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Crypto wallet application with lower transaction count

We want to build a wallet application, when user registers we want to open a specific wallet to user but there is a problem when user deposits crypto we want to transfer balance (erc20 transfer) to cold wallet then show it on database, when user want to withdraw we have to transfer erc20 also, that means for each user we need to do 2 transfers at least, is there more efficent way as solution of this problem to lower transfer counts?

Input-independence of base OT in OT extension

In [1], the authors state: […] observe that unlike [32] the initial OT phase in Protocol 52 is completely independent of the actual inputs of the parties. Thus, the parties can perform the initial OT phase before their inputs are determined. where “initial OT phase” refers to the base OT phase. In a follow-up/extension work::Listen

In [1], the authors state:

[…] observe that unlike [32] the initial OT phase in Protocol 52 is
completely independent of the actual inputs of the parties. Thus, the
parties can perform the initial OT phase before their inputs are
determined.

where “initial OT phase” refers to the base OT phase. In a follow-up/extension work by the same authors ([2]), the reference to [32] here is removed and the quote now reads:

[…] observe that the initial OT phase in Protocol 4 is completely
independent of the actual inputs of the parties. Thus, the parties can
compute the initial base-OTs before their inputs are determined.

My question is: is the claim in [1] (that [32]’s base OT phase is input-dependent) correct, or was it just a simple mistake? If it is correct, where in [32] is this shown? I could not find it but perhaps I am missing something.

References:

[1] (ALSZ) https://eprint.iacr.org/2013/552.pdf

[2] (ALSZ) https://eprint.iacr.org/2016/602.pdf

[32] (IKNP03) Y. Ishai, J. Kilian, K. Nissim, and E. Petrank. Extending oblivious transfers efficiently. In Advances in Cryptology – CRYPTO’03, volume 2729 of LNCS, pages 145–161. Springer, 2003.

Crypto wallet application with lower transaction count

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