes c = E(PK, m), and sends it to Bob. Output 1 if r ≡ u (mod q), and 0 otherwise. Public-key Cryptography: Principles of public-key cryptosystems, RSA algorithm, and security of RSA, Elliptic curve arithmetic, Elliptic curve cryptography, Cryptographic Hash … First, user AAA selects a random number, XA