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Theorem RSA-decrypt-ij-vars

prime(i), prime(i0), i1 = i * i0, 2 < i, 2 < i0, i ≠ i0, gcd(i2, (i - 1) * (i0 - 1)) = 1, 0 < i2, i2 < i1, ≡mod(i2 * i3, 1, (i - 1) * (i0 - 1)), 0 ≤ i3, j0 = j ^ i2 |%| i1, 0 ≤ j, j < i1 ⊦ j = j0 ^ i3 |%| i1

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment: RSA decrypt(encrypt(P)) = P. See also exercises/math-examples. With standard variables: prime(p), prime(q), n = p * q, 2 < p, 2 < q, p ≠ q, gcd(e, (p - 1) * (q - 1)) = 1, 0 < e, e < n, ≡mod(e * d, 1, (p - 1) * (q - 1)), 0 ≤ d, C = (P ^ e) |%| n, 0 ≤ P, P < n ⊦ P = (C ^ d) |%| n
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 24
Proof steps: 44
Used lemmas: fermat-for-rsa, congmod-def-mod, congmod-def-mod-01, mod-crt, mod-pot-pot, mod-zero-03, congmod-def, mod-zero,
Used spec theorems:
Used simplifier rules: