FIT3031 Lecture Notes - Lecture 3: Block Cipher, Public-Key Cryptography, Plaintext
17 Jun 2018
School
Department
Course
Professor
L3: Asymmetric Key Encryptions
Summary
●AKA Public Key Encrypon, Dual key encrypon
●Useful in exchange of convenonal encrypon key
●Uses two keys
○If one has one key, the other cannot be computed
○Public key : published to the public
○Private key : kept by the owner
●Data encrypted with one key and the other decrypts
●Imposes high computaonal burdens as key key sizes are much larger
●Tends to be slower
●Uses number theory concept to funcon
●Strength: ability to establish a secure channel over a non secure medium
●Provides
○Confidenality
○Authencaon
○Data integrity
Uses of public key Cryptosystem
●Encrypon/Decrypon
●Digital Signature: sender sings with private key
●Key exchange: two pares exchange keys
Components
●Plaintext : data that is input to the algorithm
●Encryption algorithm : transforms the plaintext
●Private-public keypair : pair of related keys used for encrypon and decrypon processes
○Public key
■Used by anyone
■Encrypt messages & verify signatures
○Private key
■Known the owner only
■Decrypt messages & create signatures
●Ciphertext: encrypted message
●Decryption algorithm : algorithm that take ciphertext and the match key as inputs and
produces the plaintext
Encrypon Algorithms
RSA Algorithm
●Based on the difficulty of factoring large numbers
●Block cipher where plaintext and ciphertext are integers between 0 to n-1 for some n
Key Generaon process:
1. Select large prime numbers p and q . Calculate n = pq
2. Select integer e > 1 such that GCD(e(p - 1)(q - 1)) = 1
3. Solve the congruence ed 1 mode ((p - 1), (q- 1))≡
Document Summary
Aka pu(cid:271)li(cid:272) ke(cid:455) e(cid:374)(cid:272)r(cid:455)p(cid:415)o(cid:374), dual ke(cid:455) e(cid:374)(cid:272)r(cid:455)p(cid:415)o(cid:374) Useful i(cid:374) e(cid:454)(cid:272)ha(cid:374)ge of (cid:272)o(cid:374)(cid:448)e(cid:374)(cid:415)o(cid:374)al e(cid:374)(cid:272)r(cid:455)p(cid:415)o(cid:374) ke(cid:455) If o(cid:374)e has o(cid:374)e ke(cid:455), the other (cid:272)a(cid:374)(cid:374)ot (cid:271)e (cid:272)o(cid:373)puted. Public key : pu(cid:271)lished to the pu(cid:271)li(cid:272) Private key : kept (cid:271)(cid:455) the o(cid:449)(cid:374)er. Data e(cid:374)(cid:272)r(cid:455)pted (cid:449)ith o(cid:374)e ke(cid:455) a(cid:374)d the other de(cid:272)r(cid:455)pts. I(cid:373)poses high (cid:272)o(cid:373)puta(cid:415)o(cid:374)al (cid:271)urde(cid:374)s as ke(cid:455) ke(cid:455) sizes are (cid:373)u(cid:272)h larger. Tre(cid:374)gth: a(cid:271)ilit(cid:455) to esta(cid:271)lish a se(cid:272)ure (cid:272)ha(cid:374)(cid:374)el o(cid:448)er a (cid:374)o(cid:374) se(cid:272)ure (cid:373)ediu(cid:373) Digital ig(cid:374)ature: se(cid:374)der si(cid:374)gs (cid:449)ith pri(cid:448)ate ke(cid:455) Plaintext : data that is i(cid:374)put to the algorith(cid:373) Private-public keypair : pair of related ke(cid:455)s used for e(cid:374)(cid:272)r(cid:455)p(cid:415)o(cid:374) a(cid:374)d de(cid:272)r(cid:455)p(cid:415)o(cid:374) pro(cid:272)esses. Decryption algorithm : algorith(cid:373) that take (cid:272)ipherte(cid:454)t a(cid:374)d the (cid:373)at(cid:272)h ke(cid:455) as i(cid:374)puts a(cid:374)d produ(cid:272)es the plai(cid:374)te(cid:454)t. Based o(cid:374) the di (cid:272)ult(cid:455) of fa(cid:272)tori(cid:374)g large (cid:374)u(cid:373)(cid:271)ers. Blo(cid:272)k (cid:272)ipher (cid:449)here plai(cid:374)te(cid:454)t a(cid:374)d (cid:272)ipherte(cid:454)t are i(cid:374)tegers (cid:271)et(cid:449)ee(cid:374) (cid:1004) to (cid:374)-(cid:1005) for so(cid:373)e (cid:374) Ele(cid:272)t large pri(cid:373)e (cid:374)u(cid:373)(cid:271)ers p a(cid:374)d q .
