Singhalese(锡兰人).ppt

Elliptic Curve Cryptography
Jen-Chang Liu, 2004
Adapted from lecture slides by Lawrie Brown
Ref: RSA Security’s Official Guide to Cryptography
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No Singhalese(錫蘭人), whether man or woman, would venture out of the house without a bunch of keys in his hand, for without such a talisman(護身符) he would fear that some devil might take advantage of his weak state to slip into his body.
—The Golden Bough, Sir James e Frazer
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Review: Requirement for public-key cryptography
Diffie and Hellman (1976) proposed the public-key cryptography requirement:
It putationally easy to generate a pair of keys
It putationally easy for a sender to encrypt
It putationally easy for a receiver to decrypt
It putationally infeasible for an opponent, knowing the public key, to determine the private key
It putationally infeasible for an opponent, knowing the public key and ciphtertext, to recover the plaintext
b
X = DKR (Y)
Y = EKU (X)
b
=> Trap-door one-way function
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Review: one-way function
1968, R. M. Needham’s system
1974, G. Purdy published the first detail description of such a one-way function
One-way function
Computation in Zp ,
A’s password
One-way cipher
Encrypted password list
…
…
A’s encrypted
password
Hard to invert!
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Review: (trapdoor) one-way function
domain
target
Y=f(X): easy
X=f -1 (Y): infeasible ( > polynomial time)
X=fK-1 (Y): easy if trap-door K is known
( ~ polynomial time)
The notion of “computationally infeasible” plays an important role
A enciphering transformation that can safely be regarded as
a (trapdoor) one-way function in 1994 might lose its one-way
or trapdoor status in 2004 or 2994
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Elliptic Curve Cryptography (E