Bimodal Lattice Signature Scheme (BLISS) » History » Version 4
Andreas Steffen, 12.12.2014 22:01
| 1 | 1 | Andreas Steffen | h1. Bimodal Lattice Signature Scheme (BLISS) |
|---|---|---|---|
| 2 | 1 | Andreas Steffen | |
| 3 | 1 | Andreas Steffen | BLISS is a post-quantum signature scheme based on the CRYPTO 2013 paper "Lattice Signatures and Bimodal Gaussians":https://eprint.iacr.org/2013/383 by Léo Ducas, Alain Durmus, Tancrède Lepoint, and Vadim Lyubashevsky. Starting with the strongSwan [[5.2.2]] release we offer BLISS as an IKEv2 public key authentication method and added full BLISS key and certificate generation support to the strongSwan [[IpsecPki|pki]] tool. |
| 4 | 1 | Andreas Steffen | |
| 5 | 1 | Andreas Steffen | h2. BLISS Private Key Generation |
| 6 | 1 | Andreas Steffen | |
| 7 | 1 | Andreas Steffen | strongSwan currently supports the BLISS-I, BLISS-III, and BLISS-IV schemes with a cryptographic strength of 128 bits, 160 bits and 192 bits, respectively. Using the [[IpsecPki|pki]] tool a private BLISS key can be generated as follows: |
| 8 | 1 | Andreas Steffen | <pre> |
| 9 | 1 | Andreas Steffen | pki --gen --type bliss --size 1 --debug 2 > key1.der |
| 10 | 1 | Andreas Steffen | |
| 11 | 1 | Andreas Steffen | mgf1 based on sha1 is seeded with 20 octets |
| 12 | 1 | Andreas Steffen | mgf1 generated 240 octets |
| 13 | 1 | Andreas Steffen | mgf1 based on sha1 is seeded with 20 octets |
| 14 | 1 | Andreas Steffen | mgf1 generated 240 octets |
| 15 | 1 | Andreas Steffen | l2 norm of s1||s2: 771, Nk(S): 47150 (46479 max) |
| 16 | 1 | Andreas Steffen | |
| 17 | 1 | Andreas Steffen | mgf1 based on sha1 is seeded with 20 octets |
| 18 | 1 | Andreas Steffen | mgf1 generated 220 octets |
| 19 | 1 | Andreas Steffen | mgf1 based on sha1 is seeded with 20 octets |
| 20 | 1 | Andreas Steffen | mgf1 generated 240 octets |
| 21 | 1 | Andreas Steffen | l2 norm of s1||s2: 771, Nk(S): 43332 (46479 max) |
| 22 | 1 | Andreas Steffen | |
| 23 | 1 | Andreas Steffen | secret key generation succeeded after 2 trials |
| 24 | 1 | Andreas Steffen | </pre> |
| 25 | 3 | Andreas Steffen | When generating the private key consisting of the two polynomials *s1* and *s2*, the _Nk(S)_ metric must be fulfilled. This means that often several trials are needed in order to obtain a valid BLISS private key. With the command |
| 26 | 1 | Andreas Steffen | <pre> |
| 27 | 1 | Andreas Steffen | pki --print --type bliss-priv --in key1.der |
| 28 | 1 | Andreas Steffen | |
| 29 | 1 | Andreas Steffen | private key with: |
| 30 | 1 | Andreas Steffen | pubkey: BLISS 128 bits strength |
| 31 | 1 | Andreas Steffen | keyid: d1:a3:fb:04:8d:1b:86:4f:fa:a7:d8:45:ec:e3:e3:ec:ef:7b:85:ca |
| 32 | 1 | Andreas Steffen | subjkey: e3:fc:6b:59:9a:ee:81:d5:10:3a:58:9f:e2:99:f7:7f:5c:3b:1c:96 |
| 33 | 1 | Andreas Steffen | </pre> |
| 34 | 1 | Andreas Steffen | information on the BLISS private key is displayed. |
| 35 | 2 | Andreas Steffen | |
| 36 | 1 | Andreas Steffen | Let's now generate a BLISS-IV key with 192 bit cryptographic strength in base64-encoded PEM format |
| 37 | 2 | Andreas Steffen | <pre> |
| 38 | 2 | Andreas Steffen | pki --gen --type bliss --size 4 --outform pem > key4.pem |
| 39 | 3 | Andreas Steffen | secret key generation succeeded after 6 trials |
| 40 | 1 | Andreas Steffen | </pre> |
| 41 | 1 | Andreas Steffen | The PEM key format is printable |
| 42 | 2 | Andreas Steffen | <pre> |
| 43 | 3 | Andreas Steffen | cat key4.pem |
| 44 | 3 | Andreas Steffen | |
| 45 | 1 | Andreas Steffen | -----BEGIN BLISS PRIVATE KEY----- |
| 46 | 3 | Andreas Steffen | MIIFGgYLKwYBBAGCoCoFAgQDggOBAEOoiWS7mISnnPjzFJu6REHq1REYuLfillD2 |
| 47 | 3 | Andreas Steffen | VmmCWuB1NcL6GLTRFzwCMCw8KBLpyZhEAs6QlelSWVxPuBGMuQzQsmm9A3NjrV4U |
| 48 | 3 | Andreas Steffen | 655KXTkuiTpZP00qsfKuqh6EofkQ+89YK6qZNnxAeJ/mB9Dlkq9ELPjigNlZfUkd |
| 49 | 3 | Andreas Steffen | Ky2fBJkwdKLb75WermM3tOYts0X06j7M3WX8DdVsGgIrzC57shAiD9nyhrUNHB15 |
| 50 | 3 | Andreas Steffen | b9IymR84GW4BJofKVW2GJVeUyLnh8YP33OUx6F5aEqweSbi5dGtbDbr0WmK6LmNw |
| 51 | 3 | Andreas Steffen | dKQyv+hickbXGTWifAEktjpTApYjBBB6TZgiAW2P4T3dMq2ciQUbhCl1xWUlWF+2 |
| 52 | 3 | Andreas Steffen | iZbfFrcMb4dVrWOYbQRfvURmCkvJWsXHiijK8E+pmCDCruQg7TuRlIdXCRhSZrzY |
| 53 | 3 | Andreas Steffen | +pLcY7mKBfyCvrmYmmCMRQQXeTDnGI/9VhHJ6icK6Mqy2BwRVFj9FmSsAHmF9gkL |
| 54 | 3 | Andreas Steffen | hcaPlsgpLqaoK41FcJHjMbJIjWKaHkFXMQ0K943cM0ivB3EqRG68AptqH1QxkIi6 |
| 55 | 3 | Andreas Steffen | haUuQL6Nsl/tXo4VwyiVpm1faRQW5Re9L6KbEhLgnT3JeAft0zOOlHwx5myBDAxa |
| 56 | 3 | Andreas Steffen | s8LP9H/EyzpO4uyd1eHlqZvGEmlt9lhOikLwEohWDoZIpWFKrtfzciQMOugLq4m4 |
| 57 | 3 | Andreas Steffen | n+ueVo25rvq6MRwncj0FCwlt0nAhWeP8hQYTzhgFsBeheM4OaWVRhRPQmqYFrLRZ |
| 58 | 3 | Andreas Steffen | grvkgGIQd2IDKhjqCI7gpOi/KRG5RbnyvO4zaqLNy16Lk4exZ2iin19YQpmU613j |
| 59 | 3 | Andreas Steffen | EVLsMoRTQl2tE+aB0GJ0BpE3u0Aqnrp6ZhCJmK8CybfYAGhV5sly59Cds7QtIw8r |
