This repo contains the function that the server should run to verify proofs. And the solution to the puzzle that can be run with cargo run --release.
It's expected for the server to reply with an "expired_proof" if sending the data, or "invalid_proof" in any other case
If you are reading this, the date should be the seventh of July of 2023, and you should be checking the Lambda-Ingoyama CTF challenges site. Hopefully, we managed to hijack the site, and you are reading this now.
We are not allowed to say much, but you must know it's of utmost importance that you win this challenge. So, we have decided to help.
Don't worry, it should be easy. We have found the right exploit to solve, and we are forwarding to you the solution. In case something goes wrong, we are leaving some additional data we have collected. We don't know if it's useful, but we hope it can help.
It's now up to you to take the flag.
We wish good luck.
DATA = [0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 1, 244, 155, 13, 190, 192, 74, 8, 176, 255, 42, 23, 165, 13, 35, 25, 44, 253, 38, 193, 209, 94, 199, 1, 73, 69, 64, 243, 80, 225, 218, 160, 162, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 32, 1, 124, 56, 108, 207, 100, 65, 67, 216, 14, 210, 43, 221, 77, 210, 190, 198, 193, 157, 67, 188, 89, 89, 19, 201, 32, 255, 31, 36, 18, 227, 118, 0, 37, 84, 169, 248, 13, 31, 103, 101, 193, 97, 98, 197, 44, 178, 228, 190, 22, 225, 3, 37, 2, 120, 18, 87, 9, 112, 251, 174, 58, 224, 135, 1, 231, 18, 180, 26, 21, 47, 123, 226, 113, 153, 84, 230, 25, 2, 194, 169, 229, 105, 187, 131, 105, 154, 188, 87, 83, 244, 26, 50, 53, 200, 218, 0, 0, 0, 0, 0, 0, 0, 1, 1, 30, 43, 253, 172, 254, 146, 42, 66, 169, 132, 88, 236, 4, 40, 1, 6, 148, 112, 183, 11, 253, 127, 87, 86, 53, 40, 101, 255, 246, 127, 40, 0, 0, 0, 0, 0, 0, 0, 32, 4, 179, 38, 239, 105, 249, 150, 138, 192, 48, 122, 138, 3, 253, 84, 39, 53, 124, 217, 71, 116, 89, 125, 108, 30, 38, 110, 62, 242, 165, 252, 249, 3, 173, 199, 182, 38, 0, 237, 219, 136, 113, 96, 251, 11, 11, 233, 143, 111, 105, 44, 171, 152, 88, 77, 198, 215, 51, 149, 45, 164, 186, 48, 195, 0, 0, 0, 0, 0, 0, 0, 5, 242, 214, 171, 208, 208, 99, 45, 117, 113, 218, 94, 151, 116, 145, 236, 37, 151, 218, 193, 175, 225, 79, 255, 247, 78, 176, 85, 191, 178, 22, 106, 244, 88, 161, 255, 77, 99, 149, 141, 140, 56, 102, 94, 229, 166, 144, 55, 41, 6, 191, 30, 23, 117, 110, 90, 135, 68, 81, 130, 244, 156, 145, 182, 62, 58, 82, 103, 106, 254, 246, 98, 235, 23, 210, 104, 93, 89, 46, 5, 176, 148, 129, 78, 191, 234, 80, 248, 116, 119, 150, 70, 136, 144, 138, 255, 243, 225, 223, 106, 206, 186, 196, 170, 6, 1, 146, 247, 159, 98, 185, 131, 47, 235, 147, 162, 80, 152, 165, 235, 3, 184, 151, 134, 253, 166, 240, 121, 192, 101, 133, 104, 112, 90, 65, 160, 254, 103, 179, 