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N^{2 U}

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αN^D 1 ≤ α ≤

λ(N)^{F]\_^6} m∈Z_N2 ^QR! m = 1 modN ^Q L(u) = ^m_N⁻¹ modN^F

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r, m∈Z_N ^Z6Y6X c:=g^{m+N rD6X6>'} m=L(c^α)/L(g^α)^F

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g^α = 1 +vN modN^{2 QR!.MMT} (v, N) = 1^F

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#Q N = p·q ^} J~€X6Z6<‚D

p−1 = αp2

D g ∈ Z^∗N^{2 U}

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α N^F

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U

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m ∈Z_p ∼= [0, p[^ˆ X6Š‰ "‡

U

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c=g^mr^{N QR!} r∈R hgi^F

l #QnM'Œ

m=L(c^α)/L(g^α) modp^F

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p ^{–6 QR€D} g ∈Z^∗

p^{2 U}

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pα^D 1≤α ≤p−1^D α|p−1^F

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u∈Z_p2 ^QR! u= 1 mod p ^Q Lp(u) = ^u−_p¹ modp^F

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U

QR‡

U !

m∈Z_p ∼= [0, p[ ^ˆ X6„‰'# "‡

U

<n^E <R!0‹#Z

c:=g^mr^{p QR!} r ∈RZ^∗_p^F

l

#QnM''Œ

m=Lp(c^α)/Lp(g^α) mod p^F

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