PUBLIC KEY ENCRYPTION

Bhagya Prasad
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MSc Cryptography Note on PUBLIC KEY ENCRYPTION, created by Bhagya Prasad on 05/14/2013.

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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 one-way 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 (p-1)(q-1)no number should divide neatly into e and (p-1)(q-1) 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 (p-1)(q-1)if d is the private key, thened=mod (p-1)(q-1)

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 (p-1)Choose a private key (x)- has to be greater than 1 and less than (p-1), randomly generatedCompute the key (y)y = g power x modulo p         xy = g mod p

TRAP-DOOR ONEWAY FUNCTION

RSA

ElGamal