Question: Help please ! , I don't know what to do Kicking it up a notch: 1024-bit RSA keys In this section we push the limits

 Help please ! , I don't know what to do Kicking Help please ! , I don't know what to do

Kicking it up a notch: 1024-bit RSA keys In this section we push the limits of computation and technique. 1024-bit RSA keys are still in common use, despite warnings to gradually upgrade to 2048-bit keys in the long run. Let's see what can be done, given some special conditions. Attacking the RSA modulus from a different angle Factor the moduli for the following RSA public keys: Public-Key: (1024 bit) modulus: 00: d9: 57: af: 3a: 15: 5e: 15: a8: 1f: 9f: fc: ef: 85: de: f8: b9: dc: 2d: f8: d0: d4: 03: 5d: 63: fc: 6c: ed: a6: 38: e1: 50: 07: ca: c3: dd: 8d: 3f: 16: f4: 3a: 33: a8: 1a: 18: 92: 86: 25: ea: 1f: 9a: 62: 9c: 1e: 6c: 49: 81: 74: 8d: 68: 38: 15: 5e: e4: 7a: 5f: 21: 9e: a4: 5c: d0: 48: 0f: 20: 61: 58: 69: 60: cf: aa: 08: b4: ef: 68: ea: ce: f6: dd: 27: f9: 23: 39: 51: df: af: 73: bc: 3b: 77: f8: 48: 3d: 52: 0a: 01: 61: 2f: 49: a0: de: 94: b3: 1d: d0: f4: a5: ae: fb: 65: ba: 04: dd: f3: f4: 56: d8: 64: 5d: d7 publicExponent: 65537 (0x10001) Public-Key: (1024 bit) modulus: 00: a6: 8e: a1: 94: b9: fd: c8: 62: ad: e8: d3: 96: f1: b1: ed: 8d: 5b: 78: 32: a8: 5e: 00: bb: de: 75: 4a: 53: aa: 03: 30: 5a: 24: 75: f7: 82: f7: 4f: 0a: ef: 47: 3d: 41: 99: ae: 4f: 52: 04: 1e: 8f: 8d: 98: 94: b5: c9: dd: be: 9d: 32: 2f: 60: 96: 6d: 39: 73: 79: 05: 4f: 3f: 76: fc: 20: 7a: 58: 61: af: 95: 2e: 0a: de: 5a: ed: f3: 20: d6: f2: 0a: 8a: 3f: 22: ad: 5d: dc: 00: d3: 31: 39: df: a7: 59: 2d: c0: d7: 92: f6: d6: 79: 8e: 54: f6: 2a: ff: 4c: 0e: fa: 8f: 31: 60: 52: fe: 0b: ae: 35: 0b: 75: b9: 46: 7d: 71 publicExponent: 65537 (0x10001) So you are sitting there, staring at this assignment to factor a 1024-bit RSA modulus. You have been struggling with or contemplating factoring a 512-bit integer, and now this? A friend of yours who has taken number theory swings by, looks at your computer screen, and you mumble something in frustration. He tells you something that sounds like "mind your own p's and q's, " but you haven't said anything wrong. Or was it that he said "mine your p's and q's?" Confused, yet intrigued, you start searching for an answer Kicking it up a notch: 1024-bit RSA keys In this section we push the limits of computation and technique. 1024-bit RSA keys are still in common use, despite warnings to gradually upgrade to 2048-bit keys in the long run. Let's see what can be done, given some special conditions. Attacking the RSA modulus from a different angle Factor the moduli for the following RSA public keys: Public-Key: (1024 bit) modulus: 00: d9: 57: af: 3a: 15: 5e: 15: a8: 1f: 9f: fc: ef: 85: de: f8: b9: dc: 2d: f8: d0: d4: 03: 5d: 63: fc: 6c: ed: a6: 38: e1: 50: 07: ca: c3: dd: 8d: 3f: 16: f4: 3a: 33: a8: 1a: 18: 92: 86: 25: ea: 1f: 9a: 62: 9c: 1e: 6c: 49: 81: 74: 8d: 68: 38: 15: 5e: e4: 7a: 5f: 21: 9e: a4: 5c: d0: 48: 0f: 20: 61: 58: 69: 60: cf: aa: 08: b4: ef: 68: ea: ce: f6: dd: 27: f9: 23: 39: 51: df: af: 73: bc: 3b: 77: f8: 48: 3d: 52: 0a: 01: 61: 2f: 49: a0: de: 94: b3: 1d: d0: f4: a5: ae: fb: 65: ba: 04: dd: f3: f4: 56: d8: 64: 5d: d7 publicExponent: 65537 (0x10001) Public-Key: (1024 bit) modulus: 00: a6: 8e: a1: 94: b9: fd: c8: 62: ad: e8: d3: 96: f1: b1: ed: 8d: 5b: 78: 32: a8: 5e: 00: bb: de: 75: 4a: 53: aa: 03: 30: 5a: 24: 75: f7: 82: f7: 4f: 0a: ef: 47: 3d: 41: 99: ae: 4f: 52: 04: 1e: 8f: 8d: 98: 94: b5: c9: dd: be: 9d: 32: 2f: 60: 96: 6d: 39: 73: 79: 05: 4f: 3f: 76: fc: 20: 7a: 58: 61: af: 95: 2e: 0a: de: 5a: ed: f3: 20: d6: f2: 0a: 8a: 3f: 22: ad: 5d: dc: 00: d3: 31: 39: df: a7: 59: 2d: c0: d7: 92: f6: d6: 79: 8e: 54: f6: 2a: ff: 4c: 0e: fa: 8f: 31: 60: 52: fe: 0b: ae: 35: 0b: 75: b9: 46: 7d: 71 publicExponent: 65537 (0x10001) So you are sitting there, staring at this assignment to factor a 1024-bit RSA modulus. You have been struggling with or contemplating factoring a 512-bit integer, and now this? A friend of yours who has taken number theory swings by, looks at your computer screen, and you mumble something in frustration. He tells you something that sounds like "mind your own p's and q's, " but you haven't said anything wrong. Or was it that he said "mine your p's and q's?" Confused, yet intrigued, you start searching for an

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