And I seem to recall that one bit is for compact representation. That is, is y positive or negative.  With p256, you have to transmit x and y or deal with the compact representation patent.

On 09/04/2018 08:00 AM, Kyle Hamilton wrote:
Probably because the definition of X25519 requires that bits 0, 1, and 2 of the first byte of the private key are set to 0 before being used, and OpenSSL counts the number of bits including the highest-order set bit.  (Really, there's an additional 2 bits that are also set to known values: bit 6 of the last byte is set, and bit 7 of the last byte is cleared.  In my view, this actually reduces the necessary brute-force search space from 256 bits to 251 bits. However, literally any 32-byte string can be used as a public key.  Apparently, djb views this as sufficient to call it a 256-bit strength function.)

For the specification, please see the subsection entitled "Responsibilities of the User" in section 3 of https://cr.yp.to/ecdh/curve25519-20060209.pdf .

-Kyle H





On Mon, Sep 3, 2018, 22:29 M K Saravanan <mksa...@gmail.com <mailto:mksa...@gmail.com>> wrote:

    Hi,

    When using openssl with X25519, why it shows the server temp key
    as 253 bits?

    Example:

    ---
    No client certificate CA names sent
    Peer signing digest: SHA256
    Peer signature type: RSA
    Server Temp Key: X25519, 253 bits
    ---

    I thought Curve25519 is using 256 bit keys.

    Why 253 instead of 256?

    with regards,
    Saravanan
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