251, 158, 72, 219, 186, 243, 153, 214, 57, 31, 214, 117, 150, 173, 90, 92, 149, 171, 218, 202, 7, 41, 3, 91, 206, 213, 159, 29, 67, 102, 58, 203, 175, 234, 87, 104, 216, 14, 9, 236, 226, 79, 71, 197, 62, 198, 88, 90, 94, 247, 22, 253, 125, 160, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 7, 248, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 7, 139, 231, 241, 196, 175, 249, 90, 76, 137, 191, 184, 173, 180, 107, 65, 119, 139, 169, 85, 237, 128, 176, 164, 13, 245, 92, 74, 91, 233, 212, 228, 46, 112, 174, 153, 67, 89, 22, 170, 90, 182, 28, 223, 22, 2, 188, 0, 218, 130, 241, 217, 31, 1, 16, 141, 251, 56, 142, 75, 77, 74, 60, 198, 223, 75, 24, 183, 81, 217, 125, 144, 149, 98, 40, 231, 63, 61, 98, 255, 115, 115, 81, 221, 218, 146, 100, 247, 167, 141, 210, 140, 21, 107, 183, 215, 37, 102, 235, 223, 70, 34, 70, 9, 169, 2, 102, 131, 190, 163, 155, 27, 63, 48, 85, 127, 233, 65, 149, 243, 40, 31, 227, 243, 163, 96, 79, 220, 164, 121, 234, 124, 106, 34, 8, 18, 232, 159, 169, 253, 243, 40, 255, 148, 57, 81, 153, 66, 170, 220, 214, 63, 132, 33, 166, 191, 56, 98, 212, 229, 239, 180, 46, 246, 250, 233, 72, 133, 224, 163, 130, 219, 189, 119, 152, 152, 208, 109, 229, 45, 88, 137, 198, 246, 133, 206, 143, 31, 130, 176, 67, 154, 105, 150, 224, 171, 172, 59, 39, 227, 137, 133, 214, 224, 88, 241, 245, 140, 196, 134, 19, 134, 250, 166, 12, 183, 129, 9, 128, 238, 152, 247, 128, 103, 190, 0, 0, 0, 0, 0, 0, 0, 6, 52, 24, 158, 59, 36, 19, 216, 213, 17, 195, 119, 51, 217, 14, 190, 197, 55, 65, 238, 136, 100, 30, 168, 113, 72, 239, 150, 122, 47, 73, 157, 254, 150, 26, 218, 2, 190, 92, 16, 237, 185, 24, 244, 243, 114, 241, 125, 242, 204, 71, 76, 4, 94, 241, 67, 41, 222, 225, 136, 255, 38, 217, 229, 37, 103, 243, 181, 53, 145, 137, 236, 82, 61, 216, 221, 145, 253, 181, 244, 247, 170, 65, 253, 250, 178, 21, 177, 27, 168, 111, 108, 16, 151, 56, 84, 83, 139, 42, 185, 128, 15, 225, 14, 70, 70, 13, 227, 39, 109, 84, 11, 66, 79, 65, 70, 170, 222, 26, 186, 150, 246, 180, 24, 84, 92, 180, 27, 98, 101, 127, 159, 152, 226, 51, 251, 93, 148, 22, 19, 160, 125, 91, 242, 197, 249, 67, 22, 205, 228, 77, 196, 139, 45, 205, 7, 53, 242, 50, 162, 113, 182, 185, 5, 243, 74, 6, 53, 237, 3, 58, 20, 111, 28, 156, 211, 244, 7, 112, 3, 32, 223, 94, 10, 24, 16, 228, 20, 84, 56, 236, 211, 53, 0, 0, 0, 0, 0, 0, 0, 5, 41, 91, 222, 174, 254, 1, 72, 71, 184, 150, 153, 79, 146, 16, 9, 251, 246, 59, 195, 156, 245, 249, 52, 192, 30, 190, 56, 198, 3, 7, 131, 66, 207, 46, 222, 91, 202, 149, 83, 89, 215, 125, 88, 87, 54, 116, 129, 68, 158, 43, 123, 42, 108, 240, 214, 71, 73, 185, 229, 157, 88, 149, 53, 151, 141, 180, 9, 223, 20, 80, 21, 112, 128, 110, 149, 11, 243, 217, 30, 64, 214, 6, 127, 194, 233, 76, 176, 179, 235, 139, 56, 182, 181, 239, 238, 88, 91, 250, 203, 249, 123, 