2018-08-30 00:57:22 +03:00
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/+ primitive-rsa, *test
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2018-08-29 03:58:23 +03:00
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=* rsa primitive-rsa
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2018-08-30 00:57:22 +03:00
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|%
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2018-08-29 03:58:23 +03:00
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++ test-rsakey
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=/ primes=(list @)
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:~ 2 3 5 7 11 13 17 19 23 29 31 37 41 43
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47 53 59 61 67 71 73 79 83 89 97 101 103 107
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109 113 127 131 137 139 149 151 157 163 167 173 179 181
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191 193 197 199 211 223 227 229 233 239 241 251 257 263
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269 271 277 281 283 293 307 311 313 317 331 337 347 349
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353 359 367 373 379 383 389 397 401 409 419 421 431 433
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439 443 449 457 461 463 467 479 487 491 499 503 509 521
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523 541 547 557 563 569 571 577 587 593 599 601 607 613
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617 619 631 641 643 647 653 659 661 673 677 683 691 701
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709 719 727 733 739 743 751
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==
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2018-08-30 00:57:22 +03:00
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=/ k1 (new-key:rsa 2.048 0xdead.beef)
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2018-08-29 03:58:23 +03:00
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::
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=/ k2=key:rsa
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=/ p 0x1837.be57.1286.bf6a.3cf8.4716.634f.ef85.f947.c654.da6e.e222.
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5654.9466.0ab0.a2ef.1985.1095.e3c3.9e74.9478.e3f3.ee92.f885.ec3c.
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84c3.6b3c.9731.65f9.9d1d.f743.646f.37d7.82d8.3f4a.856c.6453.b2c8.
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28d5.d720.145e.c7ab.4ba9.a9c2.6b8e.8819.7aa8.69b3.420f.dbfa.1ddb.
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4d1a.9c2e.e25a.d4de.d351.945f.d7ca.74a4.815d.5f0e.9f44.df64.39bd
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=/ q 0xf1bc.ec8f.d238.32d9.afb8.8083.76b3.82da.6274.f56e.1b5b.662b.
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ab1b.1e01.fbd5.86c5.ba98.b246.b621.f190.2425.25ea.b39f.efa2.4fb8.
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0d6b.c3c4.460d.e7df.d2f5.6604.51e0.415b.db60.db5a.6601.16c7.46ec.
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5e67.9195.f3c9.80d3.47c5.fe24.fbfd.43c3.380a.40bd.c4f5.d65e.b93b.
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60ca.5f26.4ed7.9c64.d26d.b0fe.985d.7be3.1308.34dd.b8c5.4d7c.d8a5
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=/ n (mul p q)
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=/ e 0x1.0001
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=/ d (~(inv fo (elcm:rsa (dec p) (dec q))) e)
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[[n e] `[d p q]]
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::
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|^ ^- tang
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;: weld
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(check-primes k1)
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(check-primes k2)
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==
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++ check-primes
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=, number
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|= k=key:rsa
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?> ?=(^ sek.k)
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%+ roll primes
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|= [p=@ a=tang]
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?^ a a
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?: =(0 (mod n.pub.k p))
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:~ leaf+"{(scow %ux n.pub.k)}"
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:- %leaf
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%+ weld
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"n.pub.key (prime? {(scow %f (pram n.pub.k))})"
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" divisible by {(scow %ud p)}:"
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==
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?: =(0 (mod p.u.sek.k p))
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:~ leaf+"{(scow %ux p.u.sek.k)}"
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:- %leaf
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%+ weld
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"p.u.sek.key (prime? {(scow %f (pram p.u.sek.k))})"
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" divisible by {(scow %ud p)}:"
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==
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?: =(0 (mod q.u.sek.k p))
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:~ leaf+"{(scow %ux q.u.sek.k)}"
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:- %leaf
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%+ weld
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"q.u.sek.key (prime? {(scow %f (pram q.u.sek.k))})"
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" divisible by {(scow %ud p)}:"
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==
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~
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--
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::
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++ test-rsa
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=/ k1=key:rsa
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=/ p `@ux`61
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=/ q `@ux`53
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=/ e `@ux`17
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=/ n (mul p q)
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=/ d (~(inv fo (elcm:rsa (dec p) (dec q))) e)
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[[n e] `[d p q]]
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::
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=/ k2=key:rsa
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:- [`@ux`143 `@ux`7]
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[~ `@ux`103 `@ux`11 `@ux`13]
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::
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:: ex from http://doctrina.org/How-RSA-Works-With-Examples.html
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=/ k3=key:rsa
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=/ p
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12.131.072.439.211.271.897.323.671.531.612.440.428.472.427.633.701.410.
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925.634.549.312.301.964.373.042.085.619.324.197.365.322.416.866.541.
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017.057.361.365.214.171.711.713.797.974.299.334.871.062.829.803.541
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=/ q
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12.027.524.255.478.748.885.956.220.793.734.512.128.733.387.803.682.075.
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433.653.899.983.955.179.850.988.797.899.869.146.900.809.131.611.153.
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346.817.050.832.096.022.160.146.366.346.391.812.470.987.105.415.233
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=/ n (mul p q)
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=/ e 65.537
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=/ d (~(inv fo (elcm:rsa (dec p) (dec q))) e)
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[[`@ux`n `@ux`e] `[`@ux`d `@ux`p `@ux`q]]
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=/ m3 (swp 3 'attack at dawn')
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=/ c3
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35.052.111.338.673.026.690.212.423.937.053.328.511.880.760.811.579.981.
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620.642.802.346.685.810.623.109.850.235.943.049.080.973.386.241.113.
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784.040.794.704.193.978.215.378.499.765.413.083.646.438.784.740.952.
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306.932.534.945.195.080.183.861.574.225.226.218.879.827.232.453.912.
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820.596.886.440.377.536.082.465.681.750.074.417.459.151.485.407.445.
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862.511.023.472.235.560.823.053.497.791.518.928.820.272.257.787.786
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::
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?> ?=(^ sek.k1)
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;: weld
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2018-08-29 21:09:37 +03:00
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%+ expect-eq
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2018-08-29 20:58:49 +03:00
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!> `@ux`413
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!> d.u.sek.k1
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::
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2018-08-29 21:09:37 +03:00
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%+ expect-eq
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2018-08-29 20:58:49 +03:00
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!> 2.790
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!> (en:rsa 65 k1)
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::
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2018-08-29 21:09:37 +03:00
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%+ expect-eq
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2018-08-29 20:58:49 +03:00
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!> 65
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!> (de:rsa 2.790 k1)
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::
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2018-08-29 21:09:37 +03:00
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%+ expect-eq
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2018-08-29 20:58:49 +03:00
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!> 48
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!> (en:rsa 9 k2)
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::
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2018-08-29 21:09:37 +03:00
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%+ expect-eq
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2018-08-29 20:58:49 +03:00
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!> 9
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!> (de:rsa 48 k2)
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::
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2018-08-29 21:09:37 +03:00
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%+ expect-eq
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2018-08-29 20:58:49 +03:00
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!> c3
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!> (en:rsa m3 k3)
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::
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2018-08-29 21:09:37 +03:00
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%+ expect-eq
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2018-08-29 20:58:49 +03:00
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!> m3
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!> (de:rsa c3 k3)
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2018-08-29 03:58:23 +03:00
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==
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--
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