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Cryptography - Key
Generation -
Asymmetric Key
5 minutes series
Abdul Manaf Vellakodath
Security Architect
Asymmetric Key
Key Generation - Symmetric and Asymmetric Keys
Large
Random
Number
Symmetric
Key
Generation
Algorithm
Symmetric Key
Symmetric-key algorithms[1] are algorithms for cryptography
that use the same cryptographic keys for both encryption of
plaintext and decryption of ciphertext.
Wiki
Symmetric Key
Large
Random
Number
Asymmetric
Key
Generation
Algorithm
Asymmetric cryptography, is any cryptographic system that
uses pairs of keys: public keys that may be disseminated
widely paired with private keys which are known only to the
owner.
Wiki
PRIVATE KEY
PUBLIC KEY
As demonstrated above, the keys generated by Symmetric Key and Asymmetric Key generation algorithms are fundamentally
different. Symmetric Keys can be used for both encryption and decryption. Asymmetric Private Key can decrypt what Public
Key encrypts, and vice versa.
RSA (Rivest-Shamir-Adleman) Keys - Looks like this!
Application location: http://travistidwell.com/jsencrypt/demo/
RSA Key - Generate a Keys (Private and Public)
Application location: http://travistidwell.com/jsencrypt/demo/
The above command creates an RSA Asymmetric Key Pair (i.e. A Public Key and
a Private Key)
RSA Private Key - Data Structure (Algorithm in last slide)
Product of two large prime
numbers. This part of the
Private Key is same as that
of the Public Key. See next
slide!
Length in bits is the Key
Length!
e
d
p
q
d mod(p-1)
d mod(q-1)
(inverse of
q) mod p
RSA Public Key - Data Structure
RSA Key Generation - Algorithm
https://en.wikipedia.org/wiki/RSA_(cryptosystem)#Key_generation
p = prime 1 q = prime 2
n = p x q
Totient (N) = (p - 1) x (q - 1)
Find e, a coprime to Totient (n)
Such that 1 < e < T(n)
Compute d, Modular Multiplicative
Inverse, e (mod T(n))
Public Key : n, e
Private Key : d
Simple Explanation of these algorithms!
Euler’s Totient Function Explained!
https://www.youtube.com/watch?v=GZbdmCIhmpA
Modular Multiplicative Algorithm
https://www.youtube.com/watch?v=Ou3fWpibQAs

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Cryptography - Simplified - Key Generation - Asymmetric Keys

  • 1. Cryptography - Key Generation - Asymmetric Key 5 minutes series Abdul Manaf Vellakodath Security Architect
  • 2. Asymmetric Key Key Generation - Symmetric and Asymmetric Keys Large Random Number Symmetric Key Generation Algorithm Symmetric Key Symmetric-key algorithms[1] are algorithms for cryptography that use the same cryptographic keys for both encryption of plaintext and decryption of ciphertext. Wiki Symmetric Key Large Random Number Asymmetric Key Generation Algorithm Asymmetric cryptography, is any cryptographic system that uses pairs of keys: public keys that may be disseminated widely paired with private keys which are known only to the owner. Wiki PRIVATE KEY PUBLIC KEY As demonstrated above, the keys generated by Symmetric Key and Asymmetric Key generation algorithms are fundamentally different. Symmetric Keys can be used for both encryption and decryption. Asymmetric Private Key can decrypt what Public Key encrypts, and vice versa.
  • 3. RSA (Rivest-Shamir-Adleman) Keys - Looks like this! Application location: http://travistidwell.com/jsencrypt/demo/
  • 4. RSA Key - Generate a Keys (Private and Public) Application location: http://travistidwell.com/jsencrypt/demo/ The above command creates an RSA Asymmetric Key Pair (i.e. A Public Key and a Private Key)
  • 5. RSA Private Key - Data Structure (Algorithm in last slide) Product of two large prime numbers. This part of the Private Key is same as that of the Public Key. See next slide! Length in bits is the Key Length! e d p q d mod(p-1) d mod(q-1) (inverse of q) mod p
  • 6. RSA Public Key - Data Structure
  • 7. RSA Key Generation - Algorithm https://en.wikipedia.org/wiki/RSA_(cryptosystem)#Key_generation p = prime 1 q = prime 2 n = p x q Totient (N) = (p - 1) x (q - 1) Find e, a coprime to Totient (n) Such that 1 < e < T(n) Compute d, Modular Multiplicative Inverse, e (mod T(n)) Public Key : n, e Private Key : d Simple Explanation of these algorithms! Euler’s Totient Function Explained! https://www.youtube.com/watch?v=GZbdmCIhmpA Modular Multiplicative Algorithm https://www.youtube.com/watch?v=Ou3fWpibQAs