225, 195, 124, 185, 155, 1, 191, 39, 226, 69, 188, 94, 222, 100, 132, 62, 161, 17, 58, 188, 177, 153, 25, 201, 201, 142, 219, 224, 223, 42, 12, 28, 160, 80, 206, 74, 152, 91, 82, 33, 3, 200, 14, 0, 236, 245, 12, 227, 29, 74, 235, 13, 153, 67, 215, 68, 27, 245, 183, 0, 0, 0, 0, 0, 0, 0, 4, 76, 188, 36, 226, 7, 72, 170, 180, 150, 29, 73, 3, 187, 157, 119, 63, 133, 187, 84, 97, 195, 190, 7, 46, 199, 67, 57, 91, 12, 88, 46, 32, 191, 115, 55, 47, 24, 74, 76, 44, 193, 218, 239, 205, 135, 142, 231, 57, 243, 40, 48, 202, 23, 229, 85, 88, 162, 72, 190, 23, 206, 128, 190, 122, 63, 179, 50, 187, 126, 67, 217, 148, 37, 249, 96, 160, 136, 209, 163, 184, 113, 97, 57, 206, 42, 208, 78, 28, 157, 133, 16, 225, 34, 49, 110, 246, 8, 155, 200, 45, 189, 44, 188, 16, 153, 100, 45, 10, 213, 229, 227, 83, 86, 1, 100, 5, 79, 193, 9, 214, 83, 70, 16, 241, 116, 21, 102, 219, 0, 0, 0, 0, 0, 0, 0, 3, 136, 34, 81, 0, 215, 160, 38, 104, 131, 92, 49, 58, 251, 50, 135, 98, 146, 27, 199, 33, 5, 165, 24, 53, 227, 170, 111, 80, 50, 168, 171, 1, 204, 25, 187, 131, 72, 133, 198, 32, 105, 87, 200, 51, 91, 140, 146, 244, 1, 198, 228, 250, 137, 56, 108, 219, 157, 9, 125, 49, 154, 160, 167, 148, 30, 135, 70, 54, 180, 168, 221, 46, 89, 172, 228, 25, 77, 225, 203, 76, 149, 52, 188, 230, 141, 80, 249, 158, 152, 35, 52, 91, 209, 4, 140, 8, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 5, 2, 180, 238, 33, 248, 73, 81, 86, 160, 190, 192, 49, 224, 200, 241, 155, 78, 75, 119, 205, 223, 176, 28, 195, 154, 126, 102, 29, 98, 252, 235, 208, 2, 135, 133, 75, 244, 119, 96, 170, 5, 150, 153, 38, 95, 157, 253, 60, 51, 49, 50, 210, 152, 224, 208, 83, 74, 188, 188, 226, 100, 199, 17, 113, 1, 125, 77, 110, 151, 153, 64, 195, 65, 102, 239, 152, 32, 143, 245, 249, 50, 238, 254, 140, 18, 166, 115, 143, 105, 85, 250, 154, 213, 151, 106, 24, 1, 65, 239, 190, 2, 42, 219, 51, 79, 176, 176, 28, 233, 11, 4, 252, 218, 11, 201, 82, 245, 76, 81, 122, 100, 17, 103, 72, 206, 130, 81, 197, 2, 163, 120, 51, 222, 0, 73, 37, 54, 164, 223, 148, 123, 253, 195, 162, 95, 35, 205, 119, 54, 239, 110, 135, 125, 226, 200, 236, 13, 45, 214, 102, 0, 0, 0, 0, 0, 0, 0, 5, 1, 108, 231, 61, 6, 27, 191, 48, 39, 175, 95, 244, 217, 153, 145, 139, 29, 147, 230, 73, 196, 238, 174, 103, 189, 165, 188, 216, 72, 176, 71, 109, 6, 149, 120, 152, 59, 26, 206, 20, 238, 28, 128, 246, 113, 173, 143, 93, 203, 42, 78, 198, 127, 119, 189, 234, 91, 166, 25, 49, 192, 49, 183, 33, 2, 227, 252, 241, 67, 221, 249, 169, 238, 42, 213, 175, 96, 60, 190, 170, 76, 130, 47, 145, 145, 86, 88, 236, 12, 45, 100, 62, 90, 35, 10, 183, 2, 8, 48, 142, 73, 91, 192, 19, 76, 238, 231, 185, 157, 11, 127, 95, 114, 129, 104, 81, 101, 2, 103, 86, 114, 123, 141, 60, 51, 139, 180, 216, 5, 169, 58, 183, 84, 141, 235, 115, 224, 113, 104, 134, 118, 147, 242, 