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feat: support NEW srp auth in
ipsw download dev cmd
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,92 @@ | ||
| // prime.go - Generate safe primes | ||
| // | ||
| // Copyright 2013-2017 Sudhi Herle <sudhi.herle-at-gmail-dot-com> | ||
| // License: MIT | ||
|
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| package srp | ||
|
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| /* UPDATED TO WORK WITH APPLE'S SRP IMPLEMENTATION by blacktop */ | ||
|
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| import ( | ||
| "crypto/rand" | ||
| "math/big" | ||
| ) | ||
|
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| // safePrime generates a safe prime; i.e., a prime 'p' such that 2p+1 is also prime. | ||
| func safePrime(bits int) (*big.Int, error) { | ||
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| a := new(big.Int) | ||
| for { | ||
| p, err := rand.Prime(rand.Reader, bits) | ||
| if err != nil { | ||
| return nil, err | ||
| } | ||
|
|
||
| // 2p+1 | ||
| a = a.Lsh(p, 1) | ||
| a = a.Add(a, one) | ||
| if a.ProbablyPrime(20) { | ||
| return a, nil | ||
| } | ||
| } | ||
|
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| // never reached | ||
| return nil, nil | ||
| } | ||
|
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| // Return true if g is a generator for safe prime p | ||
| // | ||
| // From Cryptography Theory & Practive, Stinson and Paterson (Th. 6.8 pp 196): | ||
| // | ||
| // If p > 2 is a prime and g is in Zp*, then | ||
| // g is a primitive element modulo p iff g ^ (p-1)/q != 1 (mod p) | ||
| // for all primes q such that q divides (p-1). | ||
| // | ||
| // "Primitive Element" and "Generator" are the same thing in Number Theory. | ||
| // | ||
| // Code below added as a result of bug pointed out by Dharmalingam G. (May 2019) | ||
| func isGenerator(g, p *big.Int) bool { | ||
| p1 := big.NewInt(0).Sub(p, one) | ||
| q := big.NewInt(0).Rsh(p1, 1) // q = p-1/2 = ((p-1) >> 1) | ||
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| // p is a safe prime. i.e., it is of the form 2q+1 where q is prime. | ||
| // | ||
| // => p-1 = 2q, where q is a prime. | ||
| // | ||
| // All factors of p-1 are: {2, q, 2q} | ||
| // | ||
| // So, our check really comes down to: | ||
| // 1) g ^ (p-1/2q) != 1 mod p | ||
| // => g ^ (2q/2q) != 1 mod p | ||
| // => g != 1 mod p | ||
| // Trivial case. We ignore this. | ||
| // | ||
| // 2) g ^ (p-1/2) != 1 mod p | ||
| // => g ^ (2q/2) != 1 mod p | ||
| // => g ^ q != 1 mod p | ||
| // | ||
| // 3) g ^ (p-1/q) != 1 mod p | ||
| // => g ^ (2q/q) != 1 mod p | ||
| // => g ^ 2 != 1 mod p | ||
| // | ||
|
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| // g ^ 2 mod p | ||
| if !ok(g, big.NewInt(0).Lsh(one, 1), p) { | ||
| return false | ||
| } | ||
|
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| // g ^ q mod p | ||
| if !ok(g, q, p) { | ||
| return false | ||
| } | ||
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| return true | ||
| } | ||
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| func ok(g, x *big.Int, p *big.Int) bool { | ||
| z := big.NewInt(0).Exp(g, x, p) | ||
| // the expmod should NOT be 1 | ||
| return z.Cmp(one) != 0 | ||
| } | ||
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| // vim: noexpandtab:sw=8:ts=8:tw=92: |
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