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January 20, 2024 14:38
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Generate RSA Prime Factors in Swift
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| /// The following algorithm recovers the prime factors of a modulus, given the public and private exponents. | |
| /// The algorithm is based on Fact 1 in [Boneh 1999]. | |
| static func calculatePrimeFactors(n: BigUInt, e: BigUInt, d: BigUInt) throws -> (p: BigUInt, q: BigUInt) { | |
| let k = (d * e) - 1 | |
| guard k & 1 == 0 else { | |
| throw RSAError.keyInitializationFailure | |
| } | |
| let t = k.trailingZeroBitCount, r = k >> t | |
| var y: BigUInt = 0 | |
| var i = 1 | |
| // If the prime factors are not revealed after 100 iterations, | |
| // then the probability is overwhelming that the modulus is not the product of two prime factors, | |
| // or that the public and private exponents are not consistent with each other. | |
| while i <= 100 { | |
| let g = BigUInt.randomInteger(lessThan: n - 1) | |
| y = g.power(r, modulus: n) | |
| guard y != 1, y != n - 1 else { | |
| continue | |
| } | |
| var j = 1 | |
| var x: BigUInt | |
| while j <= t &- 1 { | |
| x = y.power(2, modulus: n) | |
| guard x != 1, x != n - 1 else { | |
| break | |
| } | |
| y = x | |
| j &+= 1 | |
| } | |
| x = y.power(2, modulus: n) | |
| if x == 1 { | |
| let p = (y - 1).greatestCommonDivisor(with: n) | |
| let q = n / p | |
| return (p, q) | |
| } | |
| i &+= 1 | |
| } | |
| throw RSAError.keyInitializationFailure | |
| } |
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