| 60 | 3 | Andreas Steffen | 6pXl7Wd0q2sMFsUnqadcCwqoeOciqU+AwvQ+X2g4eilxV6D2TkLMMBUOYi5BqNdj |
| 61 | 3 | Andreas Steffen | a7pJAnUUMyEYvDXhMUYnjGlK3RFKHFCzCalQN0s5JLRTpLnTTy70TtvMaDJAWCwG |
| 62 | 3 | Andreas Steffen | OShSbNqr0zGNfnCsFjuppZ+5tQd7GRCgjL2uG0CDTIKEq5vmaH1d3FOldJX2uYYA |
| 63 | 3 | Andreas Steffen | O6QOKIThuiH3C0OgAQoLGoArsmFymtBXHxPZSjtE5SR+1YVCr4UEdGlSt2efJoxm |
| 64 | 3 | Andreas Steffen | eBaYki03CF2pSm7EDHxbEjDC9E3AeOfUW6Iq4dTGThjGNGnnBIbpv0mSdXFzWcZU |
| 65 | 3 | Andreas Steffen | 3rwQo51EA4HBAACSCPjwAOUCAOCCCOP/gCDzxzweEOByCAACeEP1wF+DxhwBiQTw |
| 66 | 3 | Andreas Steffen | AP/0AAQFx/z+SACPgR+ASePwOAOgAAQBwDiAV0OOCADwB0eOgAeAOORwMAPzwOQS |
| 67 | 3 | Andreas Steffen | CBuMAQOB+Px/x+AuCeRweeADzwACPyCP+RyQhgBzwOCBwSBwOB+SeQAQCOBwACAB |
| 68 | 3 | Andreas Steffen | 0eByABwQBwQAAeCBwgAAB/wACDwNyPgeQOPwAAR+OAR+AB+COAQCBx+QeB+R+B+Q |
| 69 | 3 | Andreas Steffen | CADjxwACPiARvwOBwQDjggcY7EEgAEHjcYAcogEHgccDjgcDg8fgAnjgAgfkgEgc |
| 70 | 3 | Andreas Steffen | DnjgAEbAn8ArnAhAAcAkAEgADkgAD8DgkDgkcDnkcE88jkjkgjgD9ccAg8cc8jjr |
| 71 | 3 | Andreas Steffen | kcgkABED8gAD8H/n8gAAj8AgEHj8D8D89Dfg4DAgEEAAgAj8HgkgAj8HgcHodAEk |
| 72 | 3 | Andreas Steffen | cn8DAL8AD/g//gcDkAEH/AAD/gcDnj8AkD8AcDgErkHjAAcA9AAAAcAcEEEgAAAg |
| 73 | 3 | Andreas Steffen | AYLoAgAEHgkDgYccgbk= |
| 74 | 1 | Andreas Steffen | -----END BLISS PRIVATE KEY----- |
| 75 | 1 | Andreas Steffen | </pre> |
| 76 | 3 | Andreas Steffen | At last let's generate a BLISS-III key with a cryptographic strength of 160 bits with the highest debug level enabled: |
| 77 | 3 | Andreas Steffen | <pre> |
| 78 | 3 | Andreas Steffen | pki --gen --type bliss --size 3 --debug 4 > key3.der |
| 79 | 3 | Andreas Steffen | |
| 80 | 3 | Andreas Steffen | mgf1 based on sha1 is seeded with 20 octets |
| 81 | 3 | Andreas Steffen | mgf1 generated 380 octets |
| 82 | 3 | Andreas Steffen | mgf1 based on sha1 is seeded with 20 octets |
| 83 | 3 | Andreas Steffen | mgf1 generated 380 octets |
| 84 | 3 | Andreas Steffen | l2 norm of s1||s2: 1401, Nk(S): 125552 (128626 max) |
| 85 | 3 | Andreas Steffen | |
| 86 | 3 | Andreas Steffen | secret key generation succeeded after 1 trial |
| 87 | 3 | Andreas Steffen | i f g a F G A |
| 88 | 3 | Andreas Steffen | 0 -1 1 11932 6730 11344 6400 |
| 89 | 3 | Andreas Steffen | 1 1 0 2227 1206 9396 6244 |
| 90 | 3 | Andreas Steffen | 2 -1 2 4844 496 414 4411 |
| 91 | 3 | Andreas Steffen | 3 -1 0 2768 2813 1412 6619 |
| 92 | 3 | Andreas Steffen | 4 0 2 3583 2753 3520 9237 |
| 93 | 3 | Andreas Steffen | 5 0 2 10160 2434 9512 8688 |
| 94 | 3 | Andreas Steffen | 6 0 2 8157 9071 10775 8990 |
| 95 | 3 | Andreas Steffen | 7 0 0 3862 5091 211 3126 |
| 96 | 3 | Andreas Steffen | 8 -1 0 3045 2278 5799 8812 |
| 97 | 3 | Andreas Steffen | 9 1 0 9942 5685 3335 541 |
| 98 | 3 | Andreas Steffen | 10 0 0 8236 1637 526 5000 |
| 99 | 3 | Andreas Steffen | 11 0 0 8638 9 9539 10618 |
| 100 | 3 | Andreas Steffen | 12 0 -2 11526 11882 8890 8976 |
| 101 | 3 | Andreas Steffen | 13 -1 0 12180 11895 3538 5231 |
| 102 | 3 | Andreas Steffen | 14 -2 0 6332 4243 11062 243 |
| 103 | 3 | Andreas Steffen | 15 0 0 4083 4302 3400 4000 |
| 104 | 3 | Andreas Steffen | 16 0 2 4545 6031 2766 1708 |
| 105 | 3 | Andreas Steffen | 17 0 0 1495 4119 8792 11954 |
| 106 | 3 | Andreas Steffen | 18 1 -2 5664 9450 5151 6621 |
| 107 | 3 | Andreas Steffen | 19 0 0 3580 1963 11193 1552 |
| 108 | 3 | Andreas Steffen | 20 -1 -2 7090 5950 10318 8445 |
| 109 | 3 | Andreas Steffen | 21 0 0 5180 8190 7147 11145 |
| 110 | 3 | Andreas Steffen | 22 0 -2 8455 12226 27 10533 |
| 111 | 3 | Andreas Steffen | 23 0 0 810 4585 6578 3333 |
| 112 | 3 | Andreas Steffen | 24 1 0 5316 9595 2034 7088 |
| 113 | 3 | Andreas Steffen | 25 0 0 10072 11746 10425 9554 |
| 114 | 3 | Andreas Steffen | 26 -1 0 4544 5888 7751 8402 |
| 115 | 3 | Andreas Steffen | 27 0 0 9529 10638 5983 9509 |
| 116 | 3 | Andreas Steffen | 28 0 0 6832 8019 5519 1124 |
| 117 | 3 | Andreas Steffen | 29 1 -2 8900 2356 4475 4326 |
| 118 | 3 | Andreas Steffen | 30 0 -2 4438 7452 2418 406 |
| 119 | 3 | Andreas Steffen | 31 -1 -2 363 9949 6078 3369 |
| 120 | 3 | Andreas Steffen | 32 0 0 6032 9713 11653 12232 |
| 121 | 3 | Andreas Steffen | 33 0 0 1342 11748 11094 4727 |
| 122 | 3 | Andreas Steffen | 34 -1 -2 780 9506 2687 5713 |
| 123 | 3 | Andreas Steffen | 35 1 0 1114 11518 5003 1173 |
| 124 | 3 | Andreas Steffen | 36 1 0 11561 8458 9766 5255 |
| 125 | 3 | Andreas Steffen | 37 0 0 932 4680 7848 10211 |
| 126 | 3 | Andreas Steffen | 38 0 0 4748 4235 6832 9975 |
| 127 | 3 | Andreas Steffen | 39 1 2 6338 9116 1371 9287 |
| 128 | 3 | Andreas Steffen | 40 0 0 9216 11714 11657 4532 |
| 129 | 3 | Andreas Steffen | 41 1 -2 1100 6203 6951 9887 |
| 130 | 3 | Andreas Steffen | 42 1 0 11955 9307 124 11984 |
| 131 | 3 | Andreas Steffen | 43 0 0 6550 6220 9948 11200 |