13, 250, 149, 190, 120, 44, 76, 117, 218, 24, 117, 85, 151, 159, 247, 132, 31, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 7, 50, 175, 87, 45, 195, 172, 196, 242, 143, 176, 104, 4, 46, 252, 207, 160, 199, 148, 254, 207, 171, 115, 28, 239, 47, 97, 23, 83, 246, 7, 250, 232, 250, 112, 252, 167, 23, 131, 150, 138, 92, 45, 241, 118, 230, 173, 51, 220, 239, 112, 25, 189, 238, 243, 165, 179, 27, 44, 90, 48, 170, 121, 188, 60, 253, 128, 2, 55, 121, 55, 62, 83, 197, 168, 129, 109, 12, 224, 15, 100, 43, 188, 16, 46, 127, 192, 20, 50, 184, 119, 52, 96, 66, 2, 9, 41, 121, 177, 97, 164, 144, 214, 242, 253, 50, 104, 193, 156, 224, 203, 126, 94, 86, 82, 241, 101, 79, 63, 214, 87, 197, 177, 61, 165, 15, 36, 138, 218, 40, 19, 116, 173, 222, 136, 23, 183, 205, 60, 110, 102, 30, 50, 79, 128, 137, 114, 138, 161, 193, 115, 61, 39, 34, 77, 101, 177, 140, 79, 30, 243, 251, 192, 237, 81, 134, 15, 196, 70, 38, 127, 224, 227, 27, 204, 170, 216, 174, 154, 200, 119, 244, 172, 129, 220, 102, 41, 44, 4, 141, 246, 138, 99, 13, 157, 190, 141, 236, 224, 191, 185, 186, 87, 242, 214, 99, 120, 3, 45, 248, 65, 175, 234, 67, 34, 115, 88, 166, 109, 250, 224, 214, 62, 118, 31, 0, 0, 0, 0, 0, 0, 0, 6, 250, 215, 220, 2, 135, 73, 65, 47, 245, 22, 233, 223, 177, 159, 226, 203, 25, 36, 50, 127, 4, 61, 250, 210, 211, 170, 1, 162, 203, 254, 17, 21, 75, 230, 141, 0, 3, 52, 121, 54, 62, 28, 11, 152, 90, 131, 178, 22, 107, 243, 45, 106, 141, 27, 54, 225, 190, 35, 208, 157, 196, 6, 16, 195, 34, 36, 137, 47, 91, 113, 113, 234, 251, 111, 72, 103, 174, 125, 54, 226, 221, 205, 201, 53, 181, 85, 244, 97, 23, 113, 175, 225, 239, 154, 181, 141, 214, 78, 107, 72, 150, 154, 125, 48, 26, 71, 135, 190, 145, 144, 193, 185, 29, 50, 199, 79, 202, 136, 98, 139, 79, 156, 120, 65, 82, 65, 205, 186, 175, 230, 199, 27, 129, 186, 38, 233, 237, 35, 227, 66, 120, 83, 55, 208, 115, 216, 39, 166, 92, 232, 3, 197, 159, 113, 234, 232, 75, 57, 35, 162, 226, 31, 253, 47, 154, 169, 17, 90, 147, 27, 19, 87, 244, 36, 181, 71, 88, 96, 47, 209, 79, 226, 45, 192, 239, 157, 90, 247, 28, 123, 65, 207, 0, 0, 0, 0, 0, 0, 0, 5, 89, 135, 67, 117, 193, 203, 17, 99, 237, 127, 78, 3, 232, 80, 49, 87, 131, 85, 0, 252, 105, 184, 159, 200, 194, 50, 39, 247, 213, 194, 113, 131, 210, 137, 25, 195, 225, 211, 225, 125, 169, 210, 232, 188, 119, 131, 82, 5, 103, 63, 56, 183, 108, 42, 120, 176, 50, 186, 188, 122, 31, 130, 108, 117, 39, 196, 10, 240, 252, 49, 147, 250, 85, 45, 131, 0, 197, 194, 5, 120, 38, 221, 196, 0, 230, 235, 168, 102, 153, 134, 233, 154, 251, 57, 160, 43, 252, 206, 242, 210, 34, 249, 42, 93, 192, 214, 204, 230, 29, 147, 46, 222, 179, 192, 245, 126, 143, 55, 101, 110, 1, 153, 238, 233, 92, 48, 78, 81, 228, 227, 163, 17, 21, 212, 170, 135, 186, 59, 37, 50, 243, 72, 130, 131, 0, 218, 28, 186, 44, 51, 