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55 lines
1.8 KiB
55 lines
1.8 KiB
3 years ago
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package crypto
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import (
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"math/big"
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"github.com/go-faster/errors"
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)
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// CheckDH performs DH parameters check described in Telegram docs.
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//
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// Client is expected to check whether p is a safe 2048-bit prime (meaning that both p and (p-1)/2 are prime,
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// and that 2^2047 < p < 2^2048), and that g generates a cyclic subgroup of prime order (p-1)/2, i.e.
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// is a quadratic residue mod p. Since g is always equal to 2, 3, 4, 5, 6 or 7, this is easily done using quadratic
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// reciprocity law, yielding a simple condition on p mod 4g — namely, p mod 8 = 7 for g = 2; p mod 3 = 2 for g = 3;
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// no extra condition for g = 4; p mod 5 = 1 or 4 for g = 5; p mod 24 = 19 or 23 for g = 6; and p mod 7 = 3,
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// 5 or 6 for g = 7.
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//
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// See https://core.telegram.org/mtproto/auth_key#presenting-proof-of-work-server-authentication.
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//
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// See https://core.telegram.org/api/srp#checking-the-password-with-srp.
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//
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// See https://core.telegram.org/api/end-to-end#sending-a-request.
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func CheckDH(g int, p *big.Int) error {
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// The client is expected to check whether p is a safe 2048-bit prime
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// (meaning that both p and (p-1)/2 are prime, and that 2^2047 < p < 2^2048).
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// FIXME(tdakkota): we check that 2^2047 <= p < 2^2048
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// but docs says to check 2^2047 < p < 2^2048.
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//
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// TDLib check 2^2047 <= too:
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// https://github.com/tdlib/td/blob/d161323858a782bc500d188b9ae916982526c262/td/mtproto/DhHandshake.cpp#L23
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if p.BitLen() != RSAKeyBits {
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return errors.New("p should be 2^2047 < p < 2^2048")
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}
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if err := CheckGP(g, p); err != nil {
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return err
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}
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return checkPrime(p)
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}
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func checkPrime(p *big.Int) error {
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if !Prime(p) {
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return errors.New("p is not prime number")
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}
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sub := big.NewInt(0).Sub(p, big.NewInt(1))
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pr := sub.Quo(sub, big.NewInt(2))
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if !Prime(pr) {
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return errors.New("(p-1)/2 is not prime number")
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}
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return nil
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}
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