# Yellow Paper eq 221: Why and how the sender of a signed transaction equals to the address of the signer?

Ethereum Yellow Paper: Please see equation 220 and 221. On equation 220, we obtain the transaction that can be sent to the network and will be tracked by a 256 bit transaction-id. Its right most 160-bits is equalled to S(T) which is the defined as the sender function S of the transaction.

My question is related to Equation 221 which is an assertion about: :

The assertion that the sender of a signed transaction equals the address of the signer should be self-evident

[Q] Why and how the sender of a signed transaction(`S(T) on the eq. 220`) equals the address of the signer (`A(pr)`) ? Is there any well explained documentation related to this.

Could we conclude the following statement:

``````B96...255(KEC(ECDSARECOVER(h(T),Tw,Tr,Ts))) == B96...255((KEC(ECDSAPUBKEY(pr)))
``````

Thank you for your valuable time and help.

An ethereum signature has three parameters `r`, `s` and `v`. Using `r`, `s` and the ECDSA equation you have two candidates for the public key, then using `v` you can disambiguate and know exactly which one is the public key of the signer.
Once you have the public key, you use can calculate the address with the last 20 bytes of `keccak256(publicKey)`.
• I get really confused :( what does `S(T)` stands for, is it Ethereum address of the sender, which is actually the 160-bit we obtain on eq. 215? So `KEC( ECDSARECOVER(h(T),Tw,Tr,Ts)) == KEC(ECDSAPUBKEY(pr))` you could see on my updated Q?@Ismael – alper Dec 16 '17 at 13:55