139, 141, 193, 23, 46, 123, 36, 141, 200, 30, 0, 0, 0, 0, 0, 0, 0, 4, 212, 92, 147, 16, 22, 4, 15, 223, 148, 99, 77, 62, 93, 152, 40, 99, 243, 43, 155, 240, 239, 204, 54, 72, 170, 246, 55, 224, 80, 248, 91, 9, 14, 213, 19, 23, 115, 149, 36, 21, 133, 134, 91, 27, 117, 102, 92, 246, 211, 57, 207, 229, 48, 210, 54, 157, 187, 130, 191, 17, 150, 39, 164, 181, 27, 147, 39, 197, 124, 74, 121, 0, 220, 162, 243, 148, 69, 94, 84, 251, 90, 80, 61, 45, 159, 153, 48, 195, 30, 253, 67, 175, 255, 180, 127, 222, 21, 203, 127, 117, 9, 117, 183, 240, 69, 183, 179, 170, 89, 227, 153, 231, 206, 34, 208, 170, 57, 202, 249, 221, 185, 101, 6, 32, 249, 204, 229, 203, 0, 0, 0, 0, 0, 0, 0, 3, 17, 165, 198, 222, 43, 194, 76, 230, 70, 174, 186, 237, 121, 83, 95, 10, 2, 64, 65, 5, 25, 196, 208, 69, 243, 235, 4, 128, 173, 129, 64, 228, 97, 183, 129, 186, 187, 168, 2, 155, 240, 52, 109, 36, 138, 50, 146, 116, 55, 170, 177, 37, 114, 157, 73, 11, 139, 233, 12, 75, 104, 135, 72, 59, 241, 123, 65, 227, 112, 145, 243, 205, 21, 144, 177, 63, 229, 181, 8, 125, 34, 243, 103, 172, 228, 103, 122, 80, 118, 21, 198, 146, 161, 219, 68, 82, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 72, 0, 0, 0, 0, 0, 0, 0, 7, 137, 193, 242, 224, 131, 113, 239, 3, 136, 85, 120, 105, 39, 190, 4, 115, 193, 62, 50, 116, 80, 136, 220, 70, 57, 37, 197, 214, 55, 248, 101, 244, 143, 207, 251, 50, 71, 163, 41, 104, 18, 33, 16, 128, 142, 118, 249, 125, 196, 183, 25, 226, 105, 250, 172, 123, 230, 59, 90, 225, 86, 92, 6, 41, 135, 100, 224, 133, 252, 140, 50, 226, 84, 9, 79, 23, 70, 172, 155, 40, 49, 109, 193, 108, 191, 229, 183, 234, 31, 222, 16, 103, 218, 2, 134, 131, 150, 245, 154, 236, 83, 53, 50, 120, 122, 157, 135, 85, 158, 235, 41, 194, 53, 127, 86, 141, 203, 72, 87, 218, 49, 161, 51, 21, 119, 77, 60, 119, 121, 46, 197, 171, 213, 247, 96, 87, 76, 151, 56, 39, 188, 217, 104, 176, 173, 196, 80, 166, 60, 170, 8, 205, 228, 39, 191, 91, 20, 201, 110, 24, 113, 136, 181, 101, 127, 125, 5, 198, 203, 236, 196, 169, 241, 182, 53, 200, 151, 204, 60, 16, 166, 50, 179, 114, 176, 174, 100, 239, 131, 159, 110, 163, 198, 105, 177, 206, 141, 156, 168, 167, 2, 99, 216, 222, 49, 9, 91, 56, 29, 50, 40, 68, 221, 99, 127, 215, 97, 183, 63, 71, 34, 139, 178, 161, 0, 0, 0, 0, 0, 0, 0, 32, 6, 4, 244, 32, 207, 168, 158, 167, 175, 180, 2, 201, 60, 6, 16, 168, 235, 180, 4, 241, 208, 7, 28, 217, 219, 211, 174, 115, 28, 99, 235, 82, 0, 220, 235, 49, 50, 54, 178, 216, 3, 109, 203, 116, 181, 126, 230, 207, 128, 102, 73, 121, 205, 162, 79, 82, 249, 185, 232, 82, 119, 35, 101, 113, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 7, 211, 82, 234, 110, 84, 243, 207, 144, 215, 18, 54, 0, 57, 229, 32, 0, 109, 170, 44, 167, 56, 138, 238, 9, 244, 219, 161, 221, 15, 106, 166, 213, 111, 102, 113, 245, 14, 238, 123, 