| 132 | 3 | Andreas Steffen | 44 1 0 10183 7920 2231 2050 |
| 133 | 3 | Andreas Steffen | 45 0 0 5858 10736 11843 4851 |
| 134 | 3 | Andreas Steffen | 46 1 0 4402 6459 5976 5509 |
| 135 | 3 | Andreas Steffen | 47 1 2 3354 2643 9397 11716 |
| 136 | 3 | Andreas Steffen | 48 1 -2 9937 3908 1174 11478 |
| 137 | 3 | Andreas Steffen | 49 2 0 11688 9298 10680 1833 |
| 138 | 3 | Andreas Steffen | 50 -1 2 5348 4731 12240 5286 |
| 139 | 3 | Andreas Steffen | 51 0 0 4594 1469 10189 5043 |
| 140 | 3 | Andreas Steffen | 52 0 2 6324 1006 6445 3268 |
| 141 | 3 | Andreas Steffen | 53 0 -4 2137 2707 4158 569 |
| 142 | 3 | Andreas Steffen | 54 -1 -2 340 2232 4643 9852 |
| 143 | 3 | Andreas Steffen | 55 -1 0 1784 8290 9620 3129 |
| 144 | 3 | Andreas Steffen | 56 1 0 7203 5610 11341 749 |
| 145 | 3 | Andreas Steffen | 57 0 0 6651 12057 10851 5621 |
| 146 | 3 | Andreas Steffen | 58 -1 0 383 5516 9861 2272 |
| 147 | 3 | Andreas Steffen | 59 2 0 10893 8086 1452 140 |
| 148 | 3 | Andreas Steffen | 60 0 0 7921 10970 6955 9293 |
| 149 | 3 | Andreas Steffen | 61 1 -2 4243 10170 5305 9178 |
| 150 | 3 | Andreas Steffen | 62 -1 2 3565 2730 3858 11021 |
| 151 | 3 | Andreas Steffen | 63 0 0 5697 1308 7157 8076 |
| 152 | 3 | Andreas Steffen | 64 0 -2 4079 5666 9079 5400 |
| 153 | 3 | Andreas Steffen | 65 1 0 3653 2895 1244 11606 |
| 154 | 3 | Andreas Steffen | 66 0 2 9829 6670 4713 3470 |
| 155 | 3 | Andreas Steffen | 67 1 -2 11728 5737 6142 2111 |
| 156 | 3 | Andreas Steffen | 68 1 -2 7403 10194 2903 2562 |
| 157 | 3 | Andreas Steffen | 69 -2 0 770 9857 301 4108 |
| 158 | 3 | Andreas Steffen | 70 0 -2 6771 2653 10239 2130 |
| 159 | 3 | Andreas Steffen | 71 0 0 7855 4463 7362 9248 |
| 160 | 3 | Andreas Steffen | 72 -1 0 10880 6688 3127 311 |
| 161 | 3 | Andreas Steffen | 73 -1 2 4691 8128 533 8290 |
| 162 | 3 | Andreas Steffen | 74 -1 -2 4037 3558 115 10006 |
| 163 | 3 | Andreas Steffen | 75 0 0 2284 389 6473 3776 |
| 164 | 3 | Andreas Steffen | 76 0 0 5390 9091 1720 7047 |
| 165 | 3 | Andreas Steffen | 77 0 2 4988 1314 11101 4376 |
| 166 | 3 | Andreas Steffen | 78 1 0 5858 6929 7217 3009 |
| 167 | 3 | Andreas Steffen | 79 0 0 8276 9115 9758 8600 |
| 168 | 3 | Andreas Steffen | 80 0 0 1719 3490 6518 2847 |
| 169 | 3 | Andreas Steffen | 81 0 0 3145 16 2434 10905 |
| 170 | 3 | Andreas Steffen | 82 1 0 12177 5643 1293 9983 |
| 171 | 3 | Andreas Steffen | 83 0 2 8860 7027 7247 4144 |
| 172 | 3 | Andreas Steffen | 84 0 -2 8029 11886 5161 8312 |
| 173 | 3 | Andreas Steffen | 85 0 0 6660 8970 4777 9518 |
| 174 | 3 | Andreas Steffen | 86 0 2 8940 2217 8996 6495 |
| 175 | 3 | Andreas Steffen | 87 0 0 4623 2243 11869 10300 |
| 176 | 3 | Andreas Steffen | 88 0 4 11841 4074 6347 3751 |
| 177 | 3 | Andreas Steffen | 89 -1 0 2220 12271 2346 3966 |
| 178 | 3 | Andreas Steffen | 90 0 2 11997 617 8162 8020 |
| 179 | 3 | Andreas Steffen | 91 0 -2 4335 73 10232 9399 |
| 180 | 3 | Andreas Steffen | 92 1 2 8016 10780 11912 11369 |
| 181 | 3 | Andreas Steffen | 93 0 -2 4302 7923 717 7152 |
| 182 | 3 | Andreas Steffen | 94 0 -2 8014 1252 8311 11638 |
| 183 | 3 | Andreas Steffen | 95 1 0 11580 975 1679 2699 |
| 184 | 3 | Andreas Steffen | 96 1 2 6246 3336 161 6745 |
| 185 | 3 | Andreas Steffen | 97 -1 -4 5081 9817 11892 6259 |
| 186 | 3 | Andreas Steffen | 98 0 0 4544 10997 12278 4499 |
| 187 | 3 | Andreas Steffen | 99 0 2 1616 9495 12225 10213 |
| 188 | 3 | Andreas Steffen | 100 -1 -2 8533 8912 6448 9929 |
| 189 | 3 | Andreas Steffen | 101 0 2 8850 8093 11649 9665 |
| 190 | 3 | Andreas Steffen | 102 1 -4 9776 4225 8805 9906 |
| 191 | 3 | Andreas Steffen | 103 -1 0 12203 5021 12232 10353 |
| 192 | 3 | Andreas Steffen | 104 1 2 1285 10557 8597 2897 |
| 193 | 3 | Andreas Steffen | 105 1 0 5553 11162 5268 10387 |
| 194 | 3 | Andreas Steffen | 106 -1 -2 6413 10365 11905 6694 |
| 195 | 3 | Andreas Steffen | 107 0 -2 1915 8797 5109 10630 |
| 196 | 3 | Andreas Steffen | 108 1 2 5668 7809 10108 689 |
| 197 | 3 | Andreas Steffen | 109 0 -2 5724 6433 9119 9062 |
| 198 | 3 | Andreas Steffen | 110 1 0 3193 2998 10987 4238 |
| 199 | 3 | Andreas Steffen | 111 0 2 3218 6756 10221 11532 |
| 200 | 3 | Andreas Steffen | 112 0 0 11475 1061 3999 2494 |
| 201 | 3 | Andreas Steffen | 113 0 0 1751 10398 9032 10926 |
| 202 | 3 | Andreas Steffen | 114 0 0 5049 4368 3557 9980 |
| 203 | 3 | Andreas Steffen | 115 0 0 6973 10707 10291 4631 |
| 204 | 3 | Andreas Steffen | 116 0 0 826 2759 8952 11976 |
| 205 | 3 | Andreas Steffen | 117 -2 0 11077 1210 8027 7898 |
| 206 | 3 | Andreas Steffen | 118 0 0 3361 8733 5169 237 |
| 207 | 3 | Andreas Steffen | 119 0 0 9447 10875 12077 11281 |
| 208 | 3 | Andreas Steffen | 120 0 0 7154 928 564 11601 |
| 209 | 3 | Andreas Steffen | 121 -1 -2 5099 1695 5523 11879 |
| 210 | 3 | Andreas Steffen | 122 0 -2 5533 6614 4882 7444 |
| 211 | 3 | Andreas Steffen | 123 0 2 2416 2221 11163 3679 |
