Created by Bhagya Prasad
over 6 years ago


TRAPDOOR ONEWAY FUNCTIONAnybody should be able to compute as its a public key and has two properties function should be Easy to compute function should be Hard to reverse Hence, the function that has above properties is called oneway function The receiver (the only one entity) will know the trapdoor and this forms a private key
first oneway function MULTIPLICATION OF PRIMESproduct = multiple of two large primes on polynomial wayfactorization becomes difficult with product of two large primese.g. RSA
second way function MODULAR EXPONENTIATIONmodular exponentiation with large modulusexponentiation is raising a number to a powerModular Exponentiation is raising the number to a power modulo some other numberformula f(b) = a to the power of b mod n
Invented by Rivest, Shamir and Adleman
GENERATING RSA KEY PAIRsSTEP 1 : Generate the RSA modulusn = productp = large prime 1 (min 512 bits long)q = large prime 2 (min 512 bits long)therefore, n= p x qn produced here is called RSA modulus
GENERATING RSA KEY PAIRsSTEP 2 : Generate 'e'must be greater than 1cannot be less than (p1)(q1)no number should divide neatly into e and (p1)(q1) other than 1
RSA KEY PAIRs = (n,e)(n,e) is a public keyGenerating the private key using (n.e)Private key is inverse of e modulo (p1)(q1)if d is the private key, thened=mod (p1)(q1)
Based on elliptical curve variantBasis for other important cryptographic primitives like Digital Signature EncryptionSETTING UP ElGAMALChoose a large prime (p)  has to be a number modulo, size 1024 to 2048 bitsChoose a special key (g) has to be a primitive modulo, has to be between 1 and (p1)Choose a private key (x) has to be greater than 1 and less than (p1), randomly generatedCompute the key (y)y = g power x modulo p xy = g mod p
TRAPDOOR ONEWAY FUNCTION
RSA
ElGamal