89, 203, 113, 10, 244, 32, 38, 113, 168, 15, 67, 115, 59, 226, 174, 195, 220, 59, 3, 175, 157, 164, 207, 26, 73, 118, 217, 5, 191, 245, 126, 117, 148, 238, 79, 83, 81, 221, 7, 38, 113, 179, 29, 124, 156, 118, 6, 192, 142, 96, 238, 156, 29, 147, 169, 156, 33, 111, 109, 203, 238, 207, 248, 238, 157, 136, 224, 155, 145, 94, 138, 230, 218, 203, 224, 1, 10, 132, 226, 222, 63, 34, 135, 196, 201, 178, 151, 162, 6, 244, 63, 224, 82, 21, 153, 70, 12, 222, 189, 107, 125, 1, 213, 45, 118, 82, 57, 178, 133, 176, 118, 139, 28, 249, 59, 46, 54, 147, 87, 49, 97, 15, 192, 105, 83, 183, 246, 30, 80, 31, 38, 24, 182, 251, 168, 35, 87, 81, 229, 20, 114, 228, 73, 227, 96, 74, 109, 204, 68, 168, 112, 38, 183, 114, 126, 95, 187, 74, 107, 93, 66, 118, 195, 181, 124, 49, 239, 193, 6, 236, 71, 37, 142, 7, 4, 181, 50, 61, 165, 237, 21, 201, 50, 61, 29, 0, 0, 0, 0, 0, 0, 0, 1, 6, 210, 177, 221, 168, 252, 30, 50, 241, 225, 69, 24, 110, 49, 28, 173, 137, 207, 182, 218, 121, 139, 149, 84, 109, 184, 180, 132, 189, 253, 26, 245, 0, 0, 0, 0, 0, 0, 0, 0];
OFFSET = 3 type = simple_fibonacci
The first step is to send the data to an endpoint of the server, which should reply with something like "Expired proof". After that, the next step is to inspect the proof. Most of the data will not be relevant.
Counting the amount of queries, we realize there is only 1. Now it remains to see how to exploit it.
Some additional data needs to be used, the offset, the constraints, and the blowup factor. Offset and constraint is hinted in the data. Blowup factor can be guessed or hinted.
Now, realizing, verifier is broken, we need to check that the composition polynomial and trace have the same value at z (but not enforcing this check at every point).
The "hack" has 2 ingredients:
In Round 3, the evil prover lies about H(z) so it matches the exact value the verifier will reconstruct from the trace(s). Because the constraints are not satisfied, the committed H(x)'s values are garbage. We also lied about H(z). Therefore in theory Deep(x)'s term(s) involving H are total garbage, and definitely not a low degree polynomial. But we can lie about Deep(x)'s values too. In Round 4, the evil prover anticipates the verifier will do a consistency check at some random iota_0 that compares the committed Deep(x) value at iota_0 to the RHS of Deep's definition recomputed from the commited H(iota_0) and traces(iota_0). So the prover creates Deep(x) h_1 and h_2 terms by interpolating through as many evaluations of the RHS definition as the low-degree check will allow. The number of such evaluations is LDE domain length / blowup_factor, so this ensures the single consistency check will pass with probability (LDE domain length / blowup_factor) / LDE domain length, in other words 1 / blowup_factor.