| 212 | 3 | Andreas Steffen | 124 0 -2 683 8407 7179 11214 |
| 213 | 3 | Andreas Steffen | 125 -1 0 1698 4946 8846 5627 |
| 214 | 3 | Andreas Steffen | 126 0 2 11993 1197 5067 2037 |
| 215 | 3 | Andreas Steffen | 127 -1 2 11131 10689 4543 8346 |
| 216 | 3 | Andreas Steffen | 128 1 0 11684 12052 5700 5576 |
| 217 | 3 | Andreas Steffen | 129 0 0 11081 7285 5758 2882 |
| 218 | 3 | Andreas Steffen | 130 0 0 2204 10550 10764 10396 |
| 219 | 3 | Andreas Steffen | 131 0 0 5413 6834 237 9705 |
| 220 | 3 | Andreas Steffen | 132 0 0 3139 9589 3580 1000 |
| 221 | 3 | Andreas Steffen | 133 1 0 2435 10845 11335 4375 |
| 222 | 3 | Andreas Steffen | 134 0 0 5835 9461 5820 8967 |
| 223 | 3 | Andreas Steffen | 135 1 2 1986 7566 6638 7219 |
| 224 | 3 | Andreas Steffen | 136 1 2 12005 279 4775 854 |
| 225 | 3 | Andreas Steffen | 137 0 -2 11470 3603 1399 4755 |
| 226 | 3 | Andreas Steffen | 138 0 4 3665 10794 4373 10453 |
| 227 | 3 | Andreas Steffen | 139 0 0 6909 8265 11931 11831 |
| 228 | 3 | Andreas Steffen | 140 1 2 9201 4238 3547 9596 |
| 229 | 3 | Andreas Steffen | 141 1 -2 7577 11197 9585 4684 |
| 230 | 3 | Andreas Steffen | 142 0 0 8947 1967 2051 7873 |
| 231 | 3 | Andreas Steffen | 143 0 -2 9195 2467 6347 7903 |
| 232 | 3 | Andreas Steffen | 144 1 2 11017 8525 11401 10043 |
| 233 | 3 | Andreas Steffen | 145 -1 0 1786 7054 2174 5272 |
| 234 | 3 | Andreas Steffen | 146 0 0 2541 11091 10944 11808 |
| 235 | 3 | Andreas Steffen | 147 0 0 1685 12142 9116 11391 |
| 236 | 3 | Andreas Steffen | 148 0 -2 9324 10699 11938 1090 |
| 237 | 3 | Andreas Steffen | 149 1 -2 6706 2541 7886 7480 |
| 238 | 3 | Andreas Steffen | 150 1 0 10550 1341 3839 5373 |
| 239 | 3 | Andreas Steffen | 151 -1 -2 4665 7629 5217 2934 |
| 240 | 3 | Andreas Steffen | 152 0 2 1311 6833 4048 11099 |
| 241 | 3 | Andreas Steffen | 153 1 0 11994 1783 10226 2549 |
| 242 | 3 | Andreas Steffen | 154 1 0 9953 5962 11300 10712 |
| 243 | 3 | Andreas Steffen | 155 0 -2 2781 11449 395 11045 |
| 244 | 3 | Andreas Steffen | 156 -1 4 6768 7744 9122 6955 |
| 245 | 3 | Andreas Steffen | 157 0 -2 1288 10720 7913 9198 |
| 246 | 3 | Andreas Steffen | 158 0 2 3735 3959 3762 4924 |
| 247 | 3 | Andreas Steffen | 159 1 2 2817 4147 6807 6198 |
| 248 | 3 | Andreas Steffen | 160 0 0 2935 11500 11190 4051 |
| 249 | 3 | Andreas Steffen | 161 0 2 1193 7795 11414 3350 |
| 250 | 3 | Andreas Steffen | 162 -1 -2 757 3411 9464 4481 |
| 251 | 3 | Andreas Steffen | 163 0 -2 3830 7004 11979 593 |
| 252 | 3 | Andreas Steffen | 164 0 0 11945 57 6438 9168 |
| 253 | 3 | Andreas Steffen | 165 -2 2 1844 173 7130 9844 |
| 254 | 3 | Andreas Steffen | 166 1 0 1055 4376 673 559 |
| 255 | 3 | Andreas Steffen | 167 1 0 665 1744 11877 9442 |
| 256 | 3 | Andreas Steffen | 168 -1 0 190 3421 9077 5294 |
| 257 | 3 | Andreas Steffen | 169 -1 0 5948 4923 10003 9323 |
| 258 | 3 | Andreas Steffen | 170 0 -2 66 3154 7238 10273 |
| 259 | 3 | Andreas Steffen | 171 1 0 3608 7307 8272 11128 |
| 260 | 3 | Andreas Steffen | 172 0 -2 11068 10669 7822 12269 |
| 261 | 3 | Andreas Steffen | 173 -1 -2 2289 5725 7793 11084 |
| 262 | 3 | Andreas Steffen | 174 0 -2 2045 9528 5770 5250 |
| 263 | 3 | Andreas Steffen | 175 0 -2 5369 1937 9741 7669 |
| 264 | 3 | Andreas Steffen | 176 0 0 5495 973 32 8740 |
| 265 | 3 | Andreas Steffen | 177 1 -2 187 6219 10487 11605 |
| 266 | 3 | Andreas Steffen | 178 0 0 6664 3891 6930 9183 |
| 267 | 3 | Andreas Steffen | 179 0 -2 8951 3731 4350 10057 |
| 268 | 3 | Andreas Steffen | 180 0 -2 2119 8064 2295 14 |
| 269 | 3 | Andreas Steffen | 181 0 0 5587 7068 12132 419 |
| 270 | 3 | Andreas Steffen | 182 1 0 5551 9660 4283 5818 |
| 271 | 3 | Andreas Steffen | 183 1 -2 58 319 9240 1724 |
| 272 | 3 | Andreas Steffen | 184 0 2 9694 6238 4742 12274 |
| 273 | 3 | Andreas Steffen | 185 2 2 1752 10949 7406 7643 |
| 274 | 3 | Andreas Steffen | 186 0 2 4551 4296 5533 7516 |
| 275 | 3 | Andreas Steffen | 187 0 0 5809 2080 4616 3169 |
| 276 | 3 | Andreas Steffen | 188 0 -2 4805 9682 4940 10345 |
| 277 | 3 | Andreas Steffen | 189 0 4 5232 10223 8937 9376 |
| 278 | 3 | Andreas Steffen | 190 0 -2 4985 6043 7853 528 |
| 279 | 3 | Andreas Steffen | 191 1 0 11937 4497 1366 6015 |
| 280 | 3 | Andreas Steffen | 192 1 0 7724 7554 12130 1918 |
| 281 | 3 | Andreas Steffen | 193 0 -2 2011 4752 4070 3130 |
| 282 | 3 | Andreas Steffen | 194 0 0 8272 1015 1803 3973 |
| 283 | 3 | Andreas Steffen | 195 -1 0 7832 7988 9436 5558 |
| 284 | 3 | Andreas Steffen | 196 0 -4 8854 10413 11890 8575 |
| 285 | 3 | Andreas Steffen | 197 0 0 2277 3600 263 11719 |
| 286 | 3 | Andreas Steffen | 198 -1 2 2986 1000 9583 11721 |
| 287 | 3 | Andreas Steffen | 199 0 2 2907 8991 11579 11775 |
| 288 | 3 | Andreas Steffen | 200 0 2 7872 2207 9525 1285 |
| 289 | 3 | Andreas Steffen | 201 1 0 7562 9107 2777 2830 |
| 290 | 3 | Andreas Steffen | 202 -2 -2 10678 10608 9041 10880 |
| 291 | 3 | Andreas Steffen | 203 0 0 656 11804 3455 2400 |
