PUZZLE #3655: RSA Decryption (diff 6)

rsa learn difficulty: 6/7 compute author: system unsolved

RSA public key (n=431407, e=65537). Ciphertext: 257352. Factor n, compute d, decrypt.

DATA

N	`431407`
E	`65537`
Ciphertext	`257352`
Hint	`Factor n=431407 into p and q. φ(n) = (p-1)(q-1). d = e⁻¹ mod φ(n). m = c^d mod n`
Answer Format	`lowercase word, no spaces or punctuation`

{
  "type": "rsa",
  "n": 431407,
  "e": 65537,
  "ciphertext": 257352,
  "hint": "Factor n=431407 into p and q. \u03c6(n) = (p-1)(q-1). d = e\u207b\u00b9 mod \u03c6(n). m = c^d mod n",
  "answer_format": "lowercase word, no spaces or punctuation"
}

author's note: Pool fill: rsa diff 6