CLASS 04
Sketching the blockchain: cryptographic block hash of the data generated by solving a
difficult proof-of-work puzzle; reference to the previous block hash to determine the correct
chronological ordering of blocks; new unique proof-of-work protocol for the new block.
Cryptography: deep academic research field utilizing advanced mathematical techniques
to protect data from being accessed by unauthorized people.
Key: random string consisting of hundreds of binary digits used by a cryptographic
algorithm to transform plain text into cipher text or vice versa. Symmetric: the algorithm
uses a single key for both encryption and decryption; asymmetric: a private key to encrypt,
a public key to decrypt.
Shared keys (asymmetric): Diffie-Hellman key exchange protocol
Ra=Ha , Rg=Hg à exchange à Hga=(Rg)a=S , Hag=(Ra)g=S à same secret key
R, Ha, Hg are publicly known à can be intercepted
We use discrete log problem to let the guess of the values very difficult.
Ra mod(p)=Ha , Rg mod(p)=Hg à Hga mod(p)=S , Hag mod(p)=S
The problem is that computing power is increasing and it is easier to solve these.
We use the elliptic curve (a curve that’s also naturally a group), properties:
Symmetric over the X-axis;
Given two points, if we draw a straight line between them, that line will
intercept the elliptic curve in at most one more point.
Elliptic curve discrete log problem à nA=E (“dot” operation)
g(aR)=a(gR)
Elliptic Curve Diffie-Hellman (ECDH)
aR=Ha , gR=Hg à exchange à aHg=S , gHa=S
Elliptic Curve is the solution: resilient to attacks and small in size (less bits), implement
with the Elliptic Curve Cryptography (ECC).
Downsides: difficult mathematical representation, many are patented, fail without sufficient
randomness, lack of theoretical foundation, are they really secure?, built-in trap doors.