| 292 | 3 | Andreas Steffen | 204 -1 -2 4799 3910 3626 6180 |
| 293 | 3 | Andreas Steffen | 205 -1 0 1998 5423 2614 5813 |
| 294 | 3 | Andreas Steffen | 206 0 0 2327 11665 8051 2567 |
| 295 | 3 | Andreas Steffen | 207 0 0 282 6807 4478 1129 |
| 296 | 3 | Andreas Steffen | 208 0 -2 7967 3811 12284 6446 |
| 297 | 3 | Andreas Steffen | 209 -1 0 3169 11501 11972 11650 |
| 298 | 3 | Andreas Steffen | 210 -1 0 2614 4186 5549 10021 |
| 299 | 3 | Andreas Steffen | 211 1 -2 11856 11417 10104 6753 |
| 300 | 3 | Andreas Steffen | 212 1 0 3692 2680 3800 12107 |
| 301 | 3 | Andreas Steffen | 213 0 2 4639 5506 11526 6189 |
| 302 | 3 | Andreas Steffen | 214 0 0 6373 9147 2814 9738 |
| 303 | 3 | Andreas Steffen | 215 0 0 1942 1124 9011 3124 |
| 304 | 3 | Andreas Steffen | 216 0 2 5163 558 11376 4381 |
| 305 | 3 | Andreas Steffen | 217 0 0 11687 9612 8623 84 |
| 306 | 3 | Andreas Steffen | 218 0 0 8537 3843 11615 35 |
| 307 | 3 | Andreas Steffen | 219 1 0 11885 4846 3711 6409 |
| 308 | 3 | Andreas Steffen | 220 0 2 9728 8703 2262 5270 |
| 309 | 3 | Andreas Steffen | 221 -1 -2 4928 745 4084 3453 |
| 310 | 3 | Andreas Steffen | 222 0 2 2383 5711 4946 10846 |
| 311 | 3 | Andreas Steffen | 223 0 -2 2480 3190 11514 2446 |
| 312 | 3 | Andreas Steffen | 224 0 2 8786 4156 10444 381 |
| 313 | 3 | Andreas Steffen | 225 0 0 7294 3059 859 5500 |
| 314 | 3 | Andreas Steffen | 226 0 -2 2793 4752 4311 11196 |
| 315 | 3 | Andreas Steffen | 227 -1 2 9428 8892 6184 2715 |
| 316 | 3 | Andreas Steffen | 228 1 0 3240 6263 8476 7279 |
| 317 | 3 | Andreas Steffen | 229 0 0 2533 993 6898 5972 |
| 318 | 3 | Andreas Steffen | 230 -1 2 6513 1130 623 3622 |
| 319 | 3 | Andreas Steffen | 231 -1 0 2175 455 8066 855 |
| 320 | 3 | Andreas Steffen | 232 1 -2 8930 11192 11277 6039 |
| 321 | 3 | Andreas Steffen | 233 -1 0 10052 9546 1723 3691 |
| 322 | 3 | Andreas Steffen | 234 0 0 12282 10488 5953 11501 |
| 323 | 3 | Andreas Steffen | 235 1 0 966 2764 1478 7550 |
| 324 | 3 | Andreas Steffen | 236 0 4 2689 4295 136 7671 |
| 325 | 3 | Andreas Steffen | 237 0 0 2735 10452 7686 5468 |
| 326 | 3 | Andreas Steffen | 238 -1 0 7155 3804 11767 4710 |
| 327 | 3 | Andreas Steffen | 239 1 2 6875 1049 8317 1238 |
| 328 | 3 | Andreas Steffen | 240 -1 -2 5800 4804 10126 7221 |
| 329 | 3 | Andreas Steffen | 241 0 2 10256 8623 4292 11309 |
| 330 | 3 | Andreas Steffen | 242 -1 0 9012 8378 9611 5688 |
| 331 | 3 | Andreas Steffen | 243 -1 2 4014 1882 3226 12134 |
| 332 | 3 | Andreas Steffen | 244 0 2 11698 2629 1993 9817 |
| 333 | 3 | Andreas Steffen | 245 1 -2 9293 4184 3392 10739 |
| 334 | 3 | Andreas Steffen | 246 0 2 93 852 8664 11953 |
| 335 | 3 | Andreas Steffen | 247 0 2 6230 8044 8507 6969 |
| 336 | 3 | Andreas Steffen | 248 -1 2 6093 7622 10297 8445 |
| 337 | 3 | Andreas Steffen | 249 -1 0 10974 7821 3675 3517 |
| 338 | 3 | Andreas Steffen | 250 -1 -2 4760 11952 9509 11495 |
| 339 | 3 | Andreas Steffen | 251 0 -2 7410 5638 8286 2604 |
| 340 | 3 | Andreas Steffen | 252 0 0 313 2955 7834 4178 |
| 341 | 3 | Andreas Steffen | 253 -1 0 9733 3273 12249 11493 |
| 342 | 3 | Andreas Steffen | 254 -1 0 682 9048 9531 3876 |
| 343 | 3 | Andreas Steffen | 255 1 -2 2283 179 4322 9567 |
| 344 | 3 | Andreas Steffen | 256 0 0 10470 1633 2290 9062 |
| 345 | 3 | Andreas Steffen | 257 0 -2 11005 5584 7880 6991 |
| 346 | 3 | Andreas Steffen | 258 1 -2 2732 7686 7623 8563 |
| 347 | 3 | Andreas Steffen | 259 0 0 8845 9994 6380 2032 |
| 348 | 3 | Andreas Steffen | 260 0 -2 9527 785 4071 4639 |
| 349 | 3 | Andreas Steffen | 261 0 -2 7141 5116 474 9863 |
| 350 | 3 | Andreas Steffen | 262 0 0 8896 9356 8790 4233 |
| 351 | 3 | Andreas Steffen | 263 0 -2 8781 5058 11323 5758 |
| 352 | 3 | Andreas Steffen | 264 -1 -2 2106 4848 5472 3773 |
| 353 | 3 | Andreas Steffen | 265 0 0 10312 2028 1706 5806 |
| 354 | 3 | Andreas Steffen | 266 -1 0 11587 11556 10433 7614 |
| 355 | 3 | Andreas Steffen | 267 -1 0 9354 4702 4673 11174 |
| 356 | 3 | Andreas Steffen | 268 1 2 4179 310 1572 9202 |
| 357 | 3 | Andreas Steffen | 269 0 0 231 7881 4637 8778 |
| 358 | 3 | Andreas Steffen | 270 0 0 10643 12282 3262 11823 |
| 359 | 3 | Andreas Steffen | 271 0 2 4803 573 11021 12201 |
| 360 | 3 | Andreas Steffen | 272 -1 0 11942 2736 1772 881 |
| 361 | 3 | Andreas Steffen | 273 1 0 10172 5565 7021 1748 |
| 362 | 3 | Andreas Steffen | 274 0 2 8091 902 11967 2343 |
| 363 | 3 | Andreas Steffen | 275 1 0 6507 2055 1543 1125 |
| 364 | 3 | Andreas Steffen | 276 0 0 8363 4684 8421 7891 |
| 365 | 3 | Andreas Steffen | 277 0 2 11435 7507 3108 1495 |
| 366 | 3 | Andreas Steffen | 278 1 0 1121 5376 1638 8545 |
| 367 | 3 | Andreas Steffen | 279 1 2 6659 7231 2291 9356 |
| 368 | 3 | Andreas Steffen | 280 2 -2 11535 5948 8451 10276 |
| 369 | 3 | Andreas Steffen | 281 0 2 9996 5929 11267 11752 |
| 370 | 3 | Andreas Steffen | 282 0 0 9341 11999 10535 9922 |
| 371 | 3 | Andreas Steffen | 283 0 0 1156 407 2491 5743 |
