Simetrinės KS

RSA encryption [Katz, p. 355]

AE - asymmatric encryption, AD - asymmetric decryption

Algebrines Sistemos P120M101

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Realization.

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RSA Homomorphic properties - RSA homomorfinė savybės

RSA Encryption

m = m1 ● m2 (modN)c1 = AEe(m1) = (m1)e modN, c2 = AEe(m2) = (m2)e modN.c = AEe(m) = AEe(m1 ● m2) = (m1 ● m2)e modN = (m1)e modN ● (m2)e modN = c1 ● c2 = c.

Padded RSA

RSA Signature

h1 = H(m1), h2 = H(m2)h = h1 ● h2 (modN)s1 = Sigd(h1) = (h1)d modN, s2 = Sigd(h2) = (h2)d modN.s = Sigd(h) = Sigd(h1 ● h2) = (h1 ● h2)d modN = (h1)d modN ● (h2)d modN = s1 ● s2 = s.

c1 = AEe(r1 ||m1) = (r1 ||m1)e modN, c2 = AEe(r2 ||m2) = (r2 ||m2)e modN.c = AEe[r ||m] = AEe[(r1 ||m1) ● (r2 ||m2)] = [(r1 ||m1) ● (r2 ||m2)]e modN (r1 ||m1)e modN ● (r2 ||m2)e modN

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s = Sigd(h) = Sigd(h1 ● h2) = (h1 ● h2)d modN = (h1)d modN ● (h2)d modN = s1 ● s2 = s.

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