| 372 | 3 | Andreas Steffen | 284 1 0 10878 9742 11436 7146 |
| 373 | 3 | Andreas Steffen | 285 1 0 4269 10191 6723 1057 |
| 374 | 3 | Andreas Steffen | 286 0 0 3150 6385 11151 8222 |
| 375 | 3 | Andreas Steffen | 287 -1 2 10602 12270 1942 11540 |
| 376 | 3 | Andreas Steffen | 288 -1 0 4149 9389 5193 155 |
| 377 | 3 | Andreas Steffen | 289 1 0 2220 1914 7033 2039 |
| 378 | 3 | Andreas Steffen | 290 1 -2 5849 9681 7990 10354 |
| 379 | 3 | Andreas Steffen | 291 0 -2 578 1167 9422 2925 |
| 380 | 3 | Andreas Steffen | 292 0 2 2784 4352 1474 8850 |
| 381 | 3 | Andreas Steffen | 293 0 2 2831 7803 7941 10471 |
| 382 | 3 | Andreas Steffen | 294 1 -2 1505 5309 1529 10706 |
| 383 | 3 | Andreas Steffen | 295 -1 -2 12152 3117 1462 5319 |
| 384 | 3 | Andreas Steffen | 296 0 0 12015 10147 2163 3011 |
| 385 | 3 | Andreas Steffen | 297 0 2 12204 3215 10166 351 |
| 386 | 3 | Andreas Steffen | 298 -1 0 3251 7021 9039 9355 |
| 387 | 3 | Andreas Steffen | 299 0 0 5488 2986 1862 5927 |
| 388 | 3 | Andreas Steffen | 300 1 0 7988 280 3983 11996 |
| 389 | 3 | Andreas Steffen | 301 0 -2 11691 944 6647 7206 |
| 390 | 3 | Andreas Steffen | 302 0 -2 5811 8894 11593 4438 |
| 391 | 3 | Andreas Steffen | 303 1 2 11242 8285 3494 3099 |
| 392 | 3 | Andreas Steffen | 304 0 0 1369 3781 11946 9679 |
| 393 | 3 | Andreas Steffen | 305 0 0 4923 855 11924 2443 |
| 394 | 3 | Andreas Steffen | 306 0 0 10077 6525 5892 12143 |
| 395 | 3 | Andreas Steffen | 307 0 0 5765 923 7601 5041 |
| 396 | 3 | Andreas Steffen | 308 -1 0 11585 4403 7020 7236 |
| 397 | 3 | Andreas Steffen | 309 -1 0 9508 11281 9550 8744 |
| 398 | 3 | Andreas Steffen | 310 -1 2 8015 7011 6196 851 |
| 399 | 3 | Andreas Steffen | 311 0 0 10282 6674 7084 1139 |
| 400 | 3 | Andreas Steffen | 312 -1 0 366 5463 5297 11037 |
| 401 | 3 | Andreas Steffen | 313 0 0 3271 3185 6778 10142 |
| 402 | 3 | Andreas Steffen | 314 -1 0 6295 3530 2128 3092 |
| 403 | 3 | Andreas Steffen | 315 -1 2 2446 9761 5698 9652 |
| 404 | 3 | Andreas Steffen | 316 0 0 6414 6084 11668 2854 |
| 405 | 3 | Andreas Steffen | 317 1 0 7954 11099 5621 8453 |
| 406 | 3 | Andreas Steffen | 318 1 0 8505 3817 6471 8585 |
| 407 | 3 | Andreas Steffen | 319 0 -2 10555 260 7709 1873 |
| 408 | 3 | Andreas Steffen | 320 0 0 4679 8577 2591 3492 |
| 409 | 3 | Andreas Steffen | 321 1 0 4517 10562 7356 10826 |
| 410 | 3 | Andreas Steffen | 322 0 0 5129 7378 6792 11094 |
| 411 | 3 | Andreas Steffen | 323 1 0 11014 1117 906 7306 |
| 412 | 3 | Andreas Steffen | 324 -1 -2 8930 3044 7558 1690 |
| 413 | 3 | Andreas Steffen | 325 0 -2 12034 5641 5602 3833 |
| 414 | 3 | Andreas Steffen | 326 1 0 4468 8161 11613 1703 |
| 415 | 3 | Andreas Steffen | 327 0 0 9452 5643 6465 759 |
| 416 | 3 | Andreas Steffen | 328 -1 0 4250 1062 8885 5366 |
| 417 | 3 | Andreas Steffen | 329 0 0 2562 11062 10606 12050 |
| 418 | 3 | Andreas Steffen | 330 0 0 11004 5092 1145 9690 |
| 419 | 3 | Andreas Steffen | 331 0 0 3971 4167 9338 10914 |
| 420 | 3 | Andreas Steffen | 332 0 -2 4640 2905 8263 8180 |
| 421 | 3 | Andreas Steffen | 333 -1 2 11466 11858 4479 8686 |
| 422 | 3 | Andreas Steffen | 334 -2 -2 2263 10527 11374 8335 |
| 423 | 3 | Andreas Steffen | 335 -1 2 8803 10486 6140 10827 |
| 424 | 3 | Andreas Steffen | 336 0 0 1608 10434 277 3299 |
| 425 | 3 | Andreas Steffen | 337 0 0 8846 4037 5405 10610 |
| 426 | 3 | Andreas Steffen | 338 0 2 2025 9028 11374 249 |
| 427 | 3 | Andreas Steffen | 339 0 0 7495 5760 9448 3603 |
| 428 | 3 | Andreas Steffen | 340 0 2 15 10858 10180 53 |
| 429 | 3 | Andreas Steffen | 341 0 0 2216 822 8232 10505 |
| 430 | 3 | Andreas Steffen | 342 0 0 4552 6213 8198 2721 |
| 431 | 3 | Andreas Steffen | 343 -1 0 8537 12065 4985 6616 |
| 432 | 3 | Andreas Steffen | 344 1 0 59 1083 5343 4975 |
| 433 | 3 | Andreas Steffen | 345 0 0 6820 2485 7426 8044 |
| 434 | 3 | Andreas Steffen | 346 0 -2 79 3592 780 2094 |
| 435 | 3 | Andreas Steffen | 347 0 2 6060 2269 1661 5628 |
| 436 | 3 | Andreas Steffen | 348 -1 0 483 7927 6962 9842 |
| 437 | 3 | Andreas Steffen | 349 -1 0 10399 11975 182 8453 |
| 438 | 3 | Andreas Steffen | 350 1 2 10965 8081 9568 12240 |
| 439 | 3 | Andreas Steffen | 351 -1 0 6177 9642 10608 1217 |
| 440 | 3 | Andreas Steffen | 352 0 -2 3647 7424 6312 11588 |
| 441 | 3 | Andreas Steffen | 353 0 -2 10821 5412 7478 9670 |
| 442 | 3 | Andreas Steffen | 354 0 2 7993 8400 9262 9133 |
| 443 | 3 | Andreas Steffen | 355 0 -2 12183 9287 5467 4145 |
| 444 | 3 | Andreas Steffen | 356 1 -2 11881 11278 2062 2271 |
| 445 | 3 | Andreas Steffen | 357 0 0 11023 11205 4098 9315 |
| 446 | 3 | Andreas Steffen | 358 0 0 2486 1161 4531 11806 |
| 447 | 3 | Andreas Steffen | 359 0 2 7820 8932 2128 6164 |
| 448 | 3 | Andreas Steffen | 360 0 -2 4830 2661 6650 6782 |
| 449 | 3 | Andreas Steffen | 361 0 0 1280 8451 7065 2723 |
| 450 | 3 | Andreas Steffen | 362 1 -4 3505 2948 7690 10249 |
| 451 | 3 | Andreas Steffen | 363 0 0 1931 604 857 11619 |
| 452 | 3 | Andreas Steffen | 364 -1 0 4519 1694 1682 7386 |
| 453 | 3 | Andreas Steffen | 365 1 0 7001 5943 10006 9007 |
| 454 | 3 | Andreas Steffen | 366 1 0 6867 7829 3179 9453 |
| 455 | 3 | Andreas Steffen | 367 0 2 6439 1013 9753 968 |
| 456 | 3 | Andreas Steffen | 368 0 -2 471 7027 6703 4401 |
| 457 | 3 | Andreas Steffen | 369 0 2 10693 6320 2472 5896 |
| 458 | 3 | Andreas Steffen | 370 1 0 6616 5825 5027 4446 |
| 459 | 3 | Andreas Steffen | 371 0 -4 2610 2936 10741 11669 |
| 460 | 3 | Andreas Steffen | 372 -1 0 10505 5607 7619 11326 |
| 461 | 3 | Andreas Steffen | 373 -1 0 8796 8925 6540 641 |
| 462 | 3 | Andreas Steffen | 374 0 0 7862 9942 2067 7361 |
| 463 | 3 | Andreas Steffen | 375 2 2 5933 11598 7281 2337 |
| 464 | 3 | Andreas Steffen | 376 0 0 4397 9644 2961 575 |
| 465 | 3 | Andreas Steffen | 377 0 0 11546 3667 60 496 |
| 466 | 3 | Andreas Steffen | 378 0 2 10359 897 6655 9940 |
| 467 | 3 | Andreas Steffen | 379 0 0 8042 11627 7627 4091 |
| 468 | 3 | Andreas Steffen | 380 0 2 7229 5196 10305 4323 |
| 469 | 3 | Andreas Steffen | 381 0 2 11076 8341 5590 590 |
| 470 | 3 | Andreas Steffen | 382 1 -2 5915 587 3514 10997 |
| 471 | 3 | Andreas Steffen | 383 0 0 4235 5733 1374 7164 |
| 472 | 3 | Andreas Steffen | 384 0 -2 6883 2313 3411 910 |
| 473 | 3 | Andreas Steffen | 385 2 0 5537 5149 391 10153 |
| 474 | 3 | Andreas Steffen | 386 0 0 4786 9993 11959 7183 |
| 475 | 3 | Andreas Steffen | 387 1 0 8660 4137 8672 1422 |
| 476 | 3 | Andreas Steffen | 388 -1 0 10388 8443 6742 3136 |
| 477 | 3 | Andreas Steffen | 389 -1 0 3028 4136 7848 1024 |
| 478 | 3 | Andreas Steffen | 390 -1 -2 3013 9457 3424 5692 |
| 479 | 3 | Andreas Steffen | 391 0 2 6434 10654 246 8185 |
| 480 | 3 | Andreas Steffen | 392 -1 0 5801 5730 384 4298 |
| 481 | 3 | Andreas Steffen | 393 0 0 3559 11131 6623 3040 |
| 482 | 3 | Andreas Steffen | 394 0 2 6911 3462 6279 10768 |
| 483 | 3 | Andreas Steffen | 395 0 0 2559 11098 1487 5746 |
| 484 | 3 | Andreas Steffen | 396 0 0 6942 1081 5465 2597 |
| 485 | 3 | Andreas Steffen | 397 0 0 6852 666 5872 6467 |
| 486 | 3 | Andreas Steffen | 398 0 0 10873 4863 11256 4225 |
| 487 | 3 | Andreas Steffen | 399 1 -2 3670 513 2689 1203 |
| 488 | 3 | Andreas Steffen | 400 1 0 11066 6794 6433 4163 |
| 489 | 3 | Andreas Steffen | 401 0 2 4927 11148 7593 4700 |
| 490 | 3 | Andreas Steffen | 402 0 2 5570 7675 6432 9507 |
| 491 | 3 | Andreas Steffen | 403 0 0 9882 11756 11480 4705 |
| 492 | 3 | Andreas Steffen | 404 1 2 9553 7076 9700 2926 |
| 493 | 3 | Andreas Steffen | 405 -1 2 9678 12074 7468 11797 |
| 494 | 3 | Andreas Steffen | 406 0 2 3955 2530 10255 10763 |
| 495 | 3 | Andreas Steffen | 407 1 0 10843 8488 12022 6421 |
| 496 | 3 | Andreas Steffen | 408 0 0 2514 2611 6629 2177 |
| 497 | 3 | Andreas Steffen | 409 -2 -2 1934 6748 5463 3878 |
| 498 | 3 | Andreas Steffen | 410 1 -2 2677 5860 4847 11948 |
| 499 | 3 | Andreas Steffen | 411 1 0 2065 8327 9459 7023 |
| 500 | 3 | Andreas Steffen | 412 0 0 6908 5681 530 4705 |
| 501 | 3 | Andreas Steffen | 413 0 0 10718 6791 9883 10546 |
| 502 | 3 | Andreas Steffen | 414 -1 0 10338 11007 3468 2087 |
| 503 | 3 | Andreas Steffen | 415 1 0 7817 625 11048 7745 |
| 504 | 3 | Andreas Steffen | 416 0 0 11023 4466 10734 10811 |
| 505 | 3 | Andreas Steffen | 417 0 0 6306 7136 5359 9233 |
| 506 | 3 | Andreas Steffen | 418 0 0 1858 10575 2337 11205 |
| 507 | 3 | Andreas Steffen | 419 0 0 1118 2777 6009 7711 |
| 508 | 3 | Andreas Steffen | 420 1 0 8755 4003 5535 8938 |
| 509 | 3 | Andreas Steffen | 421 -1 0 12259 1775 2505 8171 |
| 510 | 3 | Andreas Steffen | 422 0 0 5186 12038 9054 9707 |
| 511 | 3 | Andreas Steffen | 423 -1 0 8317 9867 2073 6580 |
| 512 | 3 | Andreas Steffen | 424 0 -2 3750 7074 7221 12191 |
| 513 | 3 | Andreas Steffen | 425 -1 -2 7076 6288 3318 10214 |
| 514 | 3 | Andreas Steffen | 426 0 0 4066 8076 12163 3442 |
| 515 | 3 | Andreas Steffen | 427 1 2 5009 366 10803 1339 |
| 516 | 3 | Andreas Steffen | 428 2 0 7392 9060 4955 11591 |
| 517 | 3 | Andreas Steffen | 429 -1 -4 9381 8187 9349 5579 |
| 518 | 3 | Andreas Steffen | 430 0 0 6499 4642 5787 12187 |
| 519 | 3 | Andreas Steffen | 431 1 2 11461 11653 3278 7917 |
| 520 | 3 | Andreas Steffen | 432 1 0 8976 7597 613 6477 |
| 521 | 3 | Andreas Steffen | 433 0 -2 9335 10397 6485 11019 |
| 522 | 3 | Andreas Steffen | 434 0 -2 7590 5554 4787 9128 |
| 523 | 3 | Andreas Steffen | 435 -1 -2 7109 7497 615 8655 |
| 524 | 3 | Andreas Steffen | 436 1 2 5984 709 9806 6063 |
| 525 | 3 | Andreas Steffen | 437 1 0 4451 1057 1327 2187 |
| 526 | 3 | Andreas Steffen | 438 0 0 6532 2071 1809 9139 |
| 527 | 3 | Andreas Steffen | 439 0 0 5657 1586 11166 5121 |
| 528 | 3 | Andreas Steffen | 440 0 0 3926 7845 1167 7773 |
| 529 | 3 | Andreas Steffen | 441 0 0 6347 293 1762 11582 |
| 530 | 3 | Andreas Steffen | 442 0 0 12239 10323 4500 6461 |
| 531 | 3 | Andreas Steffen | 443 1 -2 1977 3819 4233 7946 |
| 532 | 3 | Andreas Steffen | 444 0 0 5851 9874 3996 8822 |
| 533 | 3 | Andreas Steffen | 445 -1 2 3107 3834 5546 9707 |
| 534 | 3 | Andreas Steffen | 446 1 0 5636 11215 11094 5276 |
| 535 | 3 | Andreas Steffen | 447 -1 0 12270 4649 5 11911 |
| 536 | 3 | Andreas Steffen | 448 1 -2 6452 394 1732 3872 |
| 537 | 3 | Andreas Steffen | 449 -2 0 11019 764 1006 10907 |
| 538 | 3 | Andreas Steffen | 450 0 -4 11659 6297 4922 4827 |
| 539 | 3 | Andreas Steffen | 451 1 2 890 9098 11786 3678 |
| 540 | 3 | Andreas Steffen | 452 1 2 7670 7736 2460 10669 |
| 541 | 3 | Andreas Steffen | 453 0 2 2047 7505 11511 3057 |
| 542 | 3 | Andreas Steffen | 454 0 0 12148 5933 9508 9426 |
| 543 | 3 | Andreas Steffen | 455 0 0 5596 3895 2879 7412 |
| 544 | 3 | Andreas Steffen | 456 0 2 6504 2290 4180 9071 |
| 545 | 3 | Andreas Steffen | 457 1 0 8051 946 316 11380 |
| 546 | 3 | Andreas Steffen | 458 0 -2 2479 10389 6976 2480 |
| 547 | 3 | Andreas Steffen | 459 -1 0 10512 10125 6279 6329 |
| 548 | 3 | Andreas Steffen | 460 0 0 4709 6976 7912 6808 |
| 549 | 3 | Andreas Steffen | 461 0 2 6605 9934 10200 10093 |
| 550 | 3 | Andreas Steffen | 462 -1 0 949 7882 3698 1544 |
| 551 | 3 | Andreas Steffen | 463 1 -2 10292 3467 350 3293 |
| 552 | 3 | Andreas Steffen | 464 1 0 6448 9423 1313 2345 |
| 553 | 3 | Andreas Steffen | 465 0 2 692 6812 7583 6050 |
| 554 | 3 | Andreas Steffen | 466 1 0 3635 4184 2733 3816 |
| 555 | 3 | Andreas Steffen | 467 0 0 12067 5816 10128 11192 |
| 556 | 3 | Andreas Steffen | 468 0 0 9902 8712 11275 6813 |
| 557 | 3 | Andreas Steffen | 469 0 0 10938 7970 1902 7019 |
| 558 | 3 | Andreas Steffen | 470 1 0 9568 4228 242 5633 |
| 559 | 3 | Andreas Steffen | 471 0 0 2196 5792 6794 10300 |
| 560 | 3 | Andreas Steffen | 472 0 0 4075 157 8672 2560 |
| 561 | 3 | Andreas Steffen | 473 0 -4 2110 3629 9461 9122 |
| 562 | 3 | Andreas Steffen | 474 -2 -2 3412 4091 7245 4018 |
| 563 | 3 | Andreas Steffen | 475 0 0 11653 40 5765 10897 |
| 564 | 3 | Andreas Steffen | 476 0 0 10799 728 9056 10951 |
| 565 | 3 | Andreas Steffen | 477 0 0 2114 2282 3786 314 |
| 566 | 3 | Andreas Steffen | 478 -1 2 817 10585 8784 10553 |
| 567 | 3 | Andreas Steffen | 479 -1 0 3705 12125 8654 5792 |
| 568 | 3 | Andreas Steffen | 480 0 -4 1808 8664 196 4624 |
| 569 | 3 | Andreas Steffen | 481 -1 2 5841 1907 7238 7769 |
| 570 | 3 | Andreas Steffen | 482 0 0 8769 9263 6687 676 |
| 571 | 3 | Andreas Steffen | 483 0 0 3412 9123 9517 1111 |
| 572 | 3 | Andreas Steffen | 484 -1 0 4204 49 11892 6011 |
| 573 | 3 | Andreas Steffen | 485 -1 0 11196 448 3872 2642 |
| 574 | 3 | Andreas Steffen | 486 0 0 651 2142 3834 6611 |
| 575 | 3 | Andreas Steffen | 487 1 4 7208 10823 6626 12033 |
| 576 | 3 | Andreas Steffen | 488 0 -2 8558 10995 11169 2660 |
| 577 | 3 | Andreas Steffen | 489 0 0 7955 2079 1785 7697 |
| 578 | 3 | Andreas Steffen | 490 1 0 5565 11081 6935 1449 |
| 579 | 3 | Andreas Steffen | 491 0 2 11661 2880 10737 887 |
| 580 | 3 | Andreas Steffen | 492 -1 -2 2546 3372 1543 2424 |
| 581 | 3 | Andreas Steffen | 493 1 0 1667 10715 7245 11246 |
| 582 | 3 | Andreas Steffen | 494 0 0 93 456 1273 2563 |
| 583 | 3 | Andreas Steffen | 495 0 0 3205 2733 6176 7453 |
| 584 | 3 | Andreas Steffen | 496 1 0 12191 7834 2926 12258 |
| 585 | 3 | Andreas Steffen | 497 0 0 3788 5251 935 6085 |
| 586 | 3 | Andreas Steffen | 498 0 0 10114 12224 8954 11395 |
| 587 | 3 | Andreas Steffen | 499 0 -2 7464 568 5744 7972 |
| 588 | 3 | Andreas Steffen | 500 -1 0 1992 6344 10425 3471 |
| 589 | 3 | Andreas Steffen | 501 -1 0 5249 7024 675 3466 |
| 590 | 3 | Andreas Steffen | 502 0 2 8334 3338 1945 4805 |
| 591 | 3 | Andreas Steffen | 503 0 0 8566 837 6796 2416 |
| 592 | 3 | Andreas Steffen | 504 -1 2 1905 3844 2872 1612 |
| 593 | 3 | Andreas Steffen | 505 0 2 377 8680 5459 608 |
| 594 | 3 | Andreas Steffen | 506 0 0 1990 7692 10261 6844 |
| 595 | 3 | Andreas Steffen | 507 0 2 5170 9084 10608 4433 |
| 596 | 3 | Andreas Steffen | 508 0 0 11365 3048 11553 3451 |
| 597 | 3 | Andreas Steffen | 509 0 -2 12098 6095 11214 3125 |
| 598 | 3 | Andreas Steffen | 510 1 -2 1431 2633 10329 5488 |
| 599 | 3 | Andreas Steffen | 511 -1 -2 3846 4226 8410 4614 |
| 600 | 3 | Andreas Steffen | </pre> |
| 601 | 4 | Andreas Steffen | Shown are the 512 small coefficients of the private keys *f* (*s1*) and *g* (*s2*) as well as their Number Theoretic Transforms (NTT) *F* and *G*, respectively. The NTT *A* of the public key is computed as the inverse of *F* * *G* and the reverse NTT results in *a* = 1/(*f* * *g*) mod q. Sometime it happens that *F* * *G* is not invertible, so that the following debug message is output |
| 602 | 4 | Andreas Steffen | <pre> |
| 603 | 4 | Andreas Steffen | S1[91] is zero - s1 is not invertible |
| 604 | 4 | Andreas Steffen | </pre> |
| 605 | 4 | Andreas Steffen | and